The element connectivity parameterization formulation for the topology design optimization of multiphysics systems

In spite of the success of the element-density-based topology optimization method in many problems including multiphysics design problems, some numerical difficulties, such as temperature undershooting, still remain. In this work, we develop an element connectivity parameterization (ECP) formulation for the topology optimization of multiphysics problems in order to avoid the numerical difficulties and yield improved results. In the proposed ECP formulation, finite elements discretizing a given design domain are not connected directly, but through sets of one-dimensional zero-length links simulating elastic springs, electric or thermal conductors. The discretizing finite elements remain solid during the whole analysis, and the optimal layout is determined by an optimal distribution of the inter-element connectivity degrees that are controlled by the stiffness values of the links. The detailed procedure for this new formulation for multiphysics problems is presented. Using one-dimensional heat transfer models, the problem of the element-density-based method is explained and the advantage of the ECP method is addressed.