Sequentially coupled gradient-based topology and domain shape optimization

A coupled topology and domain shape optimization framework is presented that is based on incorporating the shape design variables of the design domain in the Solid Isotropic Material with Penalization topology optimization method. The shape and topology design variables are incrementally updated in a sequential fashion, using a staggered numerical update scheme. Non-Uniform Rational B-Splines are employed to parameterize the shape of the design domain. This not only guarantees a highly accurate description of the shape boundaries by means of smooth basis functions with compact support, but also enables an efficient control of the design domain with only a few control points. Furthermore, the optimization process is performed in a computationally efficient way by applying a gradient-based optimization algorithm, for which the sensitivities can be computed in closed form. The usefulness of the coupled optimization approach is demonstrated by analyzing several benchmark problems that are subjected to different types of initial conditions and domain bounds. The variation in simulation results denotes that a careful construction of the initial design domain is necessary and meaningful.