Abstract
In this paper, it has been proved 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 Hellinge-Reissner principle under the constraints of stress-strain relations.
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Communicated Xue Dawei
Project supported by the Shanghai Education Foundation for Young Scientists (98QN47)
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Jihuan, H. Further study of the equivalent theorem of Hellinger-Reissner and Hu-Washizu variational principles. Appl Math Mech 20, 545–556 (1999). https://doi.org/10.1007/BF02463752
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DOI: https://doi.org/10.1007/BF02463752