Explicit Tunnels and Cavities Control Using SIMP and MMA in Structural Topology Optimization

Abstract

The topology of a 3D continuum structure is usually characterized by the number of independent connected component and holes in the structure, where the holes include tunnels (through holes) and cavities (interior holes). The number of these features can be measured by the topological invariants of the structure (e.g., Betti numbers and Euler characteristic). The quantitative control of structural topology is important in topology optimization design because of various considerations, including design freedom, manufacturability, structural performance, and manufacturing costs. However, effective control of the structural topology during the topology optimization process remains a challenge, particularly to control the structural tunnels. To simplify the problem, only the number of tunnels (NT) and cavities (NC) of the structure are controlled in this paper. To solve the aforementioned problems, this study calculates the characteristic information of the tunnels and cavities by introducing the tunnel loops of homology theory and fire-burning method (FBM), while proposing a method for quantitative control of the 3D structural tunnels and cavities within the framework of the solid isotropic material with penalty (SIMP) interpolation of the design variable and method of moving asymptotes (MMA) optimization algorithm. The method achieves unilateral constraints over the structural tunnels and cavities by establishing explicit relationships between the element design variables in the structural topology optimization and NT as well as NC in the structure. Numerical examples demonstrate that the proposed method can effectively control the tunnels and cavities of an optimized structure.