复合材料夹芯板的屈曲分析

BUCKLING OF COMPOSITE SANDWICH PLATES

本文考虑到了横向剪切的作用 ,通过应用最小势能原理和能量变分方法建立了复合材料夹芯板的稳定性控制方程。在位移场的表达式中 ,将横向和纵向位移对 z进行泰勒展开 ,并且保留了前四项 ,在使得横向剪力满足在上下表面为零的条件下 ,选用了同一阶剪切理论相同的参数 ,即引入了参考曲面的法线转角 x,y,避免了引入横向剪力修正系数。给出了满足不同边界条件的基本项 ,采用了 Galerkin方法 ,对稳定性方程求解 ,在对控制方程线性化以后 ,通过计算系数矩阵的最小广义特征值来获得了屈曲载荷 ,并且将屈曲载荷计算值与文献做了对比 ,分析了夹芯板的几何尺寸。

Using of the principle of the stationary value of the total potential energy yields stability governing equation of composite sandwich plates with edges elastically restrained against rotation,which include the effect of transverse shear.The equation is a group of high order nonlinear partial differential equation,including four independent functions,such as displacement W,reference surface rotate angle φ x , φ y and stress function F.With the same parameters as first order transverse shear theory ,high order theory fulfil zero shear tractions on the upper and lower surfaces without using the correction factor.With the given displacement functions w, φ x , φ y ,and applying Galerkin method,the buckling problem become an general eigenvalue problem.The numerical tables included demonstrate the effects of elastic edges conditions,aspect ratio and face sheet ply pattern on the buckling loads of anisotropic sandwich plates.