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Numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element methods. (English) Zbl 0974.74055

This paper deals with the finite element approximation of variational inequalities coming from the Signorini problem on the unilateral contact between two elastic bodies. In the unilateral contact problem between two deformable solids, without friction, the authors consider a nonconforming finite element discretization. The discrete contact conditions are expressed, across the contact zone, using the mortar projection; former results are improved and optimal convergence rates are established under appropriate regularity hypotheses.

The author concludes that variational inequalities as models of unilateral contact problems are of great interest in solid mechanics, and that, from the solid mechanics point of view, the regularity assumptions seem not to be stringent and are a fair modeling tool for realistic unilateral situations of engineering interest.

MSC:
74S05Finite element methods in solid mechanics
74M15Contact (solid mechanics)
49J40Variational methods including variational inequalities