Abstract
A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu's generalized variational principle and the Hu's generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potential energy and the correct proofs of these two generalized variational principles are given. It is also proved that this is wrong if one beleives that σ ij ,e ij andu i are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained.
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Dah-wei, H. A method for establishing generalized variational principle. Appl Math Mech 6, 501–509 (1985). https://doi.org/10.1007/BF01876390
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DOI: https://doi.org/10.1007/BF01876390