各向异性矩形板的稳定性分析  

STABILITY ANALYSIS OF ANISOTROPIC RECTANGULAR PLATES

作　　者：郑荣跃[1,2] 蔺文峰[2] 黄炎[2] 

机构地区：[1]宁波大学建筑工程与环境学院,浙江宁波315211 [2]国防科技大学航天与材料工程学院,湖南长沙410073

出　　处：《工程力学》2009年第8期30-33,共4页Engineering Mechanics

基　　金：国家自然科学基金项目(50405006);宁波市自然科学基金项目(2006A610095)

摘　　要：根据各向异性矩形薄板屈曲横向位移函数的微分方程建立了一般性的解析解法。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;还有代数多项式解,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稳定问题,解中的积分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,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 differential equation for displacement function of anisotropic rectangular thin plates in stability, a general analytical solution is established. This general solution composes not only the composite solutions made by trigonometric function and hyperbolic function which can satisfy the problem of arbitrary boundary conditions along four edges, but also the algebraic polynomial with double sine series solutions which can satisfy the problem of boundary conditions at four comers. Consequently, this general solution can be used to solve stability problems of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four comers. Each critical load and buckling mode can be solved by determining the coefficient matrix from the homogeneous linear algebraic equations equal to zero. As an example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.

关 键 词：各向异性板 稳定性 一般解析解法 临界载荷 屈曲 

分 类 号：O343.9[理学—固体力学]