大变形非线性弹性力学的广义变分原理
Generalized Variational Principles on Nonlinear Theory of Elasticity with Finite Displacements
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摘要: 本文导出了大变形非线性弹性力学的两个具有σij,eij,和ui三类独立变量的广义变分原理,证明了当应力应变关系为约束条件时这两个广义变分原理是等价的.文中对某些特例也作了阐明.Abstract: Two generalized variational principles on nonlinear theory of elasticity with finite displacements in which the σiji eij and ui are all three kinds of independent functions are suggested in this paper. It is provedthat these two generalized variational principles are equivalent to each other if the stress-strain relation is satisfied as constraint. Some special cases, i.e. generalized variational principles on nonlinear theory of elasticity with small deformation, on linear theory with finite deformation and on linear theory with small deformation together with the corresponding equivalent theorems are also obtained. All of them are related to the three kinds of independent variables.
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[1] 钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,机械工程学报,15,2,(1979),1-23. [2] 钱伟长,再论弹性力学中的广义变分原理—就等价定理问题和胡海昌先生商榷,力学学报(1983),325-340. [3] 钱伟长,Incompatible elements and generalized variational principles,Advances in Applied Mechanics,Academic Press,24(1984),93-153. [4] 钱伟长.高阶拉氏乘子法和弹性理论中更一般的广义变分原理,应用数学和力学,4 (1983),137-180. [5] 钱伟长,大位移非线性弹性理论的变分原理和广义变分原理,应用数学和力学,9,1,(1988),1-11 [6] 钱伟长,《钱伟长科学论文选集》.福建教育出版社,福州(1989). [7] Synge,J.L.and W.Z.Chien,The intrinsic theory of elastic shells and plates,Th.Von Karman Anniversary Volume(1940),103-120. [8] Washizu,K.,Variational Methods in Elasticity and Plasticity,Pergamon Press,London(1968). [9] 薛大为,建立广义变分原理的一种方法,应用数学和力学,8,6 (1985),481-488 -
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