FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (5): 545-556.

FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES

何吉欢

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

收稿日期:1997-11-02 修回日期:1998-12-05 出版日期:1999-05-18 发布日期:1999-05-18
通讯作者: Xue Dawei
基金资助:
Project supported by the Shanghai Education Foundation for Young Scientists (98QN47)

FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES

He Jihuan

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

Received:1997-11-02 Revised:1998-12-05 Online:1999-05-18 Published:1999-05-18
Supported by:
Project supported by the Shanghai Education Foundation for Young Scientists (98QN47)

摘要/Abstract

摘要： In this paper, it has been pro ved that the well-known Hu-Washizu variational principle is a pseudo-generalized variational principle (pseudo-GVP). The stationary conditions of its functional may satisfy all its field equations and boundary conditions if all the variables in the functional are considered as independent variations, but there might exist some kinds of constraints. Some new pseudo-GVPs are established to distinguish them from genuine ones by the so-called inverse Lagrange multiplier method. The constrained Hu-Washizu principle, therefore, is proved to be equivalent with the Hellinger-Reissner principle under the constraints of stress-strain relations.

关键词: variational principles in elasti city, Hellinger-Reissner principle, Hu-Washizu principle, the semi-inverse method, trial-functional

Abstract: In this paper, it has been pro ved that the well-known Hu-Washizu variational principle is a pseudo-generalized variational principle (pseudo-GVP). The stationary conditions of its functional may satisfy all its field equations and boundary conditions if all the variables in the functional are considered as independent variations, but there might exist some kinds of constraints. Some new pseudo-GVPs are established to distinguish them from genuine ones by the so-called inverse Lagrange multiplier method. The constrained Hu-Washizu principle, therefore, is proved to be equivalent with the Hellinger-Reissner principle under the constraints of stress-strain relations.

Key words: variational principles in elasti city, Hellinger-Reissner principle, Hu-Washizu principle, the semi-inverse method, trial-functional

何吉欢. FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(5): 545-556.

He Jihuan. FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(5): 545-556.

参考文献

[1] Hu Haichang. Some variational principles in elasticity and plasticity, Acta Physica Sinica, 1954, 10(3): 259~ 290 (in Chinese)
[2] Chein Weizang. On generalized variational principles of elasticity and its application to plate and shell problems[A]. In: Selected Works of Chien Weizang[C]. Fuzhou: Fu-jian Education Press, 1989, 419~ 444 (in Chinese)
[3] Chein Weizang. Method of high-order lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals[A]. Applied Mathematics and Mechanics (English Edition), 1983, 4(2): 143~ 157
[4] Chien Weizang. Further study on generalized variational principles in elasticity-discussion with Mr. Hu Haichang on the problem of equivalent theorem[J]. Acta Mechanica Sinica, 1983, 4(2): 313~ 323 (in Chinese)
[5] Chien Weizang. Generalized variational principle in elasticity[J]. Engineering Mechanics in Civil Engineering, 1984 24: 93~ 152
[6] Liu Gaolian. A systematic approach to the research and transformation for variational principles in fluid mechanics with emphasis on inverse and hybrid problems[A]. Proc of 1st Int Symp Aerothermo -Dynamics of Internal Flow, 1990, 128~ 135
[7] He Jihuan. Modified Lagrange multiplier method and generalized variational principles in fluid mechanics[J].J Shanghai University(English Edition),1997,1(2),117～122.
[8] He Jihuan. Semi-inverse Method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics[J].Interl J Turbo & Jet-Engines,1997,14(1):23～28.
[9] He Jihuan. A generalized variational principle for 3-D unsteady transonic rotational flow in rotor using clebsch variables[J].Interl J Turbo & Jet-Engines,1997,14(1):17～22.
[10] He Jihuan. A variational theory for one-dimensional unsteady compressible flow:an image plane approach[J].Applied Math Modelling,1998,22:395～403.
[11] He Jihuan. A family of variational principles for compressible rotational blade-to-blade flow using semi-inverse method[J].Interl J Turbo & Jet-Engines,1998,15(2):95～100.
[12] He Jihuan. Generalized variational principle for compressible S2-flow in mixed-flow turbomachinery using semi-inverse method[J].Interl J Turbo & Jet-Engines,1998,15(2):101～107.
[13] He Jihuan. Generalized Hellinger-Reissner principle[J].ASME J Appl Mech,(accepted),1999.
[14] Hu Haichang. On Lagrange multiplier method[J]. Acta Mechanica Sinica, 1985, 17(5):426~ 434 (in Chinese)
[15] Washizu K. On the variational principles of elasticity and plasticity[R]. Aeroelastic and Structures Research Laboratory, Massachuetts Institute of Technology,Technical Report,25～18,March 1955.

FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES

FURTHER STUDY OF THE EQUIVALENT THEOREM OF HELLINGER-REISSNER AND HU-WASHIZU VARIATIONAL PRINCIPLES

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