An Efficient Gradient Projection Method for Structural Topology Optimization

TL;DR

This paper introduces a fast gradient projection method for structural topology optimization, improving efficiency through heuristic constraints handling, analytical projection approximation, and simplified search steps, validated on benchmark problems.

Contribution

It develops a novel gradient projection approach tailored for nonlinear topology optimization with efficient constraint handling and computational simplifications.

Findings

Effective on benchmark problems like MBB and 3D cantilever beam

Reduced computational costs through analytical projection approximation

Open-source MATLAB implementation available for educational use

Abstract

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.