大位移非线性弹性理论的广义变分原理

Family of Generalized Variational Principles for Nonlinear Elasticity with Finite Displacement

应用半反推法（凑合反推法）推导了大位移非线性弹性理论中的二类及三类独立变量的广义变分原理．由于半反推法不用拉氏乘子，所以可以避免由于拉氏乘子引起的临界变分现象．

In this paper, via the semi inverse method proposed by the present author, a family of generalized variational principles for nonlinear elasticity with finite displacement have been successfully deduced directly from the governing equations and boundary conditions. Without using the Lagrange multipliers, the novel method can eliminate the variational crisis (some lagrange multipliers vanish during the variation) completely. The paper also indicates the equivalent theorem of Hellinger Reissner and Hu Washizu principles.