摘要
基于相应边界支撑和载荷下的梁挠度形函数,构建板的挠度形函数,求解板的变形,并用典型算例进行了验证;对于狭长矩形板,依据其变形特点进行了修正;结果与三维有限元结果基本一致,说明了该方法的适用性和准确性.由于板结构内部的相互作用没有得到充分反映,为了更贴近板变形的物理实际,引入弹性基础梁的挠度函数代替普通梁的挠度函数,进一步完善本文方法.本文研究成果为工程板件变形的理论分析提供了准确且简便易行的计算方法.
The analytical solutions of plates,based on deflection shape functions of beams in form of separation of variables are proposed.Several typical examples are given to validate the present method.The results from the present method agree with those obtained by FEM.This indicates the accuracy of the method,and its applicability in solving special-shaped plates.Instead of those of ordinary beams,the deflection shape functions of beams on elastic foundation are used in the method,which can simulate the more complex deformation of plates better.This research provides a simple and convenient tool for analysis of plate deformations.
出处
《力学与实践》
CSCD
北大核心
2012年第2期29-33,28,共6页
Mechanics in Engineering
关键词
弹性力学
板壳理论
解析解
形函数
弹性基础梁
theory of elastic mechanics
theory of plate and shell
analytical solution
shape function
beam on elastic foundation
