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

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.

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

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.