Piecewise constant level set method for topology optimization of unilateral contact problems

The paper deals with the structural optimization of the elastic body in unilateral contact with a rigid foundation using the level set approach. A piecewise constant level set method is used to represent the evolution of 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 the original structural 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.