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

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

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.

Abstract: 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.

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