Isogeometric Analysis for topology optimization with a phase field model

We consider a phase field model for the formulation and solution of topology optimization problems in the minimum compliance case. In this model, the optimal topology is obtained as the steady state of the phase transition described by the generalized Cahn–Hilliard equation which naturally embeds the volume constraint on the amount of material available for distribution in the design domain. We reformulate the model as a coupled system and we highlight the dependency of the optimal topologies on dimensionless parameters; also, we discuss the issue of mesh dependency of the solution. We consider Isogeometric Analysis for the spatial approximation which facilitates encapsulating the exactness of the representation of the design domain in the topology optimization and is particularly suitable for the analysis of phase field problems. We demonstrate the validity of the approach and numerical approximation by solving two and three–dimensional topology optimization problems.