四边简支厚板的三维弹性分析  

Three Dimensional Elasticity Analysis of Simple Supported Orthotropic Rectangular Thick Plates

作　　者：杨正光[1] 仲政[1] 戴瑛[1] 何福保[2] 

机构地区：[1]同济大学固体力学教育部重点实验室,上海200092 [2]上海大学建筑工程学院,上海200072

出　　处：《同济大学学报（自然科学版）》2003年第12期1430-1433,共4页Journal of Tongji University:Natural Science

基　　金：国家杰出青年科学基金资助项目 ( 10 12 5 2 0 9) ;国家自然科学基金资助项目 ( 10 0 72 0 41) ;高等学校优秀青年教师教学科研奖励计划资助项目

摘　　要：将三维矩形板的位移变量按双三角级数展开 ,导出位移形式的平衡方程 ,以 3个位移分量及其一阶导数为状态变量 ,建立状态方程 .考虑四边简支边界条件 ,得到了四边简支正交各向异性三维矩形板的精确解 .由给出的均布载荷下的不同厚跨比及不同长宽比的矩形板计算结果可知 ,与已有的理论解以及有限元计算结果非常吻合 。The displacement functions of a 3D orthotropic rectangular thick plate with simple supported boundary conditions were expanded in the forms of double trigonometric series.The state equations were established based on the governing equations,in which the displacements and the first differential of displacements were assumed as state variables.The analytical solution of a 3D simple supported thick plate was derived by using the state space approach.It's noted that the presented method gives exact results and shows nice convergence and good agreement compared with the results obtained from other analytical methods and finite element methods.

关 键 词：三维厚板 状态空间法 正交各向异性材料 

分 类 号：O343[理学—固体力学]