Haslinger, Jaroslav; Neittaanmäki, Pekka Shape optimization in contact problems. (English) Zbl 0594.73108 Ber., Univ. Jyväskylä 31, 175-186 (1985). 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 Cited in 1 Review 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 Keywords:plane contact; linear-elastic sheet; rigid foundation; friction; shape optimization; contact boundary curve; minimization of the total potential energy; minimization of the discretized potential energy Citations:Zbl 0594.73109 PDFBibTeX XMLCite \textit{J. Haslinger} and \textit{P. Neittaanmäki}, Ber., Univ. Jyväskylä, Math. Inst. 31, 175--186 (1985; Zbl 0594.73108)