Structural Stability and Dynamics

Conference Organization

Organizing Committee

International Scientific Committee

Preface

Contents

A nonlinear rate dependent constitutive model for fiber-reinforced composites is presented. Through the use of a plastic potential function, effective stress and effective plastic strains are introduced, with which a single equation is established for the orthotropic and nonlinear rate dependent behavior of composites. This viscoplasticity constitutive model is employed together with a microbuckling model to predict compressive strength of composites for different strain rates. Results of qasi-static and high strain rate compression tests using off-axis composite specimens of S2/8552 glass/epoxy are reported and compared with model predictions. Excellent agreement between experimental data and predictions is found. From the experimental results as well as model predictions, it is noted that the longitudinal compressive strength of a composite is significantly influenced by the presence of shear stresses.

This paper describes recent research by the authors on the development of improved computational methods and algorithms for physically correct solution of linear and nonlinear boundary and initial value problems of structural dynamics. The difficulties and anomalies commonly encountered in the numerical simulation of problems with localized high solution gradients are critically examined and new computational methodologies are proposed and demonstrated through some well-known problems that defied physically meaningful solutions by the currently available computational formulations. The root cause of the failure of the current computational methodology when applied to these problems is the lack of desired global differentiability of the computed solution. Two essential elements of the proposed mathematical and computational framework are (1) the variational consistency (VC) of the mathematical approach used in obtaining algebraic systems from the differential systems via an integral approach, and (2) the global differentiability (or smoothness) requiring the use of higher-order spaces for local approximation. The variational consistency is a fundamentally important aspect of the proposed approach. A violation of this leads to variational inconsistent (VIC) formulation that is shown to produce degenerate computational models. The degree of global differentiability is of critical importance for three reasons, (i) If the solutions of the algebraic system to be admissible in the weak form; (ii) if the solutions from the algebraic system are to yield the same global smoothness as the analytical solutions; and (iii) to permit correct incorporation of the physics of the processes in the numerical computations. The proposed computational technology provides mathematically sound, most general, comprehensive, and complete computational platform in which all problems can be treated with the same rigor and without any bias to their form or field of application. The important issues of concern in the numerical simulation of boundary value problems (BVP) and initial value problems (IVP) arising in solid and structural mechanics (e.g., fracture mechanics), as well as in coupled problems (e.g., fluid-structure interaction) are addressed using the proposed k-version finite element methodology. Theoretical basis and supporting numerical studies will be discussed to illustrate various features of the developed methodology. It will be demonstrated that the present approach is mathematically consistent, incorporates the physics correctly, requires no ‘ad-hoc’ approaches or semi-empirical adjustments, and it is rather a natural way to simulate correct physical behavior of such problems.

Various modern developments in fiber-polymer composites and sandwich structures necessitate improved knowledge of fracture behaviour, scaling of fracture and stability. Since failure is synonymous to the loss of the stability of fracture propagation, the questions stability and fracture are closely intertwined. Typically, the stability loss in quasibrittle materials, which include fiber composites, takes place only after large stable growth of fracture or cracking. Such behaviour causes a significant non-statistical size effect, which is of paramount importance, for example, for use of composites in various new designs of large ship hulls, decks, bulkheads and masts. The lecture outlines fracture stability analysis and an asymptotic matching technique that led, at Northwestern University, to the development of deterministic as well as combined deterministic-probabilistic scaling laws for tensile fracture of laminates and for microbuckling kink-band failure of unidirectional fiber composites under compression. The analysis of fracture stability and size effect is further extended yo sandwich structures with delaminations cracks. Finally the finite-strain effect in energetic stability analysis pf the buckling of sandwich plates is discussed and the way to resolve the paradoxical differences between the Engesser-type and Haringx-type critical load formulae is pointed out. The analytical results are supported by computational and experimental studies.

This paper describes a procedure for the design of crane runway beams for the strength limit state of lateral buckling. Crane runway beams usually comprise of an I-section beam with a channel section welded to the top flange, so that the cross-section is monosymmetric rather than doubly-symmetric. The design of monosymmetric beams against lateral buckling is not straightforward, and indeed use of implicit code rules may be unconservative. Prescriptive equations are presented for the elastic buckling of a monosymmetric runway beam, and this may then be converted to a strength using the procedure of design by buckling analysis that is permitted in the Australian AS4100 Steel Structures Code. The modification of the procedure to other limit states codes is straightforward.

Collapse of shallow domes is common in many places. They are widely used in roof cover of storage bin and as glazing roof in tall buildings in cities like Hong Kong and Singapore. When they are under downward load due to underneath wind or snow loads, we need to consider snap-through buckling which, unfortunately, is not very well-documented in many design codes. In its design, the engineer needs to consider imperfection, snap-through buckling load and members strength. It appears that conventional design approach is insufficient in handling all these effectively and reliably. This paper uses eigen-mode and initial member deflection as initial geometry for buckling analysis. The design load is computed by a second-order analysis with section capacity check and the complete equilibrium path is plotted. The results demonstrate the robustness and practicality of the nonlinear analysis and design method in handling 2 and 3 dimensional frames susceptible to snap-through instability.

Many engineering structures are imperfection-sensitive. Their (initial) postbuckling behavior can be improved substantially by converting them to imperfection-insensitive structures. Such a conversion can be achieved by specific modes of stiffening of the structure. The aim of this paper is to present mathematical relations for the transition from imperfection sensitivity to insensitivity in consequence of such modes of stiffening. Koiter's initial postbuckling analysis is applied in the context of the Finite Element Method (FEM) to deduce these relations. An essential ingredient of a special form of accompanying linear eigenvalue analysis, previously used to compute estimates of stability limits, plays an important role in the derivation of these mathematical relations. The results from a numerical study performed by means of the FEM corroborate the theoretical findings.

In this paper, micro-macro interaction analyses of corrugated fiberboard are conducted by the finite element method in conjunction with the homogenization theory. It is assumed that corrugated fiberboard is piled periodically in quasi three-dimensional state. The updated Lagrangian method is adopted for the geometrically nonlinear analyses of microstructure and the scaled corrector method for detecting the buckling mode. The conclusions obtained in this study are summarized as follows. 1) The large deformation and buckling analysis based on the homogenization theory is conducted and the mechanical properties of corrugated fiberboard are investigated. 2) The micro-macro interaction analysis procedure for the buckling of the corrugated fiberboard based on the homogenization theory is newly proposed. The validity of the proposed procedure is clarified qualitatively by comparing with the experimental results.

As uniform criterion is here regarded value of main determinant of set of equilibrium equations of the considered problem. For analytical solutions of separate bar it will be considered one differential equilibrium equation as in Euler's problem or set of differential equilibrium equations – for dynamic, stability or dynamic stability. The same criterion in numerical approaches by means of Finite Differences Method or Finite Element Method is applied to main determinant of global stiffness matrix of considered structure. It was also used in programs for bar space structures for check the input data to programs whether the description of structure is correctly done… The method was tested numerically for many different problems. Moreover, some observations concerning strength analysis of composite bar structures are given.

The collapse of cylindrical shells under external fluid pressure is generally controlled by elastic buckling, material failure or a combination thereof. Composites like other laminated materials suffer from layer separation or delamination, which may affect the stiffness and stability of the structural component. Deep delaminations, near cylinder mid surface, are expected to reduce the effective flexural stiffness of the shell wall and lead to possible premature collapse. This problem is treated numerically and studied parametrically. A Fourier series-based 2-D shell finite element is formulated for delaminated composite long cylinders. The compatibility of deformation at the delamination tip is maintained by means of Lagrange multipliers. Contact between the separated layers is taken into account through a penalty formulation. A parametric study is conducted to assess the influence of delamination length, depth, and orientation on the reduction in collapse pressure of imperfect cylindrical shells.

This paper gives an overview of the revision of the well-known theorem in stability: “the addition of restraint to a structure cannot decrease its elastic critical load”, and that of its counterpart in vibration that an additional constraint or an increase in the stiffness cannot reduce any of the natural frequencies of an elastic conservative vibration system. It is pointed out by theoretical arguments and simple examples that this theorem in stability is valid only if the displacement components in the buckling direction are additionally restrained. But additional restraints on pre-buckling displacements, which are orthogonal to the direction of buckling, can decrease the elastic critical load factor of the structure. The theorem in vibration is valid if additional restraints have no effect on pre-vibration displacements, or there are no pre-vibration displacements, but additional restraints on pre-vibration displacements can decrease the natural frequencies. The latter case can happen if external loads are in the system.

This paper concerns the limit analysis of structures in the presence of constitutive instabilities. As a simple and representative illustration, a model problem involving nonassociative frictional rigid blocks is used. The formulation takes the form of a special constrained optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC). In view of the complexity of solving an MPEC directly, we propose its reformulation and solution as a nonlinear programming (NLP) problem via a penalty scheme.

This paper presents an analytical method to investigate the buckling behaviour of folded plates based on the Mindlin shear deformable plate theory. The folded plate system is formed with several rectangular segments joining at arbitrary folding angles in a rectangular planform. The edges of the plate perpendicular to the folding interfaces are considered to be simply supported and the other two remaining edges may have any combination of free, simply supported and clamped support conditions. The Mindlin plate theory is employed and both bending and inplane stretching actions of the plate are considered in the study. The general Levy type solution method in connection with the state space and domain decomposition techniques is employed to develop an analytical approach for the folded plate system. First-known exact buckling solutions are obtained for two- and three-fold folded plates of various combinations of boundary conditions and folding angles. The influence of plate thickness ratios and folding angles on the buckling load is examined. The presented exact solutions may serve as benchmark values for such plate system.

A Hamiltonian system subjected to light damping and weak stochastic excitation is called quasi Hamiltonian system. An n-degree-of-freedom (DOF) quasi Hamiltonian system is first reduced to averaged Itô stochastic differential equations by using the stochastic averaging method for quasi Hamiltonian systems. The form and dimension of the averaged Ito equations depend on the integrability and resonance of the associated Hamiltonian system. A new norm for the definitions of stochastic stability and Lyapunov exponent is introduced and the expressions for the largest Lyapunov exponent is derived from the averaged Itô equations. The necessary and sufficient condition for the asymptotic Lyapunov stability with probability one of the original quasi Hamiltonian system is obtained approximately by letting the largest Lyapunov exponent to be negative. An ergodic control problem with undetermined cost function and weighting matrix is formulated and solved by using the dynamical programming procedure to yield the optimal control. The largest Lyapunov exponent of the controlled system is minimized by proper choice of the cost function and weighting matrix and the original quasi Hamiltonian system is stabilized by the feedback control.

Multiple wave scattering in unidirectional fiber reinforced composite materials is analyzed numerically. A computational procedure based on a collocation method is proposed which solves the equations of multiple scattering expressed by the eigenfunction expansion in the long wavelength range, without recourse to analytical assumptions such as configurational averaging or quasi-crystalline approximation. The present analysis deals with the time-harmonic elastic transverse (shear) wave polarized parallel to the fibers, corresponding to the scalar Helmholtz equation. As an example, wave propagation in unidirectional SiC/Ti-alloy composite is analyzed, and the wave field in the composite is demonstrated. The phase velocity in the composite is extracted from the analysis, which is shown to increase as the fiber volume fraction increases. The frequency dependence of the velocity is also examined. It is shown that the present analysis gives results in good agreement with the results based on an existing multiple scattering theory.

Changes of ultrasonic wave velocities along the thickness direction of TMCP rolled steel plates are examined. Shear velocities that depend on both propagation and polarization directions are emphasized. Microscopic observation of two vertical planes of steel plate was performed. The effect of grain shape on the ultrasonic shear velocity was studied. For generality, study was conducted on both thick (40 mm thick) and thin (26 mm thick) steel plates. In addition, surface wave velocities were measured at plate surface and center. The results showed that the rolled steel plate exhibits the changes of the shear wave velocities in the thickness direction of the plate. The changes are reasoned to be due to changes in microstructure of the steel plate. Moreover, the high anisotropy is found in the near surface zone of the rolled steel plate.

This paper presents some experimental data on roll compaction concrete cofferdam vibration induced by underwater explosion. A formula for the bubble pulse period of underwater explosion is proposed via dimension analysis and compared with Cole formula. An experiential formula is summarized on the relation among the structure vibration velocity, explosive charge and the distance from charge to structure. The formula indicates that the structure vibration velocity is directly proportional to square root of the charge when the charge package was near the structure. When the distance is farther between the charge and the cofferdam, the peak particle velocity (PPV) is smaller.

The construction of a high-frequency asymptotic solution describing the propagation of Rayleigh waves along the curved free boundary of an inhomogeneous hyperelastic medium is given. A dispersion formula for the Rayleigh waves is derived.

We consider SH impact problem for a linearly graded inhomogeneous half-space with a stress free surface which does not coincide with the inhomogeneous symmetric plane. In our previous paper the symmetric problem was analyzed by using the Cagniard method. These results are used here as an analytical element to solve this non-symmetric problem. After the coordinate transformation is applied, SH transient responses are numerically calculated to enforce the virtual stress free boundary condition. Some results are presented in the 3-D graphic to provide a clear views of the solutions.

The Green function for a radially inhomogeneous elastic solid is presented for a time-harmonic point source. Elastic moduli and density are power functions of radial distance in the polar coordinate system, so that the associated wave velocity varies linearly in the radial direction. A critical frequency that distinguishes between wave and non-wave natures in the Green function has been found.

The frequencies of vibration of bridges represent a kind of information that is most useful for many purposes. Traditional vibration tests aimed at measuring the bridge frequencies often require on-site installation of the measurement equipment. The idea of using a vehicle moving over a bridge as a message carrier of the bridge is explored theoretically in this paper. In this preliminary study, a simple model is used for simulating the vehicle-bridge interaction response, with which approximate, but reasonably accurate, solutions are presented in closed-form. The key parameters dominating the vehicle-bridge response are identified. Concluding remarks are given concerning the feasibility of extracting the bridge frequencies from the dynamic response of a passing vehicle.

The elastodynamic response of the transformation-toughened ceramics under an instantaneous phase transformation is investigated. Some composite materials, such as Zirconia toughened ceramics, are the remarkable material, which has a high strength, a high elastic modulus, and an improved toughness, etc. Most of the good qualities are common in many ceramic composite materials. These good qualities are made possible through the phase transformation of composite particles. The transformation toughening utilizes the stress-induced phase transformation of particles, which is accompanied by a volumetric expansion. In this paper a phenomenological model is proposed to describe the situation, which involves a dynamic martensitic transformation in a spherical particle of Zirconia embedded in an infinite elastic matrix. Following the ray methods, we clarify the stress-focusing effect caused by the instantaneous phase transformation in a spherical inclusion of Zirconia. It should be noted that the mechanism in the toughening of ceramics in the steady state does not hold in the dynamic state.

Several methods have been developed recently to identify moving loads on top of a bridge deck using vibration measurements. While some of the analytical approaches give accurate results under no-noise condition, the accuracy of the final interaction forces depends on the accuracy of the measurement and is less dependent on the formulation of the different approaches. This paper looks again at the accuracy of identification with respect to the inconsistency of infinite number of modes in the measured responses and the few lower modes used in the identification.

Much of the decision-making in the real world takes place in an environment in which the objectives, the constraints, and the consequences of possible actions are not known precisely. To deal quantitatively with imprecision and uncertainty, the tools of probability and fuzzy theories can be used. This work presents two methodologies, one called the chance-constrained programming and the other called fuzzy programming, for the optimization of structural systems involving uncertainties. The first one assumes the uncertain parameters as independent random variables following normal distribution and the second one treats the uncertain parameters as fuzzy variables. Numerical examples are presented to illustrate the computational feasibility and effectiveness of the approaches presented.

Many steel rigid-frame piers were damaged by local buckling and brittle crack failure during the 1995 Hyogoken-Nanbu earthquake. Therefore, in order to improve their seismic performance, it is necessary to clarify the relationship between the horizontal load bearing capacity and the ductility of such bridge piers. In this study, monotonic and cyclic loading tests as well as elasto-plastic finite displacement analyses using shell elements were carried out to evaluate the in-plane behavior of steel rigid-frame pier. It is found that the steel rigid-frame pier has both high strength and high ductility.

This paper describes an innovative computational model developed to solve two-dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier-Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three-step finite element method. The arbitrary Lagrangian-Eulerian (ALE) method is incorporated into the model, to solve the moving boundary problems. For illustration of the present numerical code, a vortex-induced cross-flow oscillations of a circular cylinder mounted on an elastic dashpot-spring system is considered. The phenomena of the beat, lock-in, and resonance are revealed in the Reynolds number range between 100 and 110, which are much narrower than the previous results by experimental and numerical studies.

The high-cycle fatigue behavior and material damage tolerance of the materials (e.g., titanium alloys) which make up key components such as blades and disks in a gas turbine engine are two major factors that account for the life of those components. To improve the high-cycle fatigue behavior and material damage tolerance of critical engine components, a thin layer of subsurface compressive residual stress is often imparted on the components with some surface-conditioning technique. Low plasticity burnishing is an emerging surface enhancement technique, which serves this purpose and produces a mirror-smooth surface finish.

Since conditions in the engine environment (e.g., cyclic thermal and mechanical loadings) can cause significant loss of the protective layer of residual stress in surface-enhanced turbine engine components, incorporation of the beneficial effects of surface-conditioning treatments into component-life predictions can be accomplished only through development of nondestructive measurement methods capable of verifying and quantifying residual stress levels. At present, the depth profile of residual stress induced by surface-conditioning can be determined only by destructive (or at least semi-destructive) methods such as X-ray diffraction, incremental hole-drilling, etc. No nondestructive measurement technique is as yet available.

The present paper is an interim progress report of a project, which involves collaborative efforts from researchers at the University of Kentucky, the U.S. Air Force Research Laboratory, and GE Aircraft Engines. The long-term objective of this project is to develop an ultrasound technique for nondestructive inspection of the residual stress layer in surface-enhanced engine components, and its immediate focus is to explore the possibility of inferring some characteristics of the residual stress profile in LPB-treated samples from the dispersion of Rayleigh waves in those samples.

The main purpose of this study is to investigate the free vibrations of curved beams, both theoretically and experimentally. Three different geometries for the curved beams are considered in the experiments; circular beam with uniform cross-section, parabolic beams with uniform and varying cross-section. The exact solution of in-plane vibration can be given for only circular beam with uniform cross-section. For all geometries, the finite element solutions were performed by using ANSYS as a pre and post processor to analyze the frequencies and the mode shapes for five different boundary conditions. The results of exact and finite element solutions were then compared with the experimental results for all beams and the comparisons were given in tables and diagrams. Good agreement is obtained between the results.

The free out-of-plane vibration of a circular beam with uniform cross-section is investigated. The study takes into account the effects of transverse shear deformation and rotatory inertia. The governing differential equations for the out-of-plane vibrations of uniform circular beams are solved exactly by using the initial value method. The solution does not depend on the boundary conditions. It is also possible to ignore some minor effects for some specific cases. The vibration problems for circular beams that have been analyzed in the literature are solved and the results are given in the tables. The comparison study shows a good agreement between the results.

This paper deals with the large amplitude free vibrations of inclined cables in a three dimensional space. Presented herein is a model formulation which is not limited to cables having small sag-to-span ratios and takes into consideration the axial deformation effect. The nonlinear equations of motion are obtained by the principle of virtual work-energy. The spatial and temporal problems of a multi-degree-of-freedom cable model are then solved by the finite difference method. Numerical examples for the case of a specified tension of arbitrarily inclined sagged cables are given. The effects of cable inclination, cable sag and internally resonant condition on cable nonlinear dynamics are demonstrated.

Transcendental member stiffness matrices for vibration (or buckling) arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretisation errors. Assembling them into the overall structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or critical load factors) are found with certainty using the Wittrick-Williams algorithm. This paper gives equations for the recently discovered member stiffness determinant, which equals the appropriately normalised FEM stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. Vibrating Bernoulli-Euler beams and vibrating, axially loaded Timoshenko members are covered, using a recent convenient notation for the latter, such that its stiffnesses clearly limit to the Bernoulli-Euler ones when axial force, shear rigidity and rotatory inertia are neglected. The present paper gives the first ever derivation of the Bemoulli-Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

Technology transfer between disciplines is an important but relatively infrequently occurring activity. This paper deals with aspects of the transfer of the Wittrick-Williams (W-W) algorithm, and in particular its powerful and exact multi-level substructuring capability, from its parent discipline of structural engineering to a mathematical area of current and intense interest. This area involves examining the eigenvalues of systems of differential equations connected together with tree topology. In the structural analogy, the problem is that of finding the natural frequencies of a tree of co-linear bars. It is shown: that trees with 10¹² or more bars, which represent second order Sturm-Liouville equations, can be analysed in almost negligibly small computer time and without ill-conditioning; that the existence and extremely high multiplicity of multiple eigenvalues can be predicted precisely from the structural analogy; that the fragmentation of the multiplicity due to members at one level of the tree no longer being identical to those at the other levels can be predicted and; related conclusions can be drawn when the bars are replaced by beams, which represent fourth order Sturm-Liouville equations.

The paper gives short review of well known more important types of the analytical and numerical approaches, supplemented by own achievements. So, there are mentioned: classical analytical solutions, then Finite Differences Method, Finite Element Method and experiences with own Difference-Matrix Equation Method. The last was applied for separate bar with any cross-sections (full, thin-walled, composite etc.) and for large space bar structures in the range of free- , forced- and dumped vibrations. Moreover, there are shown very general and highly efficient solutions with application of 3D-time space. The paper is focused specially on the last approach, for problems with any program of loading variable in time and in space, destined e.g. for tall buildings and for bridges with mobile loads, too. The paper try to compare efficiency of mentioned approaches and to point recommended range of its application.

Finite element analysis for the dynamic characteristics of tower cranes is presented in this paper. A parameterized super element formulation for modeling the multiple-pulley cable line in crane system is derived based on the friction-free assumption for pulley-cable contact. Numerical results show that the intermediate pulleys, which are used to guide the cable, have significant effect on both static tensions and dynamic properties of tower cranes and the proposed super element model gives accurate and realistic predictions in natural frequencies of crane system. It is found that some modes are insensitive to the change of jib angle, while others decrease or increase significantly depending on the mode shapes. The bracings at mast change both the natural frequencies and the order sequence of natural modes. Jib angles and the number and locations of bracings at mast should be carefully considered in the analysis of dynamic responses of such structures.

This paper develops a finite strip-element method for the dynamic analysis of curved thick plates. A combined polynomial and trigonometric interpolation scheme is used that enables all boundary conditions to be correctly treated. The system equations are derived following standard finite element procedures, and accurate solutions are obtained with the generation and solution of few equations.

Presented herein are the fundamental vibration frequencies of rectangular plates with partially fixed edges. The frequencies are determined by the finite element method. The parameters considered in the analysis were the aspect ratio of the plate's side lengths and Kinney's fixity factors. When the plate has classical boundary conditions, frequency coefficients determined by numerical analysis show good agreement with those determined by the classical method. A simple design formula is proposed to aid structural engineers to estimate the fundamental frequencies of such restrained rectangular plates.

The Vibration characteristics of stiffened plate with a cutout subjected to in-plane forces are investigated using finite element method. The vibration frequencies and buckling load parameter for various modes of stiffened plate with cutouts having stiffeners varying in numbers and spacing subjected to in-plane loads, have been determined for simply supported and clamped edge conditions. In the structural modeling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The present approach is more flexible than any other finite element modeling in that the mesh division is independent of the location of the stiffeners.

Discrete singular convolution (DSC) for plate vibration analysis has been proposed and developed recently by the authors. In this paper, two significant studies, vibration analysis for rectangular plates with irregular internal supports and high frequency analysis for rectangular plates, are presented. The DSC vibration analysis, which is based on the strong formulation of the mechanics problem, exhibits excellent accuracy in several analytically solvable cases and therefore can be regarded as a promising method. In this method, implementation of the boundary conditions, such as the simply supported (S) edge and the clamped (C) edge, is formulated through delicate extension techniques, and internal supports are simulated through point supports. Some important results are presented. Successful applications of DSC certainly validate the robustness of the method for plate vibration analysis.

Analytical formulations using two higher order displacement models have been developed and solutions obtained for the first time to the natural frequency analysis of a simply supported composite and sandwich plates. These computational models are based on Taylor's series expansion of the displacements in the thickness coordinate and consider the realistic parabolic distribution of transverse shear strains through the laminate thickness. One of them considers the effects of both transverse shear and normal strain/stress while the other include only the effect of transverse shear deformation. In addition to above, few higher order and first order models developed by other investigators and already reported in the literature are also considered for evaluation. A simply supported square plate is considered throughout as a test problem. The equations of motion are obtained using Hamilton's principle. Analytical solutions are obtained using Navier's solution technique and by solving the eigenvalue problem. Firstly natural frequencies results using the various models are presented for symmetric composite plates and compared with the three-dimensional elasticity results available in the literature to show the accuracy of the higher order refined models considered in the present study in predicting the dynamic behaviour of laminated composite plates. After establishing the accuracy, natural frequencies results both at fundamental and higher modes using all the models are presented for a multilayer sandwich plates which will serve as benchmark solutions for future investigations.

This paper presents new optimal results for vibration of thin rectangular plates against one and two internal point supports. The p-Ritz method is employed to generate the fundamental vibration frequencies for a plate and the Nelder and Mead simplex optimal search routine is used to find the optimal point support locations. Optimal results have been obtained for square and rectangular plates with arbitrary boundary arrangements and with one and two internal point supports. The results generally show that the frequency of the plate is sensitive to the location of the internal point supports and numerous optimal locations for the point supports exist. These new optimal results will provide useful information to designers seeking to maximize the fundamental frequency in designing a plate structure.

Response of suspension bridges to aerodynamic excitation is presented using finite element approach and multi-mode analysis technique. The flutter condition of the bridge is evaluated by solving an eigen value problem. The bending moments along the bridge span and additional horizontal component of the cable tension are evaluated using a standard random vibration analysis. It is found that for accurate evaluating of the Golden Gate Suspension Bridge response to wind excitation, contribution of at least 19 modes are necessary.

In this paper, the dynamic responses of structures under high velocity impact using smooth particle hydrodynamics (SPH) approach is presented. The SPH equations, which govern the elastic large deformation dynamic response of solid structure, are derived. The proposed additional stress points are introduced into the formulation to treat tensile instability. Furthermore, in order to increase the accuracy of SPH solutions, the novel incremental rate form approach was proposed by adopting the smoothing particle method. Combining the incremental rate form approach and the leap-frog algorithm for time integration, the new solution algorithm and formulation was developed and implemented. To examine the performance of the proposed algorithm, an example on structure dynamic response under high velocity impact is given. A comparison study on the results obtained from the proposed SPH approach and those obtained from the Finite Element Method (FEM) shows that the high velocity impact problem can be effectively solved by the proposed SPH approach.

As the complexity of structural experiments increase, the needs are evident for developing an Internet-based collaborative structural experimental environment in Taiwan, denoted ISEE (Internet-based Simulations for Earthquake Engineering), among several geographical-distributed structural laboratories. The ISEE environment is constructed and integrated in the National Center for Research on Earthquake Engineering (NCREE) by using the Internet technology, experimental facility controlling technology, and the numerical analysis procedures implemented for pseudo dynamic tests. This paper focuses on the framework of the numerical analysis for distributed pseudo-dynamic tests. A new numerical analysis component has been constructed on a finite element analysis package, called OpenSEES, which is configured in the ISEE framework as the primary analysis engine to meet the needs for substructure pseudo-dynamic tests. This paper also discusses the construction of a user-defined element in the OpenSEES framework to model the substructure specimen. An example test is employed to demonstrate the interactions among the Analysis Engine, the Facility Controller, and the Data Center in the ISEE framework.

Currently, NCREE, through the use of the Internet, has constructed the Platform of Network Structural Experiment (PNSE). This platform allows structural laboratories sited at different geographical locations around the world to make full use of the Internet in transmitting experimental information promptly. Most importantly, it serves the function of allowing these laboratories to jointly carry out experiments. This platform also allows researchers around the world to visualize and take part in discussions of the undergoing experiments synchronously. This platform is constructed upon “Transmission Control Protocol/Internet Protocol (TCP/IP)”, for diverse computer operating systems and working hardware, so as to attain the objective of integrating structural laboratories. The NCREE task group has developed an application for the communication protocol: “Network Structural Experiment Protocol (NSEP)”, for the exchange of messages. Currently, the task group has performed several pseudo dynamic tests on a buckling restrained braced frame using the PNSE in order to verify the feasibility and the efficiency of the PNSE. The preliminary findings conclude that all the experimental and analytical data are transmitted accurately in the progress of testing and the experiment is accomplished successfully. However, there are still a lot of researches and developments can be done to improve the efficiency. At the time of this writing, structural laboratories at the National Center for Research on Earthquake Engineering (NCREE) and National Taiwan University (NTU) are in the status of preparing a joint pseudo dynamic testing on concrete filled steel tube columns.

A platform, termed as “Platform for Networked Structural Experiment” (PNSE) is proposed in this study. The PNSE is built based upon the Transmission Control Protocol / Internet Protocol (TCP/IP) and works with a proposed application protocol, “Network Structural Experiment Protocol” (NSEP) to realize the concept of the “Virtual Laboratory.” The platform utilizes the socket operation technology to perform the data transmission through the Internet and hence to link the structural analysis program and test facilities in structural laboratories around the globe to jointly conduct a pseudo dynamic test simultaneously. The platform also promises friendly individual participations including experiment surveillance and data sharing.

This paper deals both prediction of stable (native) protein structures and the analysis of the dynamic behavior of protein structures. An improved micro genetic algorithm with intergenerational projection technique is introduced to inversely predict the stable structure of native folded proteins. Discussions are provided on how an optimization technique, such as the genetic algorithms can be used to solve the protein structure prediction (or folding) problem. A lattice model for protein structures is used in the construction of the grand structure of proteins. Examples of predicted native protein structure are presented. Cubic structures are obtained for proteins with 27 monomers, which agree well with the reported prediction using the Monte Carlo (MC) method. For larger systems, 64 and 125 unit long proteins, structures found using the present method are not cubic but they are near-cubic and fairly compact. Methods of molecular dynamics are then used to analyze the dynamic behavior of the predicted protein structures.

This article extends a procedure that has been used to discretize the static physical system, following the assumption that a continuous flexible beam with torsional moments can be replaced by a system of rigid bars and joints, which resist relative rotation and twist of the attached bars. This model can fairly demonstrate the effect of bending, as well as warping action, caused by external transverse loading, torsional moments of the beam and moving mass. The object of this article is to present and formulate a new simple, practical and inexpensive approximate technique for determining the response of beams with different boundary conditions, carrying general transverse loading, moving mass and twisting moments. To verify the results, other solutions are obtained through the exact structural analysis and comparing of the results reveals very good agreement between both methods. However, this algorithm is shown to be much more efficient, computationally and the formulation can easily be adopted into two-dimensional structural networks and three-dimensional bodies.

The paper presents a method to predict the ultimate load carrying capacity of steel-concrete composite plate girders subjected to shear loading. In order to ascertain the accuracy of the proposed method it was applied to analyse six composite girders tested to failure in the laboratory. The values of ultimate load capacity were compared with the corresponding experimental values and with those obtained by using non-linear finite element method. It is found from the comparison that the proposed method is capable of predicting the load carrying capacity with reasonable accuracy.

This paper presents the ultimate load tests on plate girders curved in plan with centrally placed circular web opening. The parameters varied include degree of curvature and ratio of size of the opening to depth of the web. Eight girders were tested to failure under predominantly shear loading. The tests show that the ultimate load capacity of the curved girders dropped linearly with increase in the opening size. Decrease in the ultimate load capacity with increasing degree of curvature is also observed. A finite element software ‘ABAQUS’ has been used to analyse the tested girders. Comparison of analytical results with the corresponding experimental results for failure mechanism, ultimate load values and load-deflection relationships show good agreement thus validating the accuracy of analytical model.

The paper deals with a numerical investigation concerning the influence of local-plate/distortional buckling mode interaction on the elastic and elastic-plastic post-buckling behaviour of geometrically imperfect cold-formed lipped channel steel columns. All the results displayed are obtained from FEM analyses, performed by means of the code ABAQUS and adopting discretisations with 4-node shell finite elements. Such results deal with imperfection-sensitivity issues, namely the effect of the initial imperfection shape on the column (i) local-plate/distortional mode coupling evolution along the associated non linear equilibrium path and (ii) ultimate stress value and deformed configuration at collapse (elastic-plastic behaviour only).

The process of cutting a cold-formed steel C-section to specified length will produce different extent of cross section distortion along the length due to the release of residual stresses. The objective of this paper is to study the cross section distortion and the initial geometric imperfections of the C-section stub columns after cutting. A long cold-formed steel lipped C-section of grade G450 was cut into seven stub columns using a manual saw. The geometrical dimensions of all segments before and after each cutting were measured while precise measurement of the initial geometric imperfections on two stub columns were made using a laser transducer. It is found that when a C-section is cut into two segments, the extent of distortion along the length after cutting is strongly affected by the distance from the cutting section. When a stub column is cut off along the intermediate length of a long section, there is a well-defined cross section distortion pattern along the length. It should be noted that the initial out-of-straightness geometric imperfections of stub columns due to cutting are considered to be large when compared with those due to press-braking. This may couple up with the initial geometric imperfections of the section caused during the manufacturing process, leading to possible strength reduction of the stub columns.

Bleich's equivalent moment inertia coefficients for linearly and parabolically tapered compression members are applicable only to the limited boundary conditions. To extend Bleich's concept, the elastic critical loads of three types of tapered members with arbitrary boundary conditions are determined by the finite element method. The changes of critical load are represented by the algebraic functions of analysis parameters. Bleich's equivalent coefficients are expressed in terms of proposed algebraic functions. The inertia coefficients estimated by the proposed method show good agreement with Bleich's original coefficients.

This paper presents both an experimental and a numerical model for considering the coupled instability of local and global buckling in composite steel-concrete columns. The model is based on considering a single beam element, which is given a predetermined shape for out of plane deflection. Compatibility and equilibrium at the mid-height of the column are used to provide convergence of the solution as the column axial load is increased. Local and post-local buckling of the cross-section is considered at the mid-height section by utilising the results of an inelastic finite strip analysis. Post-buckling of the cross-section is considered in the elastic region by using an effective width method. For post-buckling in the inelastic range a novel method, which considers strain energy of the component plates is used. The model is calibrated with the test results and shown to be in very good agreement.

Presented herein is a theoretical study on the dynamic response of geometrically imperfect columns subjected to loads consisting of a dead load and a pulsating load. The column ends are partially restrained with respect to rotation and are not allowed to displace laterally. The governing partial differential equation of column's dynamic equilibrium is solved numerically to study its time-dependent behavior. The solution is based on an impulse recurrence formula relative to time coupled with a finite-difference discretization along the member length. The conditions leading to the dynamic instability of the column are discussed.

This document describes a simple procedure for evaluating the capacity of single angle compression struts that are supported at each end by one leg to a gusset plate or directly to a leg or stem of the chord of a truss. This procedure allows the single angle to be treated for analysis and design as a pinned-end axially loaded compression member by use of an effective slenderness ratio. The procedure considers two levels of end restraint and addresses both equal and unequal-leg angles. This procedure is being proposed for use in the next version of the American Institute of Steel Construction specification.

The use of concrete filled thin walled steel tubes in structural applications is extensive, particularly for axially loaded members. While numerous experimental studies have been carried out on tubes subjected to primarily axial loads with limited eccentricities, few studies have been carried out into the flexural behaviour of such members. Furthermore, it is recognised that thin walled tubes are not geometrically perfect, and contain initial imperfections which may have a significant effect on the buckling capacity of the tube. While a number of numerical studies have been carried out to determine the significance of initial imperfections on the local buckling of thin walled tubes, to-date studies investigating the actual shape and magnitude of these imperfections have been limited. In this paper, the results from a testing program carried out at the University of Western Sydney, in which initial imperfections have been measured, will be presented.

An accurate method for the measurement of thin walled tube specimens is presented, with particular emphasis on the shape and magnitude of the local imperfections. The methods used to physically measure tubes along with the numerical methods derived to reduce the results are explained. The measured imperfections are then processed into three-dimensional imperfection maps. This paper gives an overview over characteristics of these imperfection maps.

The objective of this paper is to evaluate the efficiency and accuracy of an approximate method for the calculation of the buckling load of rigidly jointed structures. The evaluation of the buckling load of rigid-jointed structures is complex as it often involves the instability of more than one member. The computation of the buckling load thus requires tedious nonlinear iterative analyses, mostly utilizing the finite element program. This paper presents an in-depth evaluation of the accuracy of the approximate method by correlating its results with those obtained from commercially available software packages. To that purpose, the buckling load for various rigid truss configurations is investigated using the approximate method. It is found that the approximate method is computationally simpler that the finite element method and provides accurate results, proving itself useful for use in design stages.

This paper presents an advanced modeling technique that can be applied to assess the stability of the steel structures exposed to natural compartment fire. The analysis accounts for both material and geometric nonlinear effects. The stability of overall structure with actual boundary conditions is captured instead of studying isolated members. Natural fire curve is used in contrast to the ISO standard fire, representing the real fire development in the compartment. The proposed approach is verified and used to investigate the behaviour of a three-dimensional multi-storey frame subjected to natural compartment fire. The computed results are compared to those from the conventional approach based on ISO standard fire curve and the advantage of the proposed method is highlighted. Guidelines on stability design of steel frames in natural fire using advanced analysis are proposed.

Modular steel scaffolding systems are commonly used as supporting scaffolds in building construction, and structural stability is always an important design criterion for their safe and effective use. Structural engineers often find difficult to determine the effective length of the vertical members of those scaffolding systems due to the member configurations and also the presence of bracing members. In order to study the stability behaviour of these systems, a total of three single and three double storeys modular steel scaffolding systems were tested to failure. Moreover, an advanced non-linear analysis method was adopted to evaluate the load carrying capacities of these scaffolding systems under different support conditions. This paper presents the findings of the comparison between the experimental and the numerical results on the structural stability of these modular steel scaffolding systems.

This paper is concerned with the elastic buckling of rectangular plates subject to both intermediate and end uniaxial loads. The aforementioned buckling problem is solved by decomposing the plate into two subplates at the boundary where the intermediate load acts. Each sub-plate buckling problem is solved exactly using the Levy approach and the two solutions brought together by the continuity equations at the separated edge. It is worth noting that there are 5 possible solutions for each sub-plate and consequently there are 25 solution combinations to be considered. The final solution combination depends on nature of the ratio of the intermediate load to the end load. The exact stability criterion for the plate is presented both in tabulated and in a graphical forms which should be useful for engineers designing walls or plates that have to support intermediate floors/loads.

This paper deals with the shear strength of prestressed concrete box girders having corrugated steel webs (PCBGCSW), with particular emphasis on the shear lag and the stochastic variation of material properties. First, the shear strength curve of corrugated steel web is proposed based on experimental and analytical results obtained for simply supported beams composed of corrugated steel web without and with concrete flanges. In order to evaluate the shear strength of PCBGCSW based on the shear strength curve of corrugated steel web, it is important to know the distribution of shearing force between the corrugated steel web and the concrete flanges. The effect of the concrete flanges, therefore, on the distribution of shearing force is investigated considering the shear lag behavior. Finally the stochastic variation of material properties for the evaluation of the shear strength of corrugated steel webs is discussed from the design viewpoint.

The paper is concerned with a finite element model to predict the ultimate load and behaviour of stiffened plates subjected to lateral pressure and in-plane loading. The stiffened plates considered are all simply supported along the four edges. A finite element package ABAQUS is used to simulate the behaviour of stiffened plates. Initial imperfection of stiffened plates is taken into account in the finite element analysis. Accuracy of finite element analysis is assessed by comparing ultimate load and failure shape with experimental results from other researchers. Comparison shows that the finite element method is able to predict accurately both the behaviour and ultimate load of stiffened plates.

Over the last few years, there has been an increased usage of fibre-reinforced composite (FRC) materials in structural applications, including rehabilitation and retrofitting, mainly due to superior properties such as high strength, low weight and corrosion resistance of FRC materials. These superior properties of FRCs can be exploited in applications where simple light weight construction is a priority. Plywood is one of the most widely used materials in a number of light weight applications in the construction industry. This paper presents an experimental investigation of buckling behaviour of plywood plates reinforced with advanced fibre composite materials. Plywood laminated with FRC fabrics provide a superior composite which is light and has significantly improved buckling (stability) characteristics compared to its parent plywood material. The lateral deflections corresponding to increasing in-plane compressive loads on reinforced plates were closely monitored and compared with those plates with no reinforcement. 4.5mm thick plywood laminated with three different composite fibres (namely, carbon, aramid and glass) were considered in the investigation. The results of the study indicate that FRC-reinforced plywood plates exhibit a significant reduction in deflections and increase in the load carrying capacity in buckling applications.

The usual assumption of isotropy of the material is shown here to be one of the reasons for the observed disparity between the theoretical and experimental values of the critical stress for plastic buckling of plates and shells. When the effect of plastic anisotropy that commonly occurs in thin-walled structures is included in the theoretical framework, the predicted load at the point of bifurcation can be significantly lower than that corresponding to the isotropic material. The present paper is intended to demonstrate the influence of plastic anisotropy on the critical stress for the elastic/plastic buckling of rectangular plates under unidirectional compression. The results are presented graphically to indicate how the critical stress is lowered by the presence of plastic anisotropy that is characterized by an R- value less than unity.

The tensile buckling and vibration behaviour of curved panels of square planform subjected to combinations of tension-tension, tension-compression and compression-compression edge loadings have been studied using the finite element method. The first order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is extended from the dynamic, shear deformable theory based on the Sander's first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The in-plane non-uniform stress field has been analysed under plane-stress conditions with reasonable accuracy. The effects of biaxial concentrated and patch loading on the edges are also considered in the analysis.

A postbuckling blade-stiffened composite panel was loaded in uniaxial compression, until failure. During loading beyond initial buckling, this panel was observed to undergo a secondary instability characterised by a dynamic mode shape change. These abrupt changes cause considerable numerical difficulties using standard path-following quasi-static solution procedures in finite element analysis. Improved methods such as the arc-length-related procedures do better at traversing certain critical points along an equilibrium path but these procedures may also encounter difficulties in highly non-linear problems. This paper presents a robust, modified explicit dynamic analysis for the modelling of postbuckling structures. This method was shown to predict the mode-switch with good accuracy and is more efficient than standard explicit dynamic analysis.

The failure of medium-height thin-walled cylinders is characterised by a number of horizontal ripple-like buckles across the upper half of the meridian which faces into the wind. This buckling mode has received comparatively little attention although it has been observed in previous investigations. A recent study of finite element models has shown that this failure mode is in fact the result of two successive bifurcations. The primary bifurcation mode is comprised by one large buckle. Secondary bifurcation leads to the observed failure mode. A case study using a finite element model of a thin-walled cylinder displaying this particular failure mode will be presented in this paper. Geometrically non-linear effects play a great role in the buckling behaviour and a comparison between linear and non-linear analysis is given. A supplementary eigenmode analysis illustrates the peculiar buckling mechanism.

Usual methods for analyzing lateral buckling of structural members assume cross sections of the member remain undistorted. However, when a member is thin-walled, distortion may occur and consequently reduce the resistance of the member to buckling. A mathematical model is presented here to study the effect of distortional buckling of beams. Previous studies on distortional buckling have been carried out using n^th degree polynomials to model buckling behaviour. This study provides an alternative, using Fourier Series, way to predict distortional buckling. It is believed that this method is a simple and efficient way of determining the critical buckling load and modal shapes of I-section beam-columns.

Hill-top branching is a bifurcation problem, in which the path-branching occurs exactly at a limit point of the primary path and this unusual bifurcation problem is not well realized in structural stability theory. The present study treats multiple hill-top branching. Tow or more than two bifurcation paths may be emanating from the limit point. The general solution of stiffness equations at the stability point is first described for hill-top branching. Then, the eigenvector-free pinpointing iteration to precisely locate the stability point and the branch-switching procedure to find multiple bifurcation paths will be illustrated briefly. In numerical application, a bench model for multiple hill-top branching is computed.

This paper applies the energy limit concept to the stability problem of structures and structural systems. New concepts such as, the energy capacity that measures accumulated energy in the structure before failure and virtual large displacements that lead to significant plastic deformations are introduced and defined. Proposed theory considers full load cycle, from the initiation of the instability until complete collapse of the structure. New equations for the determination of critical loads are derived, presented, and compared to known results. Proposed new equations take into consideration simultaneous effects of axial, bending, shear and torque deformations. The results of the study are substantiated by comparison with examples with known answers.

An unified Generalised Beam Theory (GBT) approach to the stability and vibration analyses of arbitrary orthotropic thin-walled members is formulated. The main steps required to establish the GBT system of homogeneous differential equations are first described and discussed. Then, the derived GBT matrices are physically interpreted, i.e., their terms are related to the member mechanical properties. Finally, the GBT equations are used to investigate the local and global stability/vibration behaviour of orthotropic (laminated plate) thin-walled channel members. The relevant buckling/vibration modes are identified and the associated bifurcation stresses/natural frequencies are evaluated.

A simple and computationally inexpensive approach is presented for obtaining the most sensitive imperfection mode corresponding to the maximum load factor of the stable bifurcation point. The critical point of an imperfect system is found by solving an anti-optimization problem, where the load factor is minimized with respect to the imperfection parameters and the nodal displacements under constraint on the lowest eigenvalue of the stability matrix. It is shown in the examples that a minor imperfection that is usually dismissed is very important in evaluating the maximum load of a flexible structure.

This paper applies the matrix-powered Lanczos method developed in quantum physics to the eigensolurion in structural dynamics. In structural problems, the power technique can be applied to the dynamic matrix. The convergence of the modified Lanczos method using the power of dynamic matrix is better than that of the conventional Lanczos method. The effectiveness of the modified Lanczos method is verified through several numerical examples. The optimal power of dynamic matrix is also presented.

A simplified method for the computation of derivatives of eigenvalues and eigenvectors associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation. The algebraic equation developed can be used to compute derivatives of both eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space, it is numerically stable and very efficient compared to previous methods. To verify the efficiency of the proposed method, the finite element model of the cantilever beam is considered.

In time history linear dynamic analysis of structures, one approach is to employ Duhamel's integral but because its lower bound is zero, for each time step the integral needs to be evaluated in the domain from zero up to the specified time. In this paper, a modified form of the Duhamel's integral is proposed in which for each time step the last time interval is integrated, therefore, it is considerably faster than its original form. In this formulation, at each time, in addition to displacement, velocity is also calculated and they are used as initial values for the next step. Then, for the solution of the next step, the transient solution is added to the effect of loads in that interval. The method proposes two integrals for displacements and the same two integrals for the velocity in one time step. Indeed, for a problem with n time steps, total number of integration intervals for Duhamel's integral is n(n+1)/2, while, for the proposed method the is just 2n. The proposed method enunciates that the savings in the computational time becomes more obvious for MDOF systems due to the fact that the aforementioned saving is the multiple of the number of modes.

This paper presents the finite element study of long-span flat concrete floor subjected to walking load. The general review of the floor vibration acceptability is presented. Series of finite element (FE) analyses have been carried out to study the effects of walking load on long-span flat concrete floor. The modeling techniques of walking load are described and discussed in details for finite element analysis. The comparison of dynamic response between simply support and fixed support floor under walking load are studied. The effects of floor thicknesses and walking frequencies are also investigated. The results presented in this study can be used as a guidance for determination methods of dynamic behavior of long-span flat concrete floor under walking load.

In this paper, stress waves in rock masses with multiple parallel fractures applied by sine load are studied with rigid block and face-to-face contact model of distinct element method (DEM). Normal stress waves in a rock pillar are analyzed, and the wave patterns of different damping ratio are presented. The effects of silent boundary conditions, soft interlayer and tensile property on the propagation characteristics of stress waves are analyzed.

In this paper the finite element procedure for analysing the postbuckling behaviours of shallow spherical shells is developed. The numerical simulations for the previously tested experimental data of pressurised thin-walled shallow spherical shells have been done by using a degenerated nine-node shell element with mixed interpolation functions. The nonlinear pre-buckling paths have been statically calculated, and then the corresponding postbuckling behaviours have also been obtained through nonlinear dynamic analysis. It is shown that if both an internal and an external viscous damping are considered, the good simulations even for the dynamic postbukling paths can be obtained.

The method proposed presently replaces the propagating rupture on the fault surface by a fictitious focal point and a seismograph station in the vicinity of the given soil site. Infinite elements are adopted in the far field and finite elements in the near field. A fictitious focal point and seismograph station scheme is used to calibrate the free field ground motion of the soil site. The seismic analysis of an embedded body, which is finite, uses the difference scheme to solve the problem. The impedance equations, governing the difference between the embedded body and the seismic free field, contain the difference displacements and the already known free-field quantities. No infinite element free-field node is involved in the analysis of the difference system. For an embedded long and slender body, the part of interest of the body should be discretized into finite elements in the near field, and the remaining part of the body into infinite elements in the far field. The analysis described for a finite body is followed; and no infinite element free-field node, beside those inside the region where the actual long body will be embedded, is involved.

This paper presents an accelerated higher order boundary element method for wave response analysis of VLFS (Very Large Floating Structures). The Fast Multipole Method (FMM) has been implemented on the higher order boundary element code using 8-node quadrilateral element. The method utilizes an iterative solver, multipole expansion of Green's function, and hierarchical algorithm using quadrant-tree. The numerical benchmark calculations have shown the efficiency of the method both in storage requirement of O(N) and computation time of O(N log N), where N is the number of unknowns for the velocity potential.

Throughout the history of computing, the innovations and advances in computer language design have been driven by the perpetual need to handle the increasing complexity of software. The programming language JAVA was developed by refining the object-oriented programming paradigm of C++ to provide a platform independent language that would be readily portable across a variety of architectures. Object Oriented Programming (OOP) in JAVA allows the programmer to remain close to the higher-level physical model of the real-world problem through the use of data abstraction, encapsulation, inheritance and polymorphism. The present paper attempts to demonstrate the programming capability and versatility offered by JAVA for writing more readable, manageable and expandable object-oriented codes for computational finite element analysis. The paper presents illustrative user code fragments of an object-oriented program that was developed in JAVA for finite element analysis of a structural system. The paper describes the salient advanced features of JAVA that elucidate why JAVA and its generation may be the programming languages of choice for scientific codes in the future.

The application of an unconditionally stable explicit pseudodynamic algorithm to solve the momentum equations of motion is illustrated herein. Since this integration method is unconditionally stable and explicit the difficulty arising from the presence of high frequency modes can be easily overcome and an explicit implementation, which is much simpler than for an implicit implementation, can be adopted for the pseudo-dynamic testing. The superiority of this pseudodynamic algorithm was verified through actual tests.

It is well known that many real systems have asymmetric mass, damping and stiffness matrices. In this case, the method for calculating eigenpair sensitivity is different from that of symmetric system. To determine the derivatives of the eigenpairs in asymmetric damped case, a modal method was recently developed by Adhikari. When a dynamic system has many degrees of freedom, only a few lower modes are available, and because the higher modes should be truncated to use the modal method, the errors may become significant. In this paper a procedure for determining the sensitivities of the eigenpairs of asymmetric damped system using a few lowest set of modes is proposed. Numerical examples show that proposed method achieves better calculating efficiency and highly accurate results when a few modes are used.

This paper presents a preliminary investigation on nonlinear wave propagation in multistory buildings. The proposed one-dimensional nonlinear wave equation solver in time domain is demonstrated to yield favorable results as conventional modal analysis method, yet it carries a most desirable feature that wave arrival time delay and higher mode contribution can be included properly. The proposed method will become superior when more sophisticated digital filter design is launched in future studies.

Lamb wave scattering analysis by an internal crack in a plate is carried out using the mode exciting method combined with the partial analysis method, which is our original method for solving a scattering problem of Lamb waves. Reflection and transmission coefficients are calculated for frequencies below the cut-off frequency of S₁ mode and for crack lengths less than 10 times of the plate thickness. Peak values in the reflection coefficients show dispersive properties for various frequencies and crack lengths. Using these dispersive characteristics, the applicability of the Lamb wave method to nondestructive evaluation of an internal crack is discussed.

We consider the (linear) elastic wave equation and construct asymptotic expansions of waves reflected by boundaries in various situations. We treat the case where a discontinuous wave like the delta function hits the boundary and the total reflection happens. We also deal with the case where a wave is reflected by a hole empty or full of some liquid, and examine the reflection rate of the backward reflected wave.

A model for predicting thermal waves within a surface-heated porous structure has been developed. The relevant phenomena for the moisture, pressure and temperature fields are coupled. Considering mass and energy transfer processes, a set of governing differential equations is presented. The solution of the problem has been obtained with a finite difference scheme.

An analytical-numerical method is proposed to analyze the surface waves in multi-layered piezoelectric cylinders. In this present method, the cylinder is divided into layer elements with three-nodal-lines along the wall thickness. The Hamilton principle is used to develop approximate dynamic equilibrium equations. The dispersion relationship for multi-layered cylinder is defined and deduced from the Rayleigh quotient and the orthogonal condition of the eigenvalues. The method of Fourier transform combined with the modal analysis is used to determine the displacement response and electronic potential to mechanical and electromechanical loads. Numerical examples are presented for calculating the frequency and group velocity dispersion behaviors, as well as electronic potential distribution in multi-layered piezoelectric cylinder.

In this study, the vibration and acoustic resonance excited by the train traffic on concrete viaduct is examined. A narrow band analysis - Fast Fourier Transform (FFT) method is used to analyze the measurement results and Finite Element Method (FEM) is employed to validate the vibration resonance frequencies of viaduct structure.

Based on the measured results of the structure-borne noise and vibration, the relationship in terms of transfer function and coherence between noise and vibration are evaluated. It is found that the dominant frequency range for noise and vibration of concrete viaduct is between 20 Hz and 157 Hz, the resonance frequencies are 43 Hz and 54 Hz and have significant tonal noise characteristics. According to its noise and vibration spectra, it shows that the vibration resonance is more significant than the acoustics resonance. The measured results are in good agreement with the theoretical results run by FEM.

In this paper, the methodology of predicting interior noise level for the tracked vehicle have been developed. The FE and BE methods were adopted to perform the vibro-acoustic analysis of tracked vehicle. In this study, the interaction forces between the tracks and the chassis hull are determined first by using ADAMS. In order to obtain the structural displacements/velocities, the structural frequency dynamic response then is carried out by using NASTRAN. Finally, the interior noise level are predicted by using software SYSNOISE. As an example, the methodology is applied to analyse the interior noise for an actual tracked vehicle. The predicted noise levels of the tracked vehicle are compared with actual measurements. The comparison of predicting results with testing results of tracked vehicle shows reasonably good agreement. Through this application, it is demonstrated that the presented methodology and analysis model for predicting interior noise level of a tracked vehicle is valid and effective.

In single-step two-stage algorithms for the approximate solution of the equations of dynamic equilibrium, the displacement and velocity of nodes at the end of a time step are expressed in terms of the values at the beginning of the time step using an amplification matrix. In this paper, a new form of the exact amplification matrix for SDOF problems is presented and some interesting properties are noted. A new family of algorithms using any order of polynomial approximation and incorporating these properties is then discussed. The algorithms are unconditionally stable, and incorporate algorithmic damping. The algorithms are then successfully used in the analysis of Bathe's pendulum.

This paper is concerned with the geometric nonlinear analysis of space framed structures emphasizing how to model the effects of geometric nonlinearity consistently. Two consistent formulations are presented in this study; one is on the basis of small rotation, while the other large rotation. The consistency makes the derived tangent stiffness matrices symmetric. Although the tangent stiffness matrices are different, these two formulations predict the same responses. It is also shown in this paper that the incremental equilibrium equations for these two formulations are the same as those derived by Yang and Kuo (1994) after some derivations. However, the tangent stiffness matrix in Yang and Kuo (1994) is asymmetric.

This paper presents a practical nonlinear analysis for the automatic design of steel space frames. The geometric nonlinearity is considered using stability functions. A direct search method is used as an automatic design technique. The unit value of each member is evaluated by using the LRFD interaction equation. The member with the largest unit value is replaced one by one with an adjacent larger member selected in the database. The weight of the steel frame is taken as an objective function. Load-carrying capacities, deflections, interstory drifts, and ductility requirement are used as constraint functions. Case studies of the planar portal frame and the space two-story frame are carried out.

This paper discusses the nonlinear analysis of two-dimensional frames with semi-rigid joints. An extensible elastica model is used for the members to correctly treat the geometric nonlinearities, and two models are considered for the semi-rigid joints. Two examples that can be used as benchmarks are considered.

In this paper we propose a new technique for obtaining an approximate probability density for the resonance and off-resonance response of a finite-damping nonlinear vibration system under both random disturbances and deterministic excitation.

In this study, the dynamical contact simulation by the finite element method (FEM) for the chemical mechanical polishing (CMP) process is presented. In order to simulate CMP, a numerical model for surface roughness layer of the polishing pad and a numerical procedure for FE contact analysis are newly presented. In the analysis model, the surface roughness layer of the polishing pad is assumed as a flat soft layer. The elastic modulus of the soft layer is treated as a fitting parameter between the experimental results and the numerical model, while the patterned wafer can be assumed as a rigid body. The distribution of contact pressure between the patterned wafer and the polishing pad is computed by FEM. The pattern topography is modified according to the pressure dependency of the polishing rate. The iterations of this numerical procedure and the topography modification give the progress of the polishing process dynamically. In order to solve the contact problems, the finite element discretization needs the minimization of total potential energy with gap-contact constraint conditions. For the practical dynamical simulation, the modified stiffness matrix with the penalty numbers is introduced, Although this numerical procedure is based on the linear contact theory, the solution process with iterative schemes is required for getting a stable contact status. Finally, several 2-D numerical analyses for CMP process are demonstrated. Compared with the experiment, the results by the proposed numerical simulation agree with the experimental results very well and the validity of the proposed numerical model for CMP process is clarified.

Kinematic Analysis is conducted to derive the geometric constraints for the geometric design of Foldable Barrel Vaults (FBV) composed of polar and translational units. Non-linear structural analysis is followed to determine the structural response of FBVs in the fully deployed configuration under static loading. Two load cases are considered: cross wind and longitudinal wind. The effect of varying member sizes, depth to span ratio and geometric imperfections is examined.

An analytical model is developed to predict the behaviour of concrete in-filled steel tubular columns under cyclic loading. Moment-Thrust-Curvature (M-P-Φ) relations and Moment-Thrust-Strain relations (M-P-ε) relations are developed for columns of circular, square and rectangular cross-sections by the method of fiber-analysis. The fiber-model is incorporated in the analysis of column subjected to axial load and cyclic bending, taking into account of the geometric and material non-linearities. Newton-Raphson technique is adopted to solve the incremental stiffness equation and a generalised stiffness parameter is used, to overcome the limitation of approaching the limit points, thereby tracing the post-buckling response. The accuracy of the model is verified by comparing with the available experimental results.

To examine the damages of structure in use is generally a challenging task., particularly when a fast inspection is required by using limited tools or even the bare eyes. The other challenge is how to evaluate the damage state after the fast safety examination. Most well know damage indexes for the structure are for the design purposes such as to estimate the possible damage state when structure is under extraordinary loading condition. The index must relate to the maximum force applied and maximum deflection or plastic deformation. To have structure's real response is generally impossible unless on-line monitoring is applied. Therefore, it is the interest of this study to find a means to evaluate the damage state through the limited data obtained by bare-eye examination or using limited tools. The evaluation was performed in the laboratory by testing the scaled down beam models and compared the data obtained by limited tools to the one obtained through data acquisition system. It was found that for the large scale, fast structure inspection this new developed simplified damage index may provide a convenient means for the damage evaluation of the structures.

This paper presents a structural analysis method for lapped moment connections between cold-formed steel Z sections. A total of 12 one point load tests on generic lapped connections between cold-formed steel Z sections with various lap lengths were carried out, and an analysis model is proposed after calibration against test data. The analysis method is based on basic structural design and analysis principles. It is found that at the ends of the laps in bolted moment connections, the combined effect due to bending and shear is always critical. Comparison between the predicted and the measured moment resistances at the ends of laps of the lapped connections is shown to be satisfactory.

A lot of steel check dams have been constructed in order to prevent rocks and driftwoods from carrying downstream when a debris flow occurs in a mountainous area in Japan. However, there is no design specification whether the damaged steel should be repaired or not depending on the damage level of steel pipes. In this paper, the load-displacement relations of the damaged hollow pipe and the damaged concrete filled tube are made cleared from two kinds of tests. From the results of the static flexural test, we suggested the serviceability limit and the ultimate limit of both steel tubes.

The collapse of the towers of World Trade Center in New York on September 11, 2001 have initiated a fresh look at the vulnerability and survivability of existing high-rise buildings subjected to impact, explosion and fire. This paper proposed a transient spread-of-plasticity analysis to assess the structural integrity of steel frames after explosion and fire. The blast loading reduces the fire resistance of steel frames due to permanent deformations in the columns.

Utilization of corrugated steel plate as web in PC girder markedly separates functionality of flanges and web in resisting external force. The web responses mainly to resist for shearing force. However, by such separation, transferring of shearing force at the point of loading into the web seems to be retarded. The so–called shear lag phenomenon in the web is thought to occur. In this study, an extended beam theory is developed by considering that the web is shear deformable and satisfies Timoshenko beam theory. The governing equations and boundary conditions are derived by the variational principle. The calculated results based on the extended theory are then verified with those by the finite element analysis on a number of girder where a good agreement is found and the shear lag phenomenon in corrugated web is revealed.

Corrugated panels used in offshore installations are designed for the possibility of an accidental hydrocarbon explosion. As this is an unlikely event, large plastic deformation is often allowed, although extensive tearing of panel must be prevented. This paper presents a numerical study using a force based failure criterion available in Abaqus/Explicit finite element code to model the tearing of a stainless steel corrugated panel subjected to dynamic blast loading. The capability of the model to predict experimental responses and its suitability for further development into a general failure criterion will be discussed.

A three-parameter model is suggested by Rice, J. [Gao et al., 1997] to simplify the analysis of mechanical and electric field in poled piezoceramic materials. Making use of the model, the governing field equations with the coupling effect of mechanical and electric field components can be reduced to two Laplacian equations in two dimensions. Thus, the conformal transformation in complex plane can be introduced for solving many boundary conditions. Considered in this paper is collinear edge cracks under uniform tensile load and electric field component. Energy density criterion S_min by Sih, G.G. [1991] is used to indicate the mechanical and electric coupling effects on the onset of rapid crack propagation. For poling perpendicular to crack, the energy density criterion S_min can increase or decrease depending on the direction of the applied electric field with reference to the poling direction. This is contrast to the result using energy release rate which remains unchanged for electric field in or against the poling direction.

Repeated thermal shock (RTS) loading is common in the operation of pressure equipment in thermal power stations. Thermal shock can produce a very high stress level near the exposed surface that eventually may lead to crack nucleation and crack growth. These cracks may either continue to grow to failure or arrest at harmless depths, depending on the thermal shock conditions.

This paper describes an experimental study of crack initiation and propagation in low carbon steel specimens exposed to repeated thermal shock. Based on experimental results on carbon steels at temperatures below the creep range in water and steam enviromnents, temperature effects of the crack growth mechanism were evaluated. Experimental results of the temperature effects on the crack growth mechanism due to RTS were presented.

In this paper, a new method for determining of 3-D residual stresses using finite element technique is presented. The method involves the measurement of strain changes in the components as a narrow slot is cut along the plane of interest. The finite element calculations are used to relate the strain changes at the measurement points to the surface forces on the slot plane. The initial residual stresses are obtained by superposing the stresses relaxed by removing these surface forces on the residual stresses measured by the hole drilling method on the slot plane after cutting. The method has been used to measure the through thickness distribution of 3-D residual stresses in a multi-pass butt welded joint.

The interactions between a macro-crack and a cluster of micro-defects are studied numerically by using a series of special finite elements each containing a defect. These special finite elements, which contain defects such as holes, cracks, and inhomogeneities, are developed based on the hybrid displacement, complex potential and conformal mapping techniques. These hybrid-type elements can be used together with the conventional finite elements without any difficulty. In this paper, the mathematical and finite element modeling procedures for the study of the above-mentioned problems are presented. The numerical results obtained are compared with the existing theoretical results.

Earthquakes in the Mid-America region are low probability-large consequence events. The purpose of this study is to develop a methodology for probabilistic performance evaluation of existing and retrofitted essential facilities (EF) such as fire stations and police stations under earthquake excitation in Mid-America. Since most essential facilities in the Mid-America region have not been designed for seismic forces, the vulnerability of such structures is a serious concern. Only un-reinforced masonry (URM) buildings, which represent most EFs in mid-America, are considered in this study. A finite element model based on ABAQUS was developed. Structural components such as walls and diaphragms in masonry buildings usually go into inelastic state under severe earthquakes and the inelastic restoring forces of the walls are dependent on the loading history. To model these response behaviors, a nonlinear force-displacement model is developed. Four wall damage models, diagonal tension, bed-joint sliding, toe crushing, and rocking are considered. The wall drift ratio is used as a measure of the overall response and damage to nonstructural components and contents such as equipments. Results show that retrofitting is needed for all buildings for satisfactory performance according to most recent code recommendations. For retrofit, the center core method is considered here. The method embeds the reinforcing bars within an existing un-reinforced masonry wall. The results show that this method only enhances the building performance moderately; other more efficient retrofit methods may be necessary.

Modal analysis based damage detection techniques depend upon the accurate estimation of the changes in natural frequencies, damping ratio and mode shapes of a structure that occur with damage. But, even a large damage in a structure reflects only small shifts of the lower natural frequencies. At higher modes of vibration perceptible shifts can be observed even for occurrence of incipient damages. Yet, it is impractical to extract modal parameters at higher modes using conventional modal testing techniques. With the emerging smart piezoceramics (PZT) based damage detection technology, impedance response functions of the structure can be obtained in the higher frequencies ranges. The electromechanical admittance signature obtained in this method is a coupling of the impedances of the bonded PZT transducer and the host structure. In this paper, a unique method for damage detection that blends the modal analysis techniques with the emerging e/m impedance technique is presented. A finite element model of a cantilever beam is adopted to simulate damage and to demonstrate the possible damage identification by this method.

This paper is concerned with characterization of contact ultrasonic transducers used for non-destructive evaluation of materials. The transducers are modeled as a normal load applied on surface of the material being tested, and the inverse problem to estimate the load from displacements given at some observation points is considered. Specifically, the inverse problem is formulated and solved for cylindrical transducers. In the inverse analysis, simulated input data are used so that we can discuss the effect of some inverse analysis parameters on accuracy of the solutions. Among various parameters, the effect of input dataset and basis functions to which unknown loads is expanded are investigated in this paper since they could have significant effects on the inversion.

A system identification based method with incomplete measurement of truncated modal flexibility is proposed for detecting damage in a structure. The stiffness of the whole structure is decomposed and represented by parameters through eigen-analysis of each structural member. The sensitivity of truncated modal flexibility to these eigen-parameters is derived. A regularized objective function containing least-squares of modal flexibility changes between the FE model and damaged structure is established and minimized by conjugate gradient method. The damage is then localized, classified and quantified through inspection on the vector of identified eigen-parameters. A numerical example of a two dimensional frame structure is presented to demonstrate the effectiveness of the proposed method.

Main body of this article is a summary of results obtained by the authors (Ammari et al, 2002). We consider the system of elastostatics for an elastic medium consisting of an imperfection of small diameter, embedded in a homogeneous reference medium. The Lamé constants of the imperfection are different from those of the background medium. We establish an asymptotic formula for the displacement vector in terms of the background solution, the location of the imperfection and its geometry. Our derivation is rigorous, and based on layer potential techniques. We introduce the concept of elastic moment tensors which is elastic version of Pólya-Szegö tensor and prove some important properties of them. We then apply these asymptotic formulas for identification the order of magnitude of the diameter of the elastic inclusion, its location, and its elastic moment tensors.

Model updating problems can be classified into identifiable and unidentifiable cases. In general, when the number of uncertain parameters is “large” and the number of data is “small”, model updating fall into the category of unidentifiable. The present paper concentrates on the more general unidentifiable case of model updating problem, in which the posterior PDF is distributed in the neighborhood of an extended and extremely complicated manifold of the parameter space. This paper presents a method for generating a set of points on the manifold using an evolution strategy for its representation and so as to calculate the posterior PDF of the uncertain parameters and predicted responses at the unobserved DOFs. A simple numerical example is employed to demonstrate the proposed method, and illustrate the difficult of deterministic methods in handling model updating problems in unidentifiable cases.

A formula for the surface impedance tensors of orthorhombic aggregates of cubic crystallites is given explicitly in terms of the material constants and the texture coefficients. Here we account for the effects of crystallographic texture only up to terms linear in the texture coefficients.

A recently developed Hilbert-Huang transform (HHT) technique is applied to the detection of the damage locations of bridge structures. The HHT may be used to identify the locations of damages which exhibit nonlinear and non-stationary behavior, since the instantaneous frequency characteristics of the measured signal can be analyzed by the HHT. Numerical simulations were conducted on two bridge systems with damages using controlled excitations with sweeping frequency. Nonlinear plastic model using a gap element is employed to model the behavior of the cracked elements in the numerical simulations. The results indicate that the HHT method can reasonably identify the damage locations based on a limited number of acceleration sensors. Experimental study has been also carried out on a steel frame to confirm the applicability of the HHT to detect a structural connection with loosened bolts.

This paper presents an effective identification algorithm for determining the parameters of structural dynamic system and hence detecting damage. Based on numerical analysis of measured responses (output) due to known excitations (input), structural parameters such as stiffness values are identified (damaged case) and compared with the intended design values (undamaged case). The focus is on identification of stiffness matrices and damage identification with incomplete measurement. With the proposed methodology, it is possible to utilize several reduced stiffness matrices, thereby enabling one to find individual stiffness coefficients. Static condensation method is employed to avoid the need of having a full set of sensors (complete measurement). To estimate individual stiffness coefficient from the condensed stiffness matrices, the genetic algorithms (GA) approach is employed to solve the resulting nonlinear equations. The efficiency of the proposed technique is shown by numerical examples for multi-storey shear buildings subjected to random excitation. The effects of input and output noise in the measurements are accounted for. While static condensation introduces errors when applied to structural dynamics problems, it is shown that the proposed methodology gives reasonably accurate identification in terms of locating and quantifying damage in an almost black-box manner.

Performing a proper regularization requires first a good understanding of the nature of the ill-posedness and then an efficient strategy on how to tread stability with efficiency and accuracy in solving the ill-posed problems. In this paper, a simple one-dimensional mechanics problem is presented to clearly and explicitly reveal the nature of ill-posedness in the inverse problem of external force estimation using a discretized (FEM) forward model. Also a novel regularization method with discretization-based filter is proposed to obtain a much more stable and accurate solution for the inverse problem. Estimation with noise-contaminated inputs is carried out, and the efficiency and accuracy of this regularization method are demonstrated. The concept of this new regularization method is applicable for all inverse problems based on methods of domain discretization. In addition, the present regularization method requires no information on the noise source.

The ramp response of an underwater object yields information about the object's size, orientation and geometrical shape, which is proportional to the area of cross section of the object perpendicular to the line of sight. Conventionally, backscattering data of full frequency range are necessary to obtain an accurate ramp response. However, it is very difficult to get the full frequency range data in practice. The Fredholm integral equation of physical optics has been utilized to formulate and compute accurately the ramp response with backscattering data of partial frequency range. Several numerical examples have been presented to verify the results using the Fredholm integral equation. It is shown that the present method is more accurate than the conventional method without using the Fredholm integral equation.

We consider the problem of determining an inclusion D made of different elastic material in an elastic isotropic body Ω from boundary measurements of traction and displacement. We prove that the volume of D can be estimated, from above and below, by an easily expressed quantity related to work, only depending on the boundary traction and displacement.

In the recent years, piezoceramics (PZT) have found its niche in structural health monitoring. Commonly known as the electro-mechanical (EM) impedance method, this method utilizes the unique properties of the PZT to sense structural damage. Current modelling efforts with this technique has however, neglected the effects of the bond layer. Thus, the response prediction reliability and repeatability of the E/M admittance (the inverse of E/M Impedance) measurements between identical smart systems arise as an issue to be addressed. In this paper, a one-dimensional E/M impedance model accounting for shear lag between the PZT patch and the host structure is presented. Numerical analysis performed on a beam specimen has shown that the repeatability of measurements and the consistency of signatures between identical smart systems can be enhanced by the use of high modulus adhesives.

Five design concepts are first explored by means of natural vibration tests on a tubular cantilever with its base provided with a partial rotational restraint. The design concepts include polyethylene empty chambers, chambers with oil, chambers with sand, mass-string assembly, and mass-string-whiskers assembly. To quantify the damping characteristics and efficiencies of the design concepts, various assemblies of each passive damping design concept are tested inside a hollow steel member. It is found that the mass-string-whiskers design concept is better than the other four design concepts.

In this paper, a weight dropping impact test was carried out in order to examine the energy absorption and the load reduction effect of the laminated fiber reinforced rubber as a shock absorber under the repeated load. It is concluded from this experiment that the load reduction effect of the laminated fiber reinforced rubber comes close that of the natural rubber with increasing the number of the weight droppings. However, the energy absorption of the laminated fiber reinforced rubber is a little bigger than that of the natural rubber even if the laminated fibers break in pieces.

This paper presents the elastic buckling of column structures with a pair of piezoelectric layers surface bonded on both sides of the columns. The governing equation coupling the piezoelectric effect is first derived based on the assumed distribution of the electric potential in the flexural direction of the piezoelectric layer and an eigenvalue problem is solved using the finite difference method. The force excited by the piezoelectric layer due to the external voltage is modelled as a follower tensile in the paper. Such follower tensile force is used to enhance the buckling capacity of the column structure. For the columns with different boundary conditions, buckling results are presented to show their variations with respect to the location of the piezoelectric layers and the applied voltages. It was found the buckling capacity of the column structure could be enhanced effectively by designing optimal location of the piezoelectric layer and the voltage applied to the piezoelectric layers.

This paper presents a new coupled electro-mechanical dynamics model of piezoelectric actuator-sensors. The new model takes the bonding layer between piezoelectric patches and host structures into account in the coupled electro-mechanical analysis by treating the bonding layer as a spring-mass-damper system. Numerical simulations are performed to reveal the effect of bonding layers as well as to demonstrate the application of the new model to debonding detection of composite repair patches.

Flutter has been observed and documented since the beginning of the era of controlled flight. The divergent and destructive oscillations of motion are a result of the interaction between the structures, dynamics and the aerodynamics. It has been shown that flutter could be controlled actively.

In this study, a 2D cantilever wing with three-degree-of-freedom was developed to show the flutter suppression. A mathematical aeroservoelastic model was created using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plate characteristics were determined from this model and verified by open loop simulation. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter simulation was conducted.

The program outputs represent in detail how adaptive materials have been used to actively suppress flutter. They demonstrate that small, carefully placed actuating plates can be used effectively to control aeroelastic response.

There is practical interest to apply active control at the global structural level and further decentralize control for more effective distributed robust control of local systems. In this paper, the effectiveness of a layered active vibration control strategy for seismically excited unbraced frames with piezoelectric sensors and stacked actuators is proposed and demonstrated. To form input-output decoupled subsystems, robust decoupling state feedback control on the reduced-order model forms the first layer. To limit transient response to the linearly elastic range and reduce detrimental effects of foreseeable uncertainties, the second layer is an uncertainty model under robust control. The third and final layer is a model-independent controller network using market-based control to mitigate unforeseeable uncertainties. The first two layers are based on state space control formulations that effectively control the design models and reduce the computational requirement of the third layer. The control effects and evaluation criteria would be based on seismic control benchmark problem.

Active control is applied to moment-resisting frames to study the energy flows among various forms, while force analogy method is used to characterize the inelastic behavior of the structure. Since force analogy method uses initial stiffness in the dynamic equilibrium equation, it can easily be represented in state space form. Hence the incorporation of active control in the inelastic dynamic analysis becomes very simple. Energy balance is then performed to study the flow of different energy forms in the actively controlled structure, and plastic energy dissipation in the structure is evaluated.

Concrete filled tube (CFT) columns combine steel and concrete in one member, which results in a member that has the beneficial qualities of both materials. A developed monotonic stress-strain relation for confined concrete is modified for the analysis of steel tube walled section columns. The influence of steel tube on the lateral response of CFT columns is studied based on the fiber analysis method; particularly, the enhancement of the ultimate compressive strain of concrete, the increase in curvature ductility capacity based on moment-curvature relationship and yield load-displacement are investigated. Inelastic dynamic analyses of CFT columns using two ground motions recorded are conducted to evaluate the seismic performance of CFT columns. The results indicate that using CFT columns provides adequate protection against the damage potential of the ground motions and shows the enhancement of seismic capacity of structures.

This paper is concerned with the earthquake behaviour of reinfoced concrete tanks. It is well known that due to better earthquake-resistant characteristics, reinforced and prestressed concrete tanks have been increasingly used over the last 40 years to store liquids such as petroleum products. The size of these tanks has since been increasing. At the same time, the requirements regarding serviceability conditions, especially environmental conditions, became more and more demanding. Therefore, the earthquake behaviour as well as the earthquake-proof design of prestressed concrete tanks of large capacities is of great interest. Responding to these necessities and taking into account the special kind of dynamic response of the tank filled with liquid, a research program involving theoretical and experimental analyses was carried out. The study includes the use of base-isolating systems.

Pounding of adjacent buildings or parts of buildings due to earthquake shaking is often implicated as a significant source of damage. The majority of theoretical studies of pounding have focused on determination of the minimum separation required to prevent pounding. While this is useful for design of new structures, a great many existing structures are not sufficiently separated to preclude pounding. For these existing structures it is clearly useful to have a measure of the expected level of damage that may occur in future earthquakes. This paper attempts to assess the effects of pounding from measured earthquake records. The concept of Maximum Impact Velocity Spectrum (MIV) is introduced. The MIV records the envelope of the maximum impact velocity obtained during the earthquake for all separation distances as a function of the structure's natural period. Several measured earthquake records are considered and some surprising results are obtained.

This paper describes the development of a web-based system for seismic performance evaluation and preliminary design of inelastic structures. The core of system includes a simple yet accurate performance-based earthquake engineering procedure based on the Capacity-Spectrum Method. The present system allows authenticated users to carry out seismic performance evaluation, preliminary design for inelastic, bridge column as well as searching previous data and results from their offices or directly from the field. Accuracy of the procedure is verified by comparing with published data. The architecture and functions of system are given. Example of the present system is presented.

This paper first explores the reason, which causes the failure of convergence and divergence problem by ATC-40 procedure A, and then proposes a modified capacity-spectrum procedure, which overcomes the deficiency. The reliability of the proposed procedure is demonstrated through one numerical example. Application of such a procedure to evaluate seismic performance is finally addressed.

The base isolated system takes advantage of enhancing the earthquake-proof performance of the structure by means of reductions of input seismic motions. In order to perform reliable evaluation of the response of structures under dynamic loads such as earthquakes, it is necessary to examine their nonlinear response characteristics. In this study, the uncertain parameter effects on the base isolated system related to the nonlinear dynamic response are examined with Monte Carlo Simulation. It is suggested that the uncertain parameters provide significant roles on the maximum responses evaluations of the base-isolated system.

Earthquake response of the elevated liquid storage tanks isolated by the elastomeric bearings is investigated under real earthquake ground motion. The tanks are isolated by implanting the isolation bearings at base of the tower structure. The isolation bearings considered are laminated rubber bearings with and without lead core. The force-deformation behaviour of the bearing without lead core is considered as linear while with lead core is represented by non-linear behaviour. The continuous tank liquid is modelled as lumped mass, which is referred as sloshing mass, impulsive mass and rigid mass. The corresponding properties such as stiffness and damping are evaluated using single-degree-of-freedom concept. For detailed investigation two types of the tanks are considered, namely slender and broad tanks. Furthermore, the response of isolated tanks is compared with corresponding non-isolated tanks, in order to measure the effectiveness of the isolation systems. In addition, the comparative study of performance of the two types of isolation systems revealed that non-linear elastomeric bearings are more effective in reducing the response of the elevated tank.

For the reliable design of structures subjected to severe seismic forces, it is very important to understand the nonlinear dynamic response characteristics. In this study, nonlinear seismic responses analyses for framed structures with soil-structure interaction, which can be represented with multi-degrees-of-freedom (MDOF) system, are carried out. It is suggested that since the nonlinear responses gives significant effects on the seismic response evaluations, it is important to perform more reasonable evaluations of the seismic responses for the total structure system.

Impact response of structures supported on the sliding systems to real earthquake ground motion is investigated. The base-isolated structure is modeled as shear building and adjacent structure as a spring-dashpot (impact) element. The seismic response is obtained by deriving differential equations of motion of the structure with sliding system and solved using Newmark's step-by-step integration technique in iterations. It is found that performance of sliding systems is hampered with impact. Investigations are carried out to find out the effect of parameters of adjacent structure such as stiffness and gap distance on response of base-isolated structure under consideration. Adversity of impact increases with rising stiffness of adjacent structure and is found quite predominant parameter. Damping in adjacent structure mainly shows influence on bearing displacements which reduce marginally with increased damping. Impact response is obtained under varied flexibility of building for different sliding systems to study the performance during impact. It is observed that with increased flexibility, the superstructure acceleration increases. Also, the superstructure accelerations increase with increments in gap distance up to a certain value and for further widening in gap distance, declining trend is observed. For the changes in base mass to floor mass ratio the responses shows meager deviation. It is concluded that superstructure accelerations increases due to the occurrence of impact in base-isolated structures, ultimately resulting into reduction in efficiency of sliding isolation systems.

A computer test-bed is being established for the first-principle simulation of multi-scale structural failure under b last loads. Since t he structural failure due to explosion involves plasticity, damage, localization, thermal softening, phase transition and fragmentation, accurate constitutive models are not yet available for building materials. Also, a robust spatial discretization method is a necessity for large-scale simulation of the transition from continuous to discontinuous failure modes without invoking a fixed mesh connectivity. In this paper, the transition from continuous to discontinuous failure modes in brittle solids is identified through the bifurcation analysis of the acoustic tensor governing rate-dependent damage. A discrete constitutive model is then used to predict material failure as a decohesion or separation of continuum. To accommodate the multi-scale discontinuities involved in structural failure, the Material Point Method is developed to be a robust spatial discretization tool for the computer test-bed. As a result, the model parameters can be calibrated based on experimental data available, and routine simulation can be performed with limited computational resources. Sample problems are considered to illustrate the potential of the proposed simple procedure.

In this paper, a mechanism-based strain gradient dependent constitutive equation for two-phase particle reinforced metal matrix composites is presented. By using this strain gradient dependent constitutive equation and the linear perturbation analysis, the effect of strain gradient on adiabatic shear banding in particle reinforced metal matrix composites is investigated. The results have demonstrated that the onset of adiabatic shear banding in the composite with small particles is more prone to occur than in the composite with large particles. This result also means that high strain gradient is a strong driving force for adiabatic shear banding in metal matrix composites.

Several modifications on conventional SHPB experimentation were adopted to investigate effects of strain rate on mechanical behaviors of foam materials in this paper. Quasi-static and dynamic stress-strain curves of rigid fiber-polyurethane foams, aluminum foams and aluminum alloy foams were investigated. All experimental results indicated that strain rate effect on foam materials were obvious, although the matrixes, some of which were strain-rate sensitive and some were not, cell sizes and densities are all different.

This paper presents a computational approach for composite materials subjected to ballistic impact. The composite materials are composed of layers of fabric embedded in a matrix material. The fabric is represented by bar elements and the matrix material is represented by solid elements. The geometric characteristics of these composite materials are three dimensional, which in turn requires a three dimensional analysis. The strength and failure characteristics of the fabric are determined directly from the actual fiber characteristics. For the matrix material it is necessary to modify the solid elements, because much of the volume of the solid elements is occupied by the volume of the fabric. The resulting modifications include the determination of effective density, stiffness, strength and failure characteristics for the solid elements. This approach has been shown to provide good agreement with experimental ballistics data. Because this approach treats each of the component materials individually (instead of blending them into a homogeneous anisotropic material), it is possible to examine the effects of individual material properties for both the fabric and the matrix material. This includes the capability to allow for failure of the fabric material and/or the matrix material. Parametric computational results are included to illustrate some of these effects.

Dynamic compressive mechanical behaviors of an S-2/SC15 glass/epoxy composite along two perpendicular directions have been determined with a pulse-shaped split Hopkinson pressure bar (SHPB). The composite specimen deforms at a nearly constant strain rate under dynamically equilibrated stress during SHPB tests. The compressive stress-strain responses along both directions were found to be strain-rate sensitive, but with different rate sensitivities.

In order to reveal the underlying mechanism governing the failure of solids subjected to impact loading, this paper presents a closed trans-scale formulation and numerical simulation of damage evolution to macroscopic failure, in particular to spallation. The trans-scale formulation consists of equations of continuum, momentum, and microdamage evolution, in which there are several time scales and length scales on meso- and macroscopic levels. With this formulation, numerical simulation on spallation is performed. The effects of several predominate dimensionless parameters, such as imposed and intrinsic Deborah numbers, on spallation are discussed.

The impact behavior of cement mortar, a heterogeneous material with damage, were experimentally studied under three different stress states: (1) one-dimensional-stress state by using the SHPB technique, (2) one-dimensional strain state at high pressures from 1 to 5 GPa by using an one stage gas gun and (3) quasi one-dimensional strain state by using an improved passive confining SHPB technique. The experimental results show that cement mortar is a kind of nonlinear rate-dependent material with internal damage evolution, and the confining pressure greatly influence its ductility and strength. The main results are given and discussed.

Dislocation density based multiple-slip constitutive formulations and specialized computational schemes are introduced to account for large-strain ductile deformation modes in polycrystalline aggregates. Furthermore, new kinematically based interfacial grain boundary regions and formulations are introduced to account for dislocation density transmission, absorption, and pile-ups that may occur due to grain boundary misorientations and properties.

The shock response of layered material systems is quite different from that of monolithic systems. Scattering inherent at the interfaces of heterogeneous materials is shown to play an important role in determining the structure of the wave profiles in layered systems. Experimental results of plate impact tests on periodic layered composites have shown an oscillatory response in the pulse duration phase of the stress wave profile. In this paper, multiple scattering at the heterogeneous interfaces is shown to explain this behavior very well. Combined with our earlier result that scattering can also be used to explain the sloping rise characteristics of the wave profile, it is concluded that scattering plays a very critical role in determining the entire structure of the shock profile. It is further shown that material heterogeneity, e.g., impedance mismatch, interface density, and thickness ratio affect the scattering processes and hence the structure of the stress wave profiles in a profound manner.

The investigation reported here is both experimental and numerical in nature. The experimental effort is to use “Thick Backing Technique” to evaluate the response of a two-layer target of ceramic facing and aluminum backing plate with a projectile. The objective of the first set of experiments is to determine the minimum thickness of ceramic facing required to defeat an armor-piercing projectile, APM2, without any damage to the aluminum. The second set of experiments is to impact targets with the determined minimum thickness of ceramic facing attached to the aluminum backing with different thickness. In so doing, the effect of thickness of backing material on the effectiveness of the ceramic on defeating the projectile is evaluated. In addition the experimental results might shed some light on what mechanical properties are required to defeat the projectile. An attempt is made to simulate these experiments using the computer code, EPIC. Comparison between the simulation and experimental results provides a basis for improving the material models used in the simulations, and also provide guidance for selecting an appropriate backing configuration to achieve the goal of minimizing the weight in defeating the projectile.

In this investigation, the minimum size of the representative volume element (RVE) of a heterogeneous material is determined experimentally using the digital image correlation (DIC) technique. The uniaxial compression experiment was conducted on the PBS 9501, a high explosive simulant material. The minimum size of the representative volume element (RVE) of the PBS 9501 heterogeneous material, where the average crystal diameter of the material is around 100μm, was determined experimentally to be 1.5mm. This result is consistent with those numerical calculations on polycrystalline materials and some other composites.

A 3-D discrete element model with connective type was presented in this paper. Accordingly, a 3-D discrete element method code, which can calculate the transitional process from connective model (for continuum) to contact model (for non-continuum), was developed. The wave propagation in a 3-D concrete block under impact loading was numerically simulated, by using this code. Comparing its numerical results with those by LS-DYNA, the accuracy of this algorithm was presented. Moreover, the failure process of the concrete block under impact loading was demonstrated, which presented the basic dynamic transitional process from continuum to non-continuum. The two numerical examples prove that the new model and its code are powerful and efficient for simulating the dynamic failure problems accompanying with the transition from continuum to non-continuum. It also shows that the discrete element method will have widespread availability and perfect development prospect.

A new three-dimensional two-phase model on meso-scales for fluid-saturated porous media is proposed. Based on this model, a three-dimensional fluid-solid mixture explicit dynamic finite element scheme is developed by adopting direct coupling technique. Using Galerkin residual method and considering the coupling effects on the fluid-solid interface, the model is discrete into solid elements, fluid elements and fluid-solid coupling elements. Moreover, three-dimensional wave propagation in the fluid-saturated porous media is numerically calculated and the propagation characteristic of main waves is discussed.

An analytical model to predict penetration of rigid projectiles into concrete targets is put forward in this paper. By assuming the resistant forces of the penetration mainly come from pressure actions behind shock waves that caused by the impact, penetration velocity can be expressed in form of material Hugoniot parameters and penetration time. The penetration will terminate when the impact pressure is less than yield strength of the target material, which gives whole duration of the penetration. Integration of the penetration velocities on the duration results in final depth of the penetration. Some experimental data are used to verify the model, and agreement between experimental data and model calculations means that the model gives a valid prediction for the penetration of thick concrete targets by rigid projectiles.

In present paper, experimental study of influence of cell size on unloading modulus, flow stress and deformation mode was carried out. Open-cell Aluminum foams and closed-cell aluminum alloy foams were compressed under split Hopkinson pressure bar (SHPB) on five controlling strain levels respectively. On each strain level it containes open-cell aluminum foam with four cell sizes.

Mechanism of mechanical properties were also discussed by metallographic observation. We can draw a conclusion that cell size has an un-neglectable effect on flow stress and densification of foams. Open cell al foam and closed-cell al alloy foam exhibit different deformation mode.

The widespread use of modeling and simulation for design of armor systems is critically dependent on the accuracy of the underlying structure of such simulations. Acceptance of these tools hinges upon end user trust in the predicted results. As the overall implementation of a design code can be composed of a number of material models, it is essential that those models accurately reflect true physical behavior. Computations are performed using the Johnson-Holmquist (JH) constitutive model for brittle materials for penetration problems into ceramics, as implemented in both the Eulerian CTH and the Lagrangian EPIC shock physics codes. The results of the computations are compared and the influence of the numerics and material model coupling are evaluated. A description of some important computational features involving finite elements and meshless particles are also outlined, with observations on the direction of future code and model development.

In the present paper asymptotic techniques are employed to analyze propagation of acceleration waves in 2-D layered material systems. The analysis makes use of the Laplace transform and Floquet theory for ODE's with periodic coefficients. Both wave-front and late-time solutions for step-pulse loading on layered half-space are presented. Wave propagation in 2-D elastic-elastic and elastic-viscoelastic bilaminates is analyzed to elucidate the effects of layer thickness, impedance mismatch and material inelasticity on elastic precursor decay and late-time dispersion.

In the present paper plate impact experiments are conducted to understand precursor decay and the late-time dispersion in 2-D layered heterogeneous material systems. The layered specimens are impacted by a hard elastic flyer plate using an 82.5 mm single-stage gas-gun facility at CWRU. The free-surface particle velocity at the rear of the target plate is measured by VALYN VISAR and compared with predictions of an analytical solution for wave propagation in a semi-infinite periodically layered material geometry.

The coupled nonlinear dynamic analyses of a Mini Tension Leg Platform (Mini TLP) using Morison wave force model as well as diffraction effects combined with Morison wave forces are presented. The computed motion as well as dynamic tether tension response amplitude operators (RAOs) are validated by tests conducted on a 1:56 scaled model tethered in a wave flume. The experimental results find good match with the diffraction model, though the structure consists mainly of small diameter members. The results clearly illustrate the inadequacy of numerical models which ignore the diffraction effects in predicting the response behaviour of structures consisting of both slender and large-diameter members.

Author Index