Interface-Filtering Structural Optimization

In this paper, we present an interface-filtering structural optimization method that optimizes structural shape and topology through successive interface movements. This interface filtering is achieved via the combination of the variable-radius-based partial-differential-equation (PDE) filtering and the Heaviside projection on a density representation. In the proposed method, designs are represented by a density field with sharp interface and no internal grey features, and a filter radius field is used as the design variable in the optimization process. With this method, any density distribution with sharp interfaces can be used as initial designs, and sharp density contrast in density distribution is preserved throughout the optimization process. An analytical relation between the maximum movements of interfaces and the maximum filter radius is given, so that the interface movement can be controlled during the optimization process. Sensitivities with respect to filter radius variables are derived. Two numerical treatments, involving the density update scheme and the radius re-initialization scheme, are developed to achieve smooth successive shape updates and avoid artificial local minima. Numerical examples, including geometric deformation problem, structural compliance minimization, thermal compliance minimization, and negative Poisson ratio problem, are presented to demonstrate the capabilities of the proposed method.