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Shape optimization in contact problems based on penalization of the state inequality. (English) Zbl 0594.73109

The paper deals with the frictionless plane contact problem of a linear- elastic sheet resting on a rigid foundation. The shape optimization is carried out in such a manner that the contact boundary curve \(\alpha\) should be the result of the minimization of the total potential energy with respect to \(\alpha\), the contact problem being described by a variational inequality. This inequality is replaced by a family of penalized state problems. The existence of their solution is proved and the relation between the optimal shapes for the original state inequality and those for the penalized equations is established. Further a proof for the convergence of a finite element approximation is given. This approximation leads to a nonlinear programming problem with box constraints, linear inequality constraints and a linear equality constraint. Instructive examples are worked out numerically showing that the contact region is enlarged and the contact pressure becomes uniform as a result of the optimization.
Reviewer: H.Bufler

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74P99 Optimization problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
49J40 Variational inequalities
49M30 Other numerical methods in calculus of variations (MSC2010)

Citations:

Zbl 0594.73108
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References:

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