VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION

Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (7): 589-601.

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VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION

钱伟长

Shanghai University of Technology; Shanghai Institute of Applied Mathematics and Mechanics

收稿日期:1986-12-25 出版日期:1987-07-18 发布日期:1987-07-18

VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION

Chien Wei-zang

Shanghai University of Technology; Shanghai Institute of Applied Mathematics and Mechanics

Received:1986-12-25 Online:1987-07-18 Published:1987-07-18

摘要/Abstract

摘要： Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1](1979), [6](1980), [2,3](1983) and[4,5](1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems.

关键词: Powell’s theory, thin-walled curve box, material constant, Fibonacci series search method, finite curve strip element theory

Abstract: Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1](1979), [6](1980), [2,3](1983) and[4,5](1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems.

Key words: Powell’s theory, thin-walled curve box, material constant, Fibonacci series search method, finite curve strip element theory

钱伟长. VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(7): 589-601.

Chien Wei-zang. VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(7): 589-601.

参考文献

[1] Chien Wei-zang,The studies of generalized variational principles in elasticity and their applications in finite element computation,Science Report,Qing-hua University,TH 78011(1978),Mechanics and Practice,l,1,16-64,1.2(1979),19-27;Chinese Journal of Mechanical Engineering,15,2(1979),1-23.(in Chinese).
[2] Chien Wei-zang,Method of high order Lagrange multiplier,and generalized variational principles of elasticity with more general forms of functionals,Applied Mathematics and Mechanics,4,2(1983),145-157.
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VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION

VARIATIONAL PRINCIPLES IN ELASTICITY WITH NONLINEAR STRESS-STRAIN RELATION

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