基于梁挠度函数的板解法  

THE ANALYTICAL SOLUTIONS OF PLATES BASED ON THE DEFLECTION SHAPE FUNCTIONS OF BEAMS

作　　者：王依兵[1] 张铮[1] 张行[1] 

机构地区：[1]北京航空航天大学,航空科学与工程学院,北京100191

出　　处：《力学与实践》2012年第2期29-33,28,共6页Mechanics in Engineering

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.

关 键 词：弹性力学 板壳理论 解析解 形函数 弹性基础梁 

分 类 号：O343[理学—固体力学]