An explicit topology and thickness control approach in SIMP-based topology optimization

In order to improve the topology optimization results for the requirements such as manufacturability and functionality, and to strengthen the link between structural topology optimization and computational topology, this paper measures the topology and thickness of the structure using topological invariants (i.e., Euler characteristic and Betti numbers) in the computational topology. Based on set theory, explicit relationships between structural topology/thickness and design variables are established, leading to the construction of solid and void constraints. These two constraints are then integrated into the SIMP-based topology optimization framework to control the minimum/maximum solid thickness and minimum void thickness while keeping the structural topology unchanged during topology optimization process. 2D and 3D numerical examples demonstrate that the new approach does have the capability to give a complete control of the topology and thickness of the optimal structure in an explicit way.