弹性力学基本方程弱形式  

Weak form of basic equations in elasticity

作　　者：刘长春[1] 吕和祥[1] 

机构地区：[1]大连理工大学工程力学系,辽宁大连116024

出　　处：《大连理工大学学报》2007年第5期634-638,共5页Journal of Dalian University of Technology

摘　　要：弹性力学基本方程正确的弱形式将是有限元分析的基础.如直接从基本方程出发,由于其整个方程可以有正负号的差异,往往得不到正确的弱形式.因此从泛函分析的角度出发,基于共轭空间的概念和泛函分析的基本定理准确地给出了弹性力学基本方程的弱形式;给出了连续介质在位移或物理常数间断面上的条件.将三维空间的弹性力学动力学方程,理解为定义在四维空间域上的运动方程,导出了弹性力学动力学方程的弱形式,在此基础上推导出了与Hamilton变分原理同样的结果.The correct weak form of basic equations in elasticity is the foundation of finite element analysis. The weak form obtained by means of the basic equations is often not correct because each basic equation could have a difference in sign （positive or negative）. The correct weak form of basic equations in elasticity is presented by means of dual space conception and basic theorem in functional analysis. The conditions on discontinuous surfaces of displacements or elasticity constants for continua are given. The dynamic equations of elasticity defined on 3-D are taken as the equations defined on a domain in 4-D, and the weak forms of dynamic equations of elasticity are given. The same results as Hamiltonls variational principle are derived from the weak form.

关 键 词：弹性力学基本方程 共轭空间 微分方程弱形式 变分原理 

分 类 号：O343[理学—固体力学]