摘要
针对大型工程建设中的Ｒｅｉｓｎｅｒ厚板弹性弯曲问题，本文采用复级数方法求解相应的常系数偏微分方程组的边值问题，并首次得到了任意边界条件下的一般解析解·该解形式简单，计算方便、可靠·以四边简支和三边固支一边自由两种支撑条件下厚板承受均布载荷为例进行了分析验算，与已有的计算结果相比，计算结果相当满意·同时本文还着重对解的收敛速度。
In this paper,by developing the complex Fourier series method to solve the boundary value problem of a system of partial differential equations with constant coefficients,for the first time a general analytic solution satisfying an arbitrary boundary condition is presented for the elastic bending of thick Reissner plates in engineering.The solution is simple and convenient to programming.Analysis and computation are performed for the uniformly loaded plates under two different supporting conditions (four simply supported edges or three clamped and one free edges),the results of which are fairly satisfactory in comparison with those available for reference.And at the same time the analytic solution has been investigated mainly in three aspects:a)speed of convergence;b)reliability(rationality);c)fitting of boundary conditions.
出处
《应用数学和力学》
CSCD
北大核心
1998年第1期79-87,共9页
Applied Mathematics and Mechanics
关键词
Reissner厚板弯曲
复级数方法
一般解析解
bending of Reissner plates,complex Fourier series method,general analytic solution
