Structural optimization of contact problems using piecewise constant level set method

The paper deals with the topology optimization of the elastic contact problems using the level set approach. A piecewise constant level set method is used to follow the evolution of design domain interfaces rather than the standard level set method. The piecewise constant level set function takes distinct constant values in each subdomain of a whole design domain. Using a two-phase approximation the original optimization problem is reformulated as an equivalent constrained optimization problem in terms of the piecewise constant level set function. Necessary optimality condition is formulated. Finite difference and finite element methods are applied as the approximation methods. Numerical examples are provided and discussed.