弹性力学广义变分原理的应用条件  

Study on Conditions of Using Generalized Variational Principles in Elasticity

作　　者：刘腾喜[1] 

机构地区：[1]湖南大学工程力学系,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2002年第2期24-29,共6页Journal of Hunan University:Natural Sciences

摘　　要：研究了在弹性力学的三类变量广义变分原理中 ,变量σij,εij和ui 是否独立 ,是否包含了应力应变关系 .指出了在应用广义变分原理时应满足下列条件 :泛函中的应变能用应变表示 ,应变余能用应力表示 ;在用广义变分原理求实际问题的近似解时 ,三类变量的试探函数可以独立选择 ,但各类变量之间应不违背力学基本关系 .Whether the variational functions σ ij ,ε ij and u i of generalized variational principles with the three kinds of variational functions in elasticity are independent,and whether the stress strain relationships are included in these principles were studied.The following conditions must be satisfied when generalized variational principles are applied:the strain energy is expressed in the form of strain functions and the strain complementary energy is expressed in the form of stress functions;When generalized variational principles are used to get the approximate solutions of practical problems,the trial functions of the three kinds of variational functions can be selected independently,and the relations among variational functions are not contrary to the essential relationships of mechanics.

关 键 词：弹性力学 广义变分原理 应用条件 应力应变关系 应变能 应变余能 变分约束条件 最小势能原理 

分 类 号：O343[理学—固体力学]