An implicit model for the integrated optimization of component layout and structure topology

Integrated design of the structure topology and involved component layout is a challenging design issue when compared with traditional topology optimization. In this paper, we propose an implicit modeling approach that works completely on an Eulerian finite element mesh throughout the whole optimization process. To this aim, implicit level-set functions and R-functions are employed to describe geometrical shapes of movable components. In particular, a modified arctan function is adopted to depict the material discontinuity along the interface between the structure domain and each component domain. They are then used for material interpolations and analytical sensitivity analysis w.r.t. both pseudo-density design variables and location design variables related to the host structure and components, respectively. Based on a variety of numerical tests, it is demonstrated that considered design problems with movable components can easily be solved by extending the SIMP material model based topology optimization approach using an Eulerian mesh and the gradient-based optimization algorithm.