Semi-inverse method and generalized variational principles with multi-variables in elasticity |
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| Authors: | He Jihuan |
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| Affiliation: | Shanghai University; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China |
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| Abstract: | ![]()
Semi-inverse method, which is an integration and an extension of Hu' s try-and-error method, Chien' s veighted residual method and Liu' s systematic method, is proposed to establish generalized variational principles with multi-variables without any variational crisis phenomenon. The method is to construct an energy trial-functional with an unknown function F , which can be readily identifled by making the trial-functional stationary and using known constraint equations. As a result generalized variational principles with two kinds of independent variables ( such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle ) and generalized variational principles with three kinds of independent variables ( such as Chien' s generalized variational principles) in elasticity have been deduced without using Lagrange multiplier method. By semi-inverse method, the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables, stress-strain relations are still its constraints. CLC numbers: 0176; 0343 Document code: A |
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| Keywords: | variational principle in elasticy Chien's generalized variational principles Hu_Washizu principle semi_inverse method trial_functional variational crisis |
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