Long Yu-qiu. Generalized Variational Principles with Several Arbitrary Parameters and the Variable Substitution and Multiplier Method[J]. Applied Mathematics and Mechanics, 1987, 8(7): 591-602.
Citation: Long Yu-qiu. Generalized Variational Principles with Several Arbitrary Parameters and the Variable Substitution and Multiplier Method[J]. Applied Mathematics and Mechanics, 1987, 8(7): 591-602.

Generalized Variational Principles with Several Arbitrary Parameters and the Variable Substitution and Multiplier Method

  • Received Date: 1984-07-01
  • Publish Date: 1987-07-15
  • The functional transformations of variational principles in elasticity are classified as three patterns: Ⅰ relaxation pattern, Ⅱ augmented pattern and III equivalent pattern.On the basis of pattern Ⅲ, the generalized variational principles with several arbitrary parameters are formulated and their functionals are defined. They are: the generalized principle of single variable u with several parameters, the generalized principle of two variables u, σ with several parameters, the generalized principle of two variables u, ε with several parameters, and the generalized principle of three veriables u, ε, σ with several parameters. From these principles, a series of new forms of equivalent functionals can be obtained. When the values of these parameters are properly chosen, a series of finite element models can be formulated.In this paper, the question of losing effectiveness for Lagrange multiplier method is also discussed. In order to "recover" effectiveness for multiplier method, a modified method, namely, the variable substitution and multiplier method, is proposed.
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