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Optimal location of a finite set of rigid inclusions in contact problems for inhomogeneous two-dimensional bodies. (English) Zbl 1477.49017

Summary: The 2D-model of an elastic body with a finite set of rigid inclusions is considered. We assume that the body can come in frictionless contact on a part of its boundary with a rigid obstacle. On the remaining part of the body’s boundary a homogeneous Dirichlet boundary condition is imposed. For a family of corresponding variational problems, we analyze the dependence of their solutions on locations of the rigid inclusions. Continuous dependency of the solutions on location parameters is established. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional on the solution space, while the control is given by location parameters of the rigid inclusions.

MSC:

49J40 Variational inequalities
49J20 Existence theories for optimal control problems involving partial differential equations
74G55 Qualitative behavior of solutions of equilibrium problems in solid mechanics
74M15 Contact in solid mechanics
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