3D material mask overlay topology optimization approach with truncated-octahedron elements

This paper presents a 3D material mask overlay topology optimization approach using truncated octahedron elements and spheroidal masks. Truncated octahedron elements provide face connectivity between two juxtaposed elements, thus, eliminating singular solutions inherently. A novel meshing scheme with Tetra-Kai-Decaheral or TKD (generic case of truncated octahedron) elements is proposed. The scheme is extended to parameterized generic-shape domains. Various benefits of implementing the elements are also highlighted, and the corresponding finite element is introduced. Spheroidal negative masks are employed to determine the material within the elements. Seven design variables define each mask. A material density formulation is proposed, and sensitivity analysis for gradient-based optimization is developed. fmincon MATLAB function is used for the optimization. The efficacy and success of the approach are demonstrated by solving structures and compliant mechanism design problems. Compliance is minimized for the former, whereas a multi-criteria arising due to flexibility and stiffness measures is extremized for optimizing the mechanisms. Convergence of the optimization is smooth. The volume constraint is satisfied and remains active at the end of the optimization.