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Domain optimization problem governed by a state inequality with a “flux” cost functional. (English) Zbl 0625.73025

The bound of a domain in \(\underset \tilde{} R^ 2\) may consist of two parts: the first part is fixed and the second is moving. The optimal shape of the domain is searched for a system governed by a unilateral elliptic boundary value problem. The later is a model for the design of a contact surface with minimal normal stresses. The penalty method is used. The original state inequality is replaced by a family of state equations with the same cost functional. The convergence of the solution of the penalized design problem is considered when the penality parameter tends to zero.
Reviewer: A.Žilinskas

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74P99 Optimization problems in solid mechanics
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49M30 Other numerical methods in calculus of variations (MSC2010)
49J40 Variational inequalities
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