  Explicit topology optimization methods have received ever-increasing interest
in recent years. In particular, a 188-line Matlab code of the two-dimensional
(2D) Moving Morphable Component (MMC)-based topology optimization method was
released by Zhang et al. (Struct Multidiscip Optim 53(6):1243-1260, 2016). The
present work aims to propose an efficient and easy-to-extend 256-line Matlab
code of the MMC method for three-dimensional (3D) topology optimization
implementing some new numerical techniques. To be specific, by virtue of the
function aggregation technique, accurate sensitivity analysis, which is also
easy-to-extend to other problems, is achieved. Besides, based on an efficient
identification algorithm for load transmission path, the degrees of freedoms
(DOFs) not belonging to the load transmission path are removed in finite
element analysis (FEA), which significantly accelerates the optimization
process. As a result, compared to the corresponding 188-line 2D code, the
performance of the optimization results, the computational efficiency of FEA,
and the convergence rate and the robustness of optimization process are greatly
improved. For the sake of completeness, a refined 218-line Matlab code
implementing the 2D-MMC method is also provided.

Optimization and Control