任意形状弹性薄板弯曲的精确解  

An Exact Method of Bending of Elastic Thin Plates with Arbitrary Shape

作　　者：周叮[1] 

机构地区：[1]南京理工大学105教研室,南京210014

出　　处：《应用数学和力学》1996年第12期1123-1127,共5页Applied Mathematics and Mechanics

基　　金：南京理工大学科研发展基金资助课题

摘　　要：本文提供了一个求解任意形状弹性薄板弯曲的新方法,在求得了极坐标系中弹性薄板弯曲微分方程的精确解后,将解代入薄板的边界条件,利用Fourier级数将边界方程展开,可确定出各待定常数,所得结果是精确的。This paper presents a new method exactly to solve the bending of elastic thin plates with arbitrary shape. First the analytic solution of differential equation of elastic thin plate is derived in polar coordinate, then the analytic solution is substituted into the boundary conditions of elastic thin plate with arbitrary shape. The boundary equations are expanded along the boundary by the use of Fourier series, all unknown coefficients can be decided. The results are exact.

关 键 词：弹性薄板 弯曲 变形 精确解 薄板 

分 类 号：O343.8[理学—固体力学]