考虑高阶横向剪切正交各向异性板非线性弯曲的微分求积分析  

Differential Quadrature Method for Bending of Orthotropic Plates With Finite Deformation and Transverse Shear Effects

作　　者：李晶晶[1] 程昌钧[1] 

机构地区：[1]上海市应用数学和力学研究所上海大学力学系,上海200072

出　　处：《应用数学和力学》2004年第8期801-808,共8页Applied Mathematics and Mechanics

基　　金：上海市重点学科建设项目

摘　　要：　采用微分求积方法(DQ方法)讨论了计及高阶横向剪切的正交各向异性弹性板的非线性弯曲问题·　导出了非线性控制方程的DQ形式,利用推广的DQWB技巧处理了高阶矩的边界条件·　进一步推广并运用新的分析技术简化了非线性方程的计算·　为说明该方法的可靠性和有效性,将考虑剪切变形及不计剪切变形的薄板的数值结果与三维弹性解析解及其它数值解进行了比较,同时研究了数值结果的收敛性,并考察了不同的节点分布对收敛速度的影响·　还考察了几何。Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature method of nonlinear analysis to the problem was presented. DQWB approach was extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

关 键 词：高阶横向剪切 有限变形 微分求积方法 DQWB途径 收敛性和比较性研究 

分 类 号：O343.8[理学—固体力学]