Analysis of Numerical Instability Factors and Geometric Reconstruction in 3D SIMP-Based Topology Optimization Towards Enhanced Manufacturability

Abstract

The advancement of topology optimization (TO) and additive manufacturing (AM) has significantly enhanced structural design flexibility and the potential for lightweight structures. However, challenges such as intermediate density, mesh dependency, checkerboard patterns, and local extrema in TO can lead to suboptimal performance. Moreover, existing AM technologies confront geometric constraints that limit their application. This study investigates minimum compliance as the objective function and volume as the constraint, employing the solid isotropic material with penalization method, density filtering, and the method of moving asymptotes. It examines how factors like mesh type, mesh size, volume fraction, material properties, initial density, filter radius, and penalty factor influence the TO results for a metallic gooseneck chain. The findings suggest that material properties primarily affect numerical variations along the TO path, with minimal impact on structural configuration. For both hexahedral and tetrahedral mesh types, a recommended mesh size is identified where the results show less than a 1% difference across varying mesh sizes. An initial density of 0.5 is advised, with a filter radius of approximately 2.3 to 2.5 times the average unit edge length for hexahedral meshes and 1.3 to 1.5 times for tetrahedral meshes. The suggested penalty factor ranges of 3–4 for hexahedral meshes and 2.5–3.5 for tetrahedral meshes. The optimal geometric reconstruction model achieves weight reductions of 23.46% and 22.22% compared to the original model while satisfying static loading requirements. This work contributes significantly to the integration of TO and AM in engineering, laying a robust foundation for future design endeavors.