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A sign preserving mixed finite element approximation for contact problems

Hild P.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 3

487-498

This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity preserving operator of averaging type which differs from the one of Chen and Nochetto. We show that this method is convergent and satisfies the same a priori error estimates as the standard approach in which the approximated contact pressure satisfies only a weak sign condition. Finally we perform some computations to illustrate and compare the sign preserving method with the standard approach.

Some continuous stress mixed formulations and inf-sup test

Berkovic M., Mijuca D., Grozdanović Ines

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 1

141-153

The most frequent motivation for the use of mixed methods is their robustness in the presence of certain limiting and extreme situations. At variance, the main goal of the present paper is to reconsider the use of mixed formulation as a tool for wider application, i.e., to study the stability of the proposed procedure treating problems in elasticity otherwise well suited for the solution by the usual displacement method. Computational procedure for the inf-sup test is outlined, and the results are given.