各向异性矩形板的剪切屈曲分析

Shear buckling analysis of anisotropic rectangular plates

根据各向异性矩形薄板剪切屈曲横向位移函数的微分方程建立了一般性的解析解。该一般解包括三角函数和双曲线函数组成的解,它能满足四个边为任意边界条件的问题;该一般解还包括代数多项式解,它能满足四个角的边界条件问题。因此,这一解析解可用于精确地求解任意边界的各向异性矩形板的剪切屈曲问题。其中待定常数可由四边和四角的边界条件来确定,由此得出的齐次线性代数方程系数矩阵行列式等于零可以求得各阶临界载荷及其屈型。结合配点法,利用变形的对称和反对称性,以及对称迭层正方形板均可使计算更简单。以四边平夹的对称角铺设复合材料迭层板为例进行了计算和讨论。

According to differential equation for displacement function of anisotropic rectangular thin plates in shear buckling,a general analytical solution is established.This general solution is composed of trigonometric function and hyperbolic function,which satisfies arbitrary boundary conditions along four edges.There is another solution of algebraic polynomial which satisfies the boundary conditions at four corners.Consequently,this general solution can be used to solve shear bucking problem of anisotropic rectangular plates with arbitrary boundaries accurately.The undetermined constants can be determined by boundary conditions at four edges and four corners.Therefore,the critical load and buckling mode can be obtained by equating coefficient matrix of the homogeneous linear algebraic equations to zero.Combining with the collocation method,making use of symmetries and antisymmetries of the deformation,the calculation is simplified significantly.A composite symmetric laminated plate with four clamped edges is taken as an example is calculated and discussed in the paper.