Energy method solution for the postbuckling response of an axially loaded bilaterally constrained beam

Bistable and multistable structures have shown great usefulness in many applications such as MEMS actuation and energy harvesting. Bistability of structures can be achieved through buckling. Confining a buckled beam between two lateral constraints allows it to buckle into higher modes as the axial load increases. This paper presents a theoretical study of the postbuckling response of a bilaterally constrained elastica subjected to gradually increased axial load. Equilibrium states are determined using an energy method. Under small deformation assumptions, the total potential energy is minimized under the defined constraints. The presented model allows for an accurate representation of the flatting behavior and the increase in the length of contact areas with the lateral constraints before the sudden snapping between equilibrium states. Mode transitions are manifested by jumps in the response curves. Previously developed models based on geometry and symmetries overestimate the required forces for higher equilibrium modes and do not match experimental observations. Results are validated with experimental force–displacement measurements under both force- and displacement-control. The kinetic energy released during buckling mode transitions is determined by a dynamic analysis.     

Postbuckling and mode jumping analysis of composite laminates using an asymptotically correct, geometrically non-linear theory

An analytic method is presented in this paper to study the postbuckling and mode jumping behavior of bi-axially compressed composite laminates. The governing partial differential equations (PDEs) are derived rigorously from an asymptotically correct, geometrically non-linear theory. A novel and relatively simpler solution approach is developed to solve the two coupled fourth-order PDEs, namely, the compatibility equation and the dynamic governing equation. The generalized Galerkin method is used to solve boundary value problems corresponding to antisymmetric angle-ply and cross-ply composite plates, respectively. The variety of possible modal interactions is expressed in an explicit and concise form by transforming the coupled non-linear governing equations into a system of non-linear ordinary differential equations (ODEs).

The comparison between the present method and the finite element analysis (FEA) shows a pretty good match in their numerical results in the primary postbuckling region. While the FEA may lose its convergence when solution comes close to the secondary bifurcation point, the analytic approach has the capability of exploring deeply into the post-secondary buckling realm and capture the mode jumping phenomenon for various combinations of plate configurations and in-plane boundary conditions. Free vibration along the stable primary postbuckling and the jumped equilibrium paths are also studied.     

Postbuckling analysis of columns resting on an elastic foundation

The postbuckling response of perfect and geometrically imperfect elastic columns resting on an elastic Winkler type foundation is thoroughly discussed. This is established by employing an approximate analytic technique leading to very reliable results in the vicinity of the critical state. It was found that the critical state of perfect columns is a stable symmetric bifurcation point and consequently there is no sensitivity to initial geometrical imperfections. Moreover, a simple but readily analyzed mechanical model is proposed to simulate the salient features of buckling mechanism of the column on elastic foundation with those of the model. The simplicity, reliability and efficiency of the proposed analysis as well as the successful modeling of the buckling mechanism of the column by that of a single mode mechanical model are illustrated with the aid of numerical examples.     

轴对称压—弯下圆板中圆脱层的后屈曲扩展

本文分析了周边承受轴对称压一弯载荷的圆板中薄圆脱层的后屈曲扩展.运用基于四阶龙格-库塔积分公式的打靶法得到无量纲形式Von Karman非线性方程组的单参数解族.利用与路径无关的M积分导出能量释放率表达式并给出相应的数值解.文中还探讨了分叉、跳跃及扩展的可能性.     

Influence of corner stresses on the stability characteristics of composite skew plates

Stability characteristics of composite skew plates subjected to in-plane compressive load are investigated here using the shear deformable finite element approach. The influences of high prebuckling stresses at the corner regions of isotropic and composite skew plates on their stability characteristics are emphasized for different load direction, boundary condition and laminate stacking sequence. The non-linear governing equations based on von Kármán's assumptions are solved by Newton-Raphson technique to get the hitherto unreported postbuckling equilibrium paths of composite skew plates loaded between two rigid flat platens. The variation of out-of-plane deformation and end-shortening with compressive in-plane load are examined for simply supported and clamped skew plates made of isotropic, symmetric and unsymmetric laminates. Marguerre's shallow shell theory is employed to study the effect of sinusoidal imperfection on the non-linear behavior of composite skew plates.     

安全壳中钢衬壳热屈曲问题理论与实验研究(Ⅱ)──实验部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题,但实验研究方面的文章发表得不多文中以200兆瓦核电站安全壳中钢衬壳为研究对象,采用局部1：1模型,测得了钢衬壳热屈曲温度和应变载荷,给出了钢衬壳屈曲和初始后屈曲过程中挠度和温度关系、以及膜应变和温度关系,实验测得钢衬壳具有局域屈曲的现象,实验屈曲载荷与理论结果符合较好     

Delamination growth of laminated composite cylindrical shells

The local buckling may occur in delaminated cylindrical shells under axial compression. This often causes delamination growth and structure failure. Based on the variational principle of moving boundary, in this paper, the postbuckling governing equations for the laminated cylindrical shells are derived, and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells is analyzed, and the effects of delamination sizes and depths, the boundary conditions, the material properties and the laminate stacking sequences on delamination growth are discussed.