TOPOLOGY OPTIMIZATION WITH ISOGEOMETRIC ANALYSIS IN A PHASE FIELD APPROACH

Topology optimization for structural problems aims at finding the optimal distribution of a material in a design domain such that an objective
functional is minimized under certain onstraints. A typical problem is represented by the minimum compliance case where the goal is the generation of the stiffest structure for a prescribed external load and with a limited amount of material. We consider for the solution of these
problems the phase field approach which allows a smooth description of the material properties in the design domain and provides geometric information of the interfaces between the material and the void. With this aim, the
objective functional is perturbed with a Cahn-Hilliard type penalty term; in this manner, the solution of the topology optimization problem
corresponds to the steady state of a phase transition model based on the generalized Cahn-Hilliard equations. For the spatial approximation of these equations we use Isogeometric Analysis thus allowing to close the gap between the geometry, the analysis and the optimization procedure without the introduction of any geometrical approximation of the design domain. Finally, the stiffness of the optimal topologies obtained with this procedure can be further improved by using a shape optimization technique.