TY - JOUR A1 - Shyshkanova, Ganna A1 - Walther, Andrea T1 - Optimization of a punch shape with a doubly connected contact domain N2 - 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. Y1 - 2023 UR - https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/523 ER -