Concurrent topology optimization of multiscale composite structures in Matlab

This paper presents the compact and efficient Matlab codes for the concurrent topology optimization of multiscale composite structures not only in 2D scenario but also considering 3D cases. A modified SIMP approach (Sigmund 2007) is employed to implement the concurrent topological design, with an energy-based homogenization method (EBHM) to evaluate the macroscopic effective properties of the microstructure. The 2D and 3D Matlab codes in the paper are developed, using the 88-line 2D SIMP code (Struct Multidisc Optim 43(1): 1–16, 2011) and the 169-line 3D topology optimization code (Struct Multidisc Optim 50(6): 1175–1196, 2014), respectively. This paper mainly contributes to the following four aspects: (1) the code architecture for the topology optimization of cellular composite structures (ConTop2D.m and ConTop3D.m), (2) the code to compute the 3D iso-parametric element stiffness matrix (elementMatVec3D.m), (3) the EBHM to predict the macroscopic effective properties of 2D and 3D material microstructures (EBHM2D.m and EBHM3D.m), and (4) the code to calculate the sensitivities of the objective function with respect to the design variables at two scales. Several numerical examples are tested to demonstrate the effectiveness of the Matlab codes, which are attached in the Appendix, also offering an entry point for new comers in designing cellular composites using topology optimization.