A Moving Morphable Voids Approach for Topology Optimization With Closed B-Splines

Abstract

Topology optimization with moving morphable voids (MMVs) is studied in this paper. B-spline curves are used to represent the boundaries of MMVs in the structure. Kreisselmeier–Steinhauser (KS)-function is also implemented to preserve the smoothness of the structural boundary in case the intersection of the curves happen. In order to study the influence of continuity, we propose pseudo-periodic closed B-splines (PCBSs) to construct curves with an arbitrary degree. The selection of PCBS parameters, especially the degree of B-spline, is studied and discussed. The classic Messerschmitt–Bolkow–Blohm (MBB) case is taken as an example in the numerical experiment. Results show that with the proper choice of B-spline degrees and number of control points, PCBSs have enough flexibility and stability to represent the optimized material distribution. We further reveal the mechanism of the merging process of holes and find that high-order degree PCBS could preserve more separated voids. A support beam design problem of microsatellite is also studied as an example to demonstrate the capability of the proposed method.