乏晰边界条件的弹性体静力问题的解和最小位能、余能原理  

The Solution of the Problems in Elastostatics and the Principles of Least-Potential Energy and Least-Complementary Energy with Fuzzy Boundary Conditions

作　　者：云天铨 

机构地区：[1]武汉华中工学院

出　　处：《应用数学和力学》1981年第1期13-20,共8页Applied Mathematics and Mechanics

摘　　要：本文把弹性力学静力问题的解定义在集合论基础上,并推广到乏晰边界条件情形.给出最小位能、余能原理在乏晰边界条件下新的推广,以及最小元位能解的存在和唯一性定理,从而证明弹性力学静力问题的拟解是存在的.In this paper, the solution of the problems in elastostatics is defined on "Set Theory" and extended to fuzzy boundary conditions. Both of the principles of least-potential energy and least-complementary energy are also extended to fuzzy boundary conditions. A theorem of the existence and uniqueness of the solution of minimum elemental potential energy is given and thus the existence of a quasisolution of the problems in elastostatics is proved.

关 键 词：边界条件 应力函数 位移函数 位移模式 静力问题 橡胶 聚合物 弹性体 余能原理 距离空间 拓扑空间 度量空间 位移边界 拟解 

分 类 号：TU3[建筑科学—结构工程]