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Optimization of a punch shape with a doubly connected contact domain

Submission Status:accepted for publication
  • The objective is to optimize the pressure distribution under a rigid punch having a doubly connected contact domain close to a circular ring and interacting with an elastic half-space. The required design variable is the punch shape. The functional to be minimized is the root-mean-square deviation of the pressure distribution from some given distribution. An analytical technique is developed for solving the problem for the punches with doubly connected shape, by reducing to a sequence of similar problems for the circular ring punches using expansions of the simple layer potential. The method of expansion in terms of a small parameter is used. The simple layer potential expansion is proposed when mapping a doubly connected integration domain onto a circular ring by transforming the integration variables and transforming the coordinates of the pole of the kernel. As a result, a sequence of similar problems was obtained for a circular ring to determine the functions characterizing the distribution of normal pressure under the punch in the form of a non-circular ring, as well as the normal displacements, from where the optimal punch shape is determined.

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Author:Ganna Shyshkanova, Andrea Walther
Document Type:Article
Language:English
Date of Publication (online):2023/06/27
Release Date:2023/06/27
Institutes:Humboldt-Universität zu Berlin
Subprojects:B10
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International