  This paper presents an efficient gradient projection-based method for
structural topological optimization problems characterized by a nonlinear
objective function which is minimized over a feasible region defined by
bilateral bounds and a single linear equality constraint. The specialty of the
constraints type, as well as heuristic engineering experiences are exploited to
improve the scaling scheme, projection, and searching step. In detail, gradient
clipping and a modified projection of searching direction under certain
condition are utilized to facilitate the efficiency of the proposed method.
Besides, an analytical solution is proposed to approximate this projection with
negligible computation and memory costs. Furthermore, the calculation of
searching steps is largely simplified. Benchmark problems, including the MBB,
the force inverter mechanism, and the 3D cantilever beam are used to validate
the effectiveness of the method. The proposed method is implemented in MATLAB
which is open-sourced for educational usage.
