Premium
Shape and topology optimization of contact problems by level set methods
Author(s) -
Myśliński Andrzej
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700128
Subject(s) - shape optimization , topology optimization , boundary (topology) , material derivative , mathematics , topology (electrical circuits) , level set method , optimization problem , domain (mathematical analysis) , boundary value problem , mathematical optimization , mathematical analysis , computer science , finite element method , engineering , structural engineering , combinatorics , segmentation , artificial intelligence , image segmentation
Abstract This paper deals with the numerical solution of a topology and shape optimization problems of an elastic body in unilateral contact with a rigid foundation. The contact problem with the prescribed friction is considered. The structural optimization problem consists in finding such shape of the boundary of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. In the paper shape as well as topological derivatives formulae of the cost functional are provided using material derivative and asymptotic expansion methods, respectively. These derivatives are employed to formulate necessary optimality condition for simultaneous shape and topology optimization. Level set based numerical algorithm for the solution of the shape optimization problem is proposed. Level set method is used to describe the position of the boundary of the body and its evolution on a fixed mesh. This evolution is governed by Hamilton – Jacobi equation. The speed vector field driving the propagation of the boundary of the body is given by the shape derivative of a cost functional with respect to the free boundary. Numerical examples are provided. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)