Multi-material topology optimization using scaled boundary finite element method

This work introduces the use of Scaled Boundary Finite Element Method (SBFEM) in Multi-Material Topology Optimization (MMTO) problems, which is new in the literature. SBFEM is implemented and its performance is tested across different density interpolation-based MMTO methods: the Alternating Active-Phase (AAP) algorithm, SIMP with mapping based interpolation, and polygonal mesh based MMTO, PolyMat which uses Discrete Material Optimization (DMO) combined with Zhang–Paulino–Ramos (ZPR) update scheme. First, a comprehensive description of implementation of SBFEM with each of the chosen MMTO methods is given. Then, we present the results of MMTO using SBFEM on a few benchmark problems with different choices of materials, volume fractions and mesh sizes. In the AAP and SIMP with mapping based interpolation we use four-noded quadrilateral mesh on rectangular design domains, while for the polygonal mesh, more complicated domains are chosen. We further compare the performance of SBFEM with finite element method (FEM), the use of which as the underlying analysis tool is de facto in topology optimization literature. Results show that the computational performance of SBFEM is comparable to FEM in case of quad mesh, whereas SBFEM outperforms FEM in case of unstructured polygonal mesh. This is because the semi-analytical nature of SBFEM makes it especially well-suited for polygonal discretizations. The results from a few benchmark problems affirm SBFEM’s effectiveness for MMTO applications in complex geometries. Future work will focus on implementation of SBFEM in more complicated topology optimization problems like arresting crack growth or MMTO problems with semi-infinite domains.