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Semi-inverse method and generalized variational principles with multi-variables in elasticity

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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.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P R China

    He Jihuan

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  1. He Jihuan
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Communicated by Zhao Xinghua

CLC numbers: 0176; 0343

Document code: A

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Jihuan, H. Semi-inverse method and generalized variational principles with multi-variables in elasticity. Appl Math Mech 21, 797–808 (2000). https://doi.org/10.1007/BF02428378

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  • DOI: https://doi.org/10.1007/BF02428378

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