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Contact Pressure over Doubly Connected Rectangular Domains and Punch Shape Optimization

Submission Status:accepted for publication
  • Contact problems arise in a variety of industrial processes, engineering and biomechanical systems. 3-D contact problem for a rigid punch with a doubly connected base bounded by the lines close to rectangles is in consideration. An analytic-numerical technique is developed for its solving. The problem contains Fredholm integral equations of the first kind, which are transformed into the second kind by means of regularization. Using the simple layer potential expansion, the kernels of the integrals are presented in the form of expansions in the powers of the polar radius. The difference between the values of the desired function at different points and the subsequent interpolation of the terms are proposed to smooth the kernels and eliminate singularities. The integral equations are reduced to one-dimension and then solved using quadrature formulas. Subsequently a punch shape is taken as a desired function, and as a minimizing functional is considered the root-mean-square deviation of the pressure distribution arising under the punch from some optimal distribution. In this case, the values of the total forces and moments applied to the punch are assumed to be given, which leads to restrictions imposed on the distributions by the equilibrium conditions. The normal displacements are determined which arising under the action of the found contact pressure on the elastic half-space. The desired punch shape is found using the simple layer potential. A solution to the problem is obtained for the punch with the doubly connected base bounded by lines close to rectangles.

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Author:Ganna Shyshkanova, Andrea Walther
Document Type:Preprint
Language:English
Date of Publication (online):2022/09/27
Release Date:2022/09/28
Tag:contact problem; integral equations; shape optimization; simple layer potential
Institutes:Humboldt-Universität zu Berlin
Subprojects:B10
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International