Generalized variational principles on nonlinear theory of elasticity with finite displacements
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Two generalized variational principles on nonlinear theory of elasticity with finite displacements in which the σij, eij and ui are all three kinds of independent functions are suggested in this paper. It is proved that 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.
Key wordsfinite displacement nonlinear theory of elasticity generalized variational principle three kinds of independent variables
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- Chien, W. Z., The studies of generalized variational principles in elasticity and their applications in finite element computations,Chinese Journals of Mechanical Engineering,15, 2 (1979), 1–23. (in Chinese)Google Scholar
- Chien, W. Z., Further study on generalized variational principles in elasticity-discussion with Mr Hu Hai-chang on the problem of equivalent theorem,Journal of Mechanics, July (1983), 325–340. (in Chinese)Google Scholar
- Chien, W. Z., Incompatible elements and generalized variational principles,Advances in Applied Mechanics, Academic Press,24 (1984), 93–153.Google Scholar
- Chien, W. Z., The method of high order Lagrange multiplier and the generalized variational principles in elasticity with more general forms of functionals,Applied Mathematics and Mechanics,4, 2 (1983), 143–157.Google Scholar
- Chien, W. Z., Variational principles and generalized variational principles for nonlinear elasticity with finite displacement,Applied Mathematics and Mechanics,9, 1 (1988), 1–12.Google Scholar
- Chien, W. Z.,Selected Works of Wei-Zang Chien, Fujian Education Press (1989).Google Scholar
- Synge, J. L. and W. Z. Chien, The intrinsic theory of elastic shells and plates,Th. Von Karman Anniversary Volume (1940), 103–120.Google Scholar
- Washizu, K.,Variational Methods in Elasticity and Plasticity, Pergamon Press, London (1968).Google Scholar
- Hsueh, D. W., A method for establishing generalized variational principle,Applied Mathematics and Mechanics,6, 6, (1985), 481–488.Google Scholar