International Journal of Structural Stability and Dynamics

This paper is concerned with the vibration problem of initially stressed micro/nano-beams. The vibration problem is formulated on the basis of Eringen's nonlocal elasticity theory and the Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of initial stress, transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. These equations are solved analytically for the vibration frequencies of micro/nano-beams with different initial stress values and boundary conditions. The effect of the initial stress on the fundamental frequency and vibration mode shape of the beam is investigated. The solutions obtained provide a better representation of the vibration behavior of initially stressed micro/nano-beams which are stubby and short, since the effects of small scale, transverse shear deformation and rotary inertia are significant and cannot be neglected.

This paper presents a two-node catenary cable element for the analysis of three-dimensional cable-supported structures. The stiffness matrix of the catenary cable element was derived as the inverse of the flexibility matrix, with allowances for selfweight and pretension effects. The element was then included, along with the beam and truss elements, in a geometric nonlinear analysis program, for which the procedure for computing the stiffness matrix and for performing iterations was clearly outlined. With the present element, each cable with no internal joints can be modeled by a single element, even for cables with large sags, as encountered in cable nets, suspension bridges and long-span cable-stayed bridges. The solutions obtained for all the examples are in good agreement with the existing ones, which indicates the accuracy and applicability of the element presented.

In the present study, a nonlinear finite element formulation is developed for analysis of axially moving two-dimensional materials, based on the classical thin plate theory. Using Green's strain definition, the membrane stresses variation due to transverse displacements is considered. Hamilton's principle is employed to obtain the secant stiffness matrix, the in-plane and out-of-plane gyroscopic matrices and the dynamic stability matrix due to centripetal acceleration for a traveling thin plate. In order to extract the numerical results, a p-version finite element is adopted by selecting only an quadrilateral super element with Lagrangian interpolation functions. With a few test cases, the reliability of the formulation and the solution procedure is shown.

Developed herein are the scaling laws for physical modeling of anti-symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration experiments. In the absence of experimental data, the validity of the scaling laws is verified by numerical experiments. This is accomplished by calculating theoretically the buckling loads and fundamental frequencies of the model and substituting into the scaling laws to obtain the corresponding values of the prototype. The predicted values of the prototype from the scaling laws are then compared with existing closed-form solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and length-to-radius ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the need for costly experiments. In reality, either due to the complexity of the scaling laws or to economize experimental cost and time, it may not be feasible to construct the model to fulfil the scaling laws completely. Thus, several possible models of partial similitude are investigated numerically. These include models with distortion in laminated material properties, stacking sequences and number of plies. Model with distortion in material properties yields a high percentage of discrepancy and is not recommended.

Buckling and postbuckling behaviors of multi-walled carbon nanotubes (MWCNTs) under a compressive force are studied. MWCNTs are modeled by Donnell's shallow shell nonlinear theory with the allowance of van der Waals (vdW) interaction between the walls. It is shown herein that the buckling load decreases while the buckling strain increases as the innermost radius of MWCNT increases. For the postbuckling behavior, the shortening-load curves show an initial steep gradient that gradually level up when the radius of the innermost tube changes from a small value to a large value. However, the deflection-load curves are almost level for various radii of MWCNTs. In addition, the analytical results showed that the shortening-load curves are almost linear but the deflection-load curves are nonlinear and the stability of MWCNTs can be enhanced by adding tubes.

The modeling, updating and validation of a structural health monitoring oriented finite element model (FEM) of the Tsing Ma suspension bridge towers are presented in this paper. The portal-type bridge tower is composed of two hollow reinforced concrete legs and four deep pre-stressed cross-beams with a steel truss cast in the concrete of each cross-beam to form a narrow corridor for access between two legs. Except that steel trusses are modeled by beam elements, all structural components are modeled by solid elements to facilitate local damage detection, in particular at member joints. The established tower model is then updated using sensitivity-based model updating method taking the natural frequencies identified from field measurement data as reference. Furthermore, a two-level validation criterion is proposed and implemented to examine the replication performance of the updated finite element model of the bridge tower in terms of (1) natural frequencies in higher modes of vibration and (2) dynamic characteristics of the tower-cable system. The validation results show that a good replication of dynamic characteristics is achieved by the updated tower model when compared to the field measurement results. Finally, stress distribution and concentration of the bridge tower are investigated through nonlinear static analysis of the tower-cable system.

The purpose of this paper is to compare the design equation of Allowable Stress Design (ASD) with that of Load and Resistance Factor Design (LRFD) concerning the member stability for the economic design of cable-stayed bridges. Both elastic and inelastic buckling analyses are carried out for the cable-stayed bridges with the effective buckling lengths of the key members calculated. The axial-flexural interaction equations prescribed in ASD and LRFD are used to check the stability of main members in cable-stayed bridges. Parametric studies are performed for the bridges with a center span of 300, 600, 900, and 1200 m of different girder depths. Peak values of the interaction equations are calculated at the intersection between the girder and towers. Since the peak values of the interaction equations by inelastic buckling analysis are less than those by elastic buckling analysis, a more economical design of the girder and towers can be achieved using the inelastic buckling analysis. In addition, the use of LRFD specifications can result in a more economical design by about 20% on average than the ASD specifications for steel cable-stayed bridges.

This paper presents the dynamic infinite element formulations that have been developed for soil-structure interaction analysis both in frequency domain and time domain by the present authors and our colleagues during the past 20 years. Axisymmetric, 2D and 3D layered half-space soil media were considered in the developments. The displacement shape functions of the infinite elements were established using approximate expressions of analytical solutions in frequency domain to represent the characteristics of multiple waves propagating into the unbounded outer domain of the media. The shape functions were determined in terms of the excitation frequency as well as the spatial and material characteristics of the far-field soil region. Thereby the element mass and stiffness matrices are frequency dependent. As for time domain analysis, the shape functions were further simplified to obtain closed-form frequency-dependent mass and stiffness matrices, which can analytically be transformed into time domain terms by the Fourier transform. The proposed infinite elements were verified using benchmark examples, which showed that the present formulations are very effective for the soil-structure interaction analysis either in frequency or in time domain. Example applications to actual soil-structure interaction problems are also given to demonstrate the capability and versatility of the present methodology.

This technical note presents the parametric identification of multi-degree-of-freedom nonlinear dynamic systems in the time domain using a combination of Levenberg–Marquardt (LM) method and Genetic Algorithm (GA). Here the crucial initial values to the LM algorithm are supplied by GA with a small population size. Two nonlinear systems are studied, the complex one having two nonlinear spring-damper pairs. The springs have cubic nonlinearity (Duffing oscillator) and dampers have quadratic nonlinearity. The effects of noise in the acceleration measurements and sensitivity analysis are also studied. The performance of combined GA and LM method is compared with pure LM and pure GA in terms of solution time, accuracy and number of iterations, and convergence and great improvement is observed. This method is found to be suitable for the identification of complex nonlinear systems, where the repeated solution of the numerically difficult equations over many generations requires enormous computational effort.