Smooth topological design of 3D continuum structures using elemental volume fractions

Abstract Topology optimization has emerged as a powerful tool for generating innovative designs. However, several topology optimization algorithms are finite element (FE) based where mesh-dependent zigzag or blurry boundaries are rarely avoidable. This paper presents a continuum topological design algorithm capable of obtaining smooth 3D topologies based on elemental volume fractions. Parametric studies are thoroughly conducted to determine the proper ranges of the parameters in the proposed algorithm. The numerical results confirm the robustness of the proposed algorithm. Furthermore, it is shown that very small penalty coefficients can be used to obtain clear and convergent topologies. The effectiveness of the proposed algorithm is further proven via numerical comparison with a well-established topology optimization framework. Because of the smooth boundary representation, optimized topologies are suitable for additive manufacturing (AM) without redesign or post-processing.