Structural Optimization of Variational Inequalities Using Piecewise Constant Level Set Method

Abstract

The paper deals with the shape and topology optimization of the elliptic variational inequalities using the level set approach. The standard level set method is based on the description of the domain boundary as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton-Jacobi equation. In the paper a piecewise constant level set method is used to represent interfaces rather than the standard method. The piecewise constant level set function takes distinct constant values in each subdomain of a whole design domain. Using a two-phase approximation and a piecewise constant level set approach the original structural optimization problem is reformulated as an equivalent constrained optimization problem in terms of the level set function. Necessary optimality condition is formulated. Numerical examples are provided and discussed.