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

Long Yu-qiu

Volume 8 Issue 7

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Article Navigation > Applied Mathematics and Mechanics > 1987 > 8(7): 591-602

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.

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.

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

Long Yu-qiu

Qinghua University, Beijing

Received Date: 1984-07-01
Publish Date: 1987-07-15

Abstract

Abstract

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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References(4)

References

[1]	钱伟长,高阶拉氏乘子法和弹性理论中更一般的广义变分原理,应用数学和力学,4,2 (1983),137-150.
[2]	陈万吉,更一般的杂交广义变分原理及有限元模型,合肥工业大学学报,4 (1983).
[3]	Taylor R.L.,O.C.Zienkiewicz,Complementary energy with penalty functions in finite element anaysis,Energy Methods in Finite Element Analysis,John Wiley & Sons(1979).
[4]	Oden J.T.,Penalty-finite element methods for constrained problems in elasticity,Proc.of Symposium on Finite Element Method(1982).

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