Research on Explicit Topology Construction and Shape Optimization via Hole Deformation

Abstract

Topology optimization provides innovative solutions for lightweight structural design by rationally arranging material distribution. It enhances structural performance while reducing material consumption and structural weight, thereby significantly lowering production and operational costs and generating enormous economic benefits. In the development of topology optimization, the density-based method has gained widespread adoption due to its easy-to-understand principles. However, this method still faces the following challenges when applied to engineering applications. First, the geometric models generated by topology optimization lack explicit parameter descriptions, leading to data interaction barriers with Computer Aided Design (CAD) systems. Second, due to element discretization and density penalty mechanisms, structural boundaries exhibit rough and blurred characteristics. These problems severely constrain the iterative efficiency of structural design and manufacturing feasibility. To address these issues, this paper proposes a strategy for geometric reconstruction and shape optimization of topology optimization results. The reconstruction process begins with extracting isolines from the density field as a set of contour points. These points are subsequently interpolated with B-spline curves to explicitly represent the geometric boundaries. Shape optimization is then carried out by adjusting the positions of the B-spline control points. Compared to post-processing methods based on graphics techniques for topology optimization, which ignore the volume constraint and performance loss, the structures reconstructed in this paper exhibits the following advantages: structural boundaries are smoothed and characterized with explicit parameters, reducing performance loss caused by geometric reconstruction while satisfying volume constraints. This paper successfully establishes compatibility between topology optimization and CAD systems, facilitating the transition from conceptual design to manufacturing.