Directional maximum length scale control in density-based topology optimization

In this paper, directional maximum length scale control for both the solid and void phases is proposed for density-based topology optimization with a lower computational cost. The method introduces porosity and material rate in the locally searched domain to achieve the length scale control for the solid and void phases, respectively. To enable directional length scale control, local rectangle and cylinder searches are utilized instead of conventional circle or cylinder searches. The computational cost, including both local search time and occupied memory, is analyzed and compared with that of conventional searches. The proposed method is based on the three-field approach, and a p-mean function is employed to aggregate the local maximum length scale control constraints into a single global constraint. The optimization formulations and sensitivity analysis of the related optimization responses are subsequently derived. Three numerical tests are conducted to demonstrate the effectiveness and potential engineering applications of the proposed method.