Topology optimization by penalty (TOP) method

In traditional structural topology optimization (TO), the material properties of continuum finite elements of fixed form and coupling are varied to find the optimal topology that satisfies the design problem. We develop an alternative, fundamental formulation where the design space search is dependent on the coupling, and the goal of the topology optimization by penalty (TOP) method is to determine the optimal finite element coupling constraints. By this approach, seemingly disparate topology design problems, e.g., the topology design of structural supports, topology optimization for fluid mechanics problems, topology optimization with convective heat transfer, topology optimization by the element connectivity parameterization method, and the optimal layout of structural joints, can be understood as related formulations under a common topology optimization umbrella, and more importantly, this general framework can be applied to new design problems. For example, in modern multibody dynamics synthesis, the geometric form of finite elements of fixed material properties and interconnectivity are varied to find the optimal topology that satisfies the mechanism design problem. The a priori selection of coupling, e.g., by revolute or translational joints, severely limits the design space search. The TOP method addresses this limitation in a novel way. We develop the methodology and apply the TOP method to the diverse design problems discussed above.