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Shape optimization in contact problems. (English) Zbl 0594.73108

Authors consider the plane contact problem of a linear-elastic sheet resting on a rigid foundation, the friction being assumed to be given. The shape optimization is defined 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 \(\alpha\). After establishing the basic relations an equivalent variational inequality is derived which is the basis for a finite element approximation of the contact problem. Next the minimization of the discretized potential energy with respect to the design (shape) variables is carried out iteratively by a gradient algorithm. A numerical example demonstrates the effect of the shape optimization on the magnitude of the contact region and the contact stress distributions.
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
49M37 Numerical methods based on nonlinear programming
90C52 Methods of reduced gradient type
49J40 Variational inequalities

Citations:

Zbl 0594.73109
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