弹性膜结构静力学的各类变分原理  

VARIATIONAL PRINCIPLES FOR NONLINEAR ELASTOSTATICS OF MEMBRANE STRUCTURES

作　　者：李纬华[1] 罗恩[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275

出　　处：《工程力学》2008年第3期58-63,共6页Engineering Mechanics

基　　金：高校博士点基金科研基金项目(20030558025);国家自然科学基金项目(10172097)

摘　　要：通过罗恩早已提出的一条简单而统一的新途径,系统地建立了弹性膜结构静力学的各类变分原理。首先给出膜结构静力学的广义虚功原理的表式,然后从该式出发,不仅能得到膜结构静力学的虚功原理,而且通过所给出的广义Legendre变换,还能系统地成对导出弹性膜结构静力学的3类变量、2类变量变分原理以及总势能驻值原理和总余能驻值原理的互补泛函。同时,通过这条新途径还能清楚地阐明这些原理的内在联系。By a simple and unified new way proposed by Luo, some variational principles for nonlinear elastostatics of membrane structures can be established systematically. An important integral relation is given, which can be considered as the generalized principle of virtual work for statics of membrane structures in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work for statics of membrane structures, but also to derive systematically the complementary functionals for three-field, two-field variational principles and principles of stationary total potential energy and stationary total complementary energy for nonlinear elastostatics of membrane structures by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.

关 键 词：膜结构 几何非线性 弹性静力学 变分原理 互补关系 

分 类 号：O316[理学—一般力学与力学基础] TU311.1[理学—力学]