Pixel-based shape optimization in 3D using constrained density-based topology optimization

Abstract

This work extends a recently proposed shape optimization algorithm for three-dimensional thick solids. The proposed algorithm is based on a constrained density-based topology optimization method, resulting in a gradient-based many-variable optimization method for the solid boundary. The method uses finite element neighbor information, which is stored and utilized using rapid graph theory operations to identify the solid’s boundary and constrain the optimization algorithm to only evolve that region. The proposed method requires minimal problem setup while offering a relatively high flexibility and design freedom for the solid’s boundary definition. Furthermore, the result can be seamlessly integrated with scientific visualization and manufacturing software, supporting formats such as STL, OBJ, and X3D. Current shape optimization algorithms (and commercial tools) for volumetric (thick) three-dimensional solids are relatively few and complicated to use, whereas the proposed method excels at exactly these types of problems, thus backing the novelty, merit, and significance of this work. In other words, the proposed algorithm’s ideal application is to optimize volumetric and relatively thick components which are optimized by carving, sculpting, or reshaping the solid. On the other hand, lattice-like designs which are made by interconnected relatively thin members will not benefit from the proposed algorithm, and standard (unconstrained) topology optimization will not change the connectivity either, thus achieving the same result as the proposed method. The effectiveness and shortcomings of the proposed algorithm are highlighted through a set of examples.