Finite element method of a kind of new variational principle

Abstract

A new variational principle is used to establish more reasonable finite element method, which set no limits to physical equations, that is, appropriate to general situations including elasticity, plasticity and rheology. According to theory of finite element method, tanking the Lagrange multiplier as unknown variables with unit joint stress, the corresponding calculating formula of the finite element method is derived. Through solving the equations about basic unknown variables, all unknown variables such as the strains and stresses in the whole solving area, can be work out. A problem about elastic body and a problem about Maxwell body are given and work out, and the results are both identical with the results in the corresponding literature. So the finite element calculating formula can be used to solve the problem of structure analysis with different stress-strain relations and may offer a new alternative way for some more complex problems, for example, the study on the elasticity-plasticity interface. And the other difference with the finite element calculation of common generalized variational principles is: the Lagrange multipliers are not determined beforehand, but to join in the calculating of finite element to get their physical meaning, the train of thought is more natural and the range for solving is expanded.

Keywords

the least work consumption principle / variational principle / finite element method / elasticity / plasticity / rheology

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