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

He Jihuan

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(7): 721-731

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.

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.

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

He Jihuan

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

Received Date: 1999-10-20
Rev Recd Date: 2000-01-30
Publish Date: 2000-07-15

Abstract

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 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.
- variational principle in elasticy,
- Chien’s generalized variational principles,
- Hu-Washizu principle,
- semiinverse method,
- trial-functional,
- variational crisis

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References(18)

References

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