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 or 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 manner. 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. The resulting element density variables are then used to scale the Young's modulus in each element using the Ersatz material approach. In this work we employ a modified material interpolation method, in which the element density variables, based on a per-element integration of a regularized Heaviside operator applied to the level-set function, are used as element connectivity design variables. The resulting crisp boundary topology optimization method exploits the advantages of ECP in the field of complex nonlinearities and eliminates the need for penalization by the implicit level-set description of the design.