Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method (Q1108840)

The functional transformations of variational principles in elasticity are classified as three patterns: relaxation pattern, augmented pattern, and equivalent pattern. On the basis of equivalent pattern, the generalized variational principles with several arbitrary parameters are formulated. From these principles, a series of new forms of equivalent functionals can be obtained. When the values of the parameters are properly chosen, a series of finite element models can be formulated. The question of losing effectiveness for the Lagrange multiplier method is also discussed. In order to ``recover'' effectiveness for the multiplier method, a modified method, namely, the variable substitution and multiplier method, is proposed.