PCM-BESO: a reformative multi-constraints topology optimization method using point cloud modeling oriented to additive manufacturing

This paper introduces a novel method for multi-constraints bi-directional evolutionary structural optimization (BESO) using point cloud modeling (PCM-BESO). It improves upon the primary BESO method by utilizing finite element model nodes as design variables and updating the model’s point cloud by adding or removing nodes based on sensitivity analysis. By utilizing α-shape generation and refinement technology based on Delaunay triangulation, the point cloud is geometrically reconstructed to obtain more accurate representations and smoother boundaries in optimized design. Additionally, a boundary growth technique is included in PCM-BESO to expand the point cloud outside the boundary, enabling topology optimization beyond the initial design domain. To solve multi-constraints optimization problems, this paper proposes the stress uniformity information entropy constraint that measures stress distribution uniformity while considering volume and displacement constraints. Moreover, two new dynamic evolution rate functions are introduced to enhance convergence speed and stability. Numerical results demonstrate that the method is effective for multi-constraints optimization of 2D and 3D structures and can be well combined with additive manufacturing. When breaking through the initial design domain, the method provides an optimal topology with significantly improved performance, which is particularly useful for structures with limited initial design domain.