International Journal of Structural Stability and Dynamics

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the edge-based smoothing cells. The transverse shear strains within the Reissner–Mindlin quadrilateral element are obtained using the edge-consistent interpolation approach. At the beginning, the performance of the present numerical technique is examined for the buckling analysis of trapezoidal panels under in-plane compressive or shear stresses. Thereafter, new results on the buckling and postbuckling behaviors of trapezoidal composite plates are presented, for which comparable numerical results are rare in the literature. Representative numerical results are presented to highlight the interaction between the higher pre-buckling stresses and increased stiffness near the shorter edge with fiber orientation and loading direction on the buckling resistance of trapezoidal panels.

This paper investigates the nonlinear instability of eccentrically stiffened functionally graded (ES-FG) sandwich truncated conical shells subjected to the axial compressive load. The core of the FG sandwich truncated conical shells, assumed to be thin, is made of pure metal or ceramic materials and the two skin layers are made of a FG material. The shell reinforced by orthogonal stiffeners (stringers) is also made of FG materials. The change of spacing between the stringers in the meridional direction is considered. The governing equations are derived using the Donnell shell theory with von Karman geometrical nonlinearity along with the smeared technique for stiffeners. The resulting coupled set of three nonlinear partial differential equations with variable coefficients in terms of displacement components are solved by the Galerkin’s method. The closed-form expressions for determining the critical buckling load and for analyzing the postbucking load–deflection curves are obtained. The accuracy of present formulation is verified by comparing the results obtained with available ones in the literature. The effects of various parameters such stiffeners, foundations, material properties, geometric dimensions on the stability of the shells are studied in detail.

An analytical mechanics approach to derive equations of motion from vector kinematic description of rigid bar assemblies is developed. It is shown that various holonomic constraints governing multibody mechanical systems can be modeled using vector kinematics without using trigonometric/transcendental functions. The principle of virtual work is utilized to derive a map between the generalized coordinates associated with the vector approach and the angular velocity vector associated with the rigid bars. The utility of the vector approach is demonstrated by deriving the dynamics of tensegrity systems and a carpal wrist joint.

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

A mathematical model using the fiber approach is presented in this paper for quantifying the strength and fire-resistance of eccentrically loaded slender concrete-filled steel tubular (CFST) columns with rectangular sections incorporating the interaction of local and global buckling. The model utilizes the thermal simulator to ascertain the temperature distribution in cross-sections, and the nonlinear global buckling analysis to predict the interaction responses of local and global buckling of loaded CFST slender columns to fire effects. The initial geometric imperfection, air gap between the concrete and steel tube, tensile concrete strength, deformations caused by preloads, and temperature-dependent material behavior are included in the formulation. The computational theory, modeling procedure and numerical solution algorithms are described. The computational model is verified by existing experimental and numerical results. The structural responses and fire-resistance of CFST columns of rectangular sections exposed to fire are investigated. The mathematical model proposed is demonstrated to be an efficient computer simulator for the fire-performance of slender CFST columns loaded eccentrically.

Transverse collaborative working performance (TCWP) is of great importantce to assembled beam bridges’ safety and serviceability, which can be charaterzied by the ability of transvese connections (hinge joints) to transfer force. This paper proposes a multi-beam model connected by distributed springs for assembled beam bridges’ modal characteristic analysis. Both the strain and displacement modal shape (surface) of this multi-beam model can be expressed as a product of longitudinal base function and transverse proportional coefficient vector, which can be obtained explicitly by solving a matrix eigenvalue problem. The transverse proportional coefficient vectors in the solutions can be seen as transverse modal shapes in a cross-section. Then, two types of monitoring indexes (baseline-free and baseline-required) based on transverse modal shapes for hinge joint damage detection and TCWP monitoring are constructed. The applicability of indexes proposed is proved by numerical simulations in different damage cases and index analysis in consideration of modal noise or not.

This study is concerned with design of a tuneable vibration absorber by using an inertial actuator (IA) with its proof-mass acceleration used as feedback signal. Acceleration feedback control loop can produce virtual mass effect, and the natural frequency of the IA can be shifted. The main advantage of the proposed IA-based tuneable vibration absorber is that the control loop is very simple and does not require any low-pass filter or integrator. Finally, the experimental results are presented to verify the tuning capability and control performance of the proposed vibration absorber.

Based on the modified couple stress theory, an attempt is made in this study to analyze the nonlinear snap-through instability of shallow sandwich arches. The microstructure-dependent functionally graded material (FGM) arch with surface bonded piezoelectric actuator layers is analyzed. The piezo-FGM sandwich arch is subjected to uniform transverse pressure load in thermo-electrical environment. All material properties of the FGM micro arch are assumed to be temperature- and position-dependent. The governing equilibrium equations of the piezo-FGM sandwich arch are established with the aid of virtual displacement principle and the uncoupled thermoelacticity theory. The obtained governing differential equations are based on the first-order shear deformation shallow arch theory of the Timoshenko and von Kármán nonlinear assumptions. These equilibrium equations contain three coupled ordinary differential equations in terms of displacements. The nondimensional governing equations are solved for the cases of piezo-FGM sandwich arches with simply supported and clamped boundary conditions by using the two-step perturbation technique. Analytical closed-form solutions are derived to give the deflected shape of the piezo-FGM sandwich arch with immovable ends. Comparison is made with the existing results for the cases of FGM arch without couple stress and piezoelectric layers, where good agreement is obtained. The nonlinear behavior of the sandwich arches is highly affected by the couple stress, piezoelectric layers, temperature change, volume fraction index, and geometrical properties of the arch.

The present study aims to analyze the buckling and post-buckling behavior of the geometrically imperfect functionally graded pin-ended tube. Imperfect FGM tube is surrounded by nonlinear elastic medium and is subjected to the axial compression or various thermal loads. Pinned-pinned boundary conditions are movable or immovable for the FGM tube under axial compression or thermal loads, respectively. In thermal analysis, different types of thermal loads such as uniform temperature rise, linear temperature distribution, and heat conduction are analyzed and contrasted. Displacement field of the FGM tube satisfies the tangential traction-free boundary conditions on the inner and outer surfaces. Properties of the FGM tube are assumed to be temperature-dependent and are distributed through the radial direction of tube using a power law function. The governing equilibrium equations of the FGM tube are obtained by means of the virtual displacement principle. These are nonlinear coupled differential equations based on a higher order shear deformation tube theory and the von Kármán nonlinear assumption. The coupled nonlinear dimensionless differential equations are solved using the two-step perturbation method. These asymptotic solutions are as explicit functions of the axial compression or different types of thermal load. Numerical results are provided to explore the effects of the linear and nonlinear spring stiffness of elastic medium and imperfection parameter of the tube. The effects of the volume fraction index and two geometrical parameters of the FGM tube are also included.

This paper developed an analytical model for a piezoelectric energy harvester (PEH) composed of a piezoelectric bimorph and a stopper as shown in Fig. 1, which was subjected to a harmonic excitation. Frequency-up-conversion, which has proved to improve the energy harvesting efficiency, was achieved due to the mechanical impact between the piezoelectric bimorph and the stopper. The piezoelectric bimorph was modeled as Euler–Bernoulli beam. A bi-modal approach was adopted to animate the beam stopper reaction. When the tip of the bimorph is free for motion, a cantilever beam function is adopted, while the tip encounters a stop, a clamped-pinned beam function is used to model the bimorph. The periodic solutions and their corresponding output voltage and power were obtained. With the same initial conditions and base excitations, the output energies of transient vibrations are compared for two cases: (1) without impact between the piezoelectric beam and the stopper; (2) with impact by reducing the gap distance between the piezoelectric beam and the stopper. With the purpose of maximizing the output power, from the steady-state analytical solutions, we studied the optimum gap between the piezoelectric beam and the stopper when the base excitations are fixed and initial conditions are set to zero.

Reinforced concrete (RC) beams under the impact loading are typically prone to suffer shear failure in the local response phase. In order to enhance the understanding of the mechanical behavior of the RC beams, their dynamic response and shear demand are numerically investigated in this paper. A 3D finite-element model is developed and validated against the experimental data available in the literature. Taking advantage of the above calibrated numerical model, an intensive parametric study is performed to identify the effect of different factors including the impact velocity, impact mass and beam span-to-depth ratio on the impact response of the RC beams. It is found that, due to the inertial effect, a linear relationship exists between the maximum reverse support force and the peak impact force, while negative bending moments also appear in the shear span. In addition, the local response of the RC beams can be divided into a first impact stage and a separation stage. A shear plug is likely to be formed near the impact point at the first impact stage and a shear failure may be triggered near the support by large support forces. Based on the simulation results, simplified methods are proposed for predicting the shear demand for the two failure modes, whereas physical models are also established to illustrate the resistance mechanism of the RC beams at the peak impact force. By comparing with the results of the parametric study, it is concluded that the shear demand of the RC beams under the impact loading can be predicted by the proposed empirical formulas with reasonable accuracy.

Severe vibrations may occur on slender structures like footbridges and cantilever stands due to human-induced loads such as walking, jumping or bouncing. Currently, to develop a load model for structural design, the main features, such as periodicity and stationarity of experimental load records, are artificially extracted and then mathematically modeled. Different physical features have been included in different load models, i.e. no unified load model exists for different individual activities. The recently emerged generative adversarial networks can be used to model high-dimensional random variables. The probability distribution of these variables learned from real samples can be used to generate new samples, avoiding extracting features artificially. In this paper, a new model is proposed which combines the conditional generative adversarial networks and Wasserstein generative adversarial networks with gradient penalty to generate individual walking, jumping and bouncing loads. The generator of the model has five fully connected layers and a one-dimensional convolutional layer, and the discriminator has five fully connected layers. After one million training steps using the experimental records, the generator can generate high-quality samples similar to real samples in waveform. Finally, by comparing the power spectral densities and single degree of freedom system’s responses of the generated samples with real samples, it is further proved that the proposed generative adversarial network model can be used to simulate various human-induced loads. Source code of the model along with its trained weights is provided to the readers to further analysis and application.

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

There exist various potential energy formulations dealing with the linear buckling and second-order nonlinear analysis of framed structures with different degrees of refinement in the kinematic model. However, the geometric stiffnesses derived often give rise to different structural behaviors, which indeed represents a confusion regarding their qualified usage in bifurcation and post-buckling analysis. This study aims to carry out a comprehensive evaluation of the validity of the geometric stiffness for use at the predictor and corrector phrases of an incremental analysis based on the rigid-body motion test. To remove the unbalanced element forces caused by the nonqualified geometric stiffness, a supplementary correction matrix is developed according to simple kinematic and static analysis in the context of rigid rotations. An updated Lagrangian approach-based force recovery procedure (FRP) is presented for updating the element forces with improved reliability and efficiency, when using relatively large step size. Some benchmark problems which exhibit compound three-dimensional nonlinear behavior of framed structures are solved to clarify the capabilities of rigid-body qualified and nonqualified geometric stiffnesses along with the existing FRPs for different mesh sizes, step sizes and load patterns. It is shown that the proposed procedure can be adopted to predict correct buckling loads and post-buckling equilibrium paths without adding extra computational costs.

Low-frequency harvesters are attractive due to their availability in the ambient environment. The paper presents the design, analysis and optimization of the magnetic levitation harvester. A new nonlinear model of the electromechanical coupling, depending on the magnet position versus coil is proposed. Additionally, the influence of magnetic suspension (stiffness), load resistance and magnet-coil configuration on the foldover effect is shown.

This paper presents an improved generalized procedure for dealing with the stability of thin-walled beams under combined symmetric loads based on the energy method. The differential equations for the case of complex loading conditions were developed using an axis transformation matrix. The work caused by external loads was related to the work of internal forces to simplify the computational procedure. The thin-walled beam subjected to axial force $F$, bending moment $M$ at both ends, and concentrated load $P$ at midspan was studied. The case of a concentrated load $P$ replaced by a distributed load $q$ over partial beam length was also examined. The stability region boundary of the beam was derived by two approaches: one was to estimate an approximate angle of twist prior to determination of the deflection and the other was to do it in the reverse way. Numerical results reveal that the first approach yields less error than the second; however, the outcome obtained by the former was more cumbersome than the latter. Above all, both approaches provided feasible results and are useful for further applications dealing with the stability analysis of thin-walled beams.