He Jihuan. Semi-Inverse Method and Generalized Variational Principles With Multi-Variables in Elasticity[J]. Applied Mathematics and Mechanics, 2000, 21(7): 721-731.
Citation: He Jihuan. Semi-Inverse Method and Generalized Variational Principles With Multi-Variables in Elasticity[J]. Applied Mathematics and Mechanics, 2000, 21(7): 721-731.

Semi-Inverse Method and Generalized Variational Principles With Multi-Variables in Elasticity

  • Received Date: 1999-10-20
  • Rev Recd Date: 2000-01-30
  • Publish Date: 2000-07-15
  • 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 systematiic 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 readilyi-dentified 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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