A Level-set-based Topology Optimization using the Element-connectivity-parameterization Method

This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element-connectivity-parameterization method (ECP). The combined advantages of both methods open up the possibility to treat a wide range of optimization problems involving complex physical and/or geometrical nonlinearities in a general and elegant way. The level-set method features shape optimization on a fixed mesh, leading to intrinsically black-and-white designs. This approach allows a clear description of location and orientation of the interface, whereas topological changes can still be handled easily. A popular concept used in conventional level-set methods is to map the level-set function to volume-fraction design variables for every element of a finite element mesh using the Ersatz-material approach. In this work we employ a modified Ersatz-material formulation, in which the element-connectivity design variables are based on a per-element integration of a regularized Heaviside operator applied to the level-set function. The resulting crisp-boundary topology optimization method exploits the abilities of ECP in the field of complex nonlinearities and eliminates the need for penalization by the implicit level-set description of the design. Keywords: Topology optimization, level-set method, element-connectivity-parameterization method (ECP), geometrical nonlinearities.