基于混合算法的自由曲面网格结构多目标优化

Multi-objective optimization of free-form grid structures based on hybrid algorithm

摘要:

为有效提高自由曲面网格结构的性能,改进了自由曲面网格结构的多目标优化方法,基于NURBS技术生成自由曲面,以曲面控制点高度为优化变量,结构应变能为静力性能优化目标,提出了以综合考虑曲面相似性、流畅性以及网格规整性的几何综合量化指标为几何优化目标；将目标函数的敏感度与进化算法NSGA-II结合,提出了敏感度混合进化算法。进行了自由曲面索撑网壳与自由曲面空间网格结构的多目标优化。研究结果表明:与其他3种算法相比,敏感度混合进化算法不仅可获得精确性、均匀性更好的Pareto解集,而且明显提高了算法的优化效率；两个结构优化后的应变能分别下降了21.2%、60.9%,几何综合量化指标分别下降了15.4%、30.9%；优化后结构自身的力学性能有所提高,以综合量化指标为目标函数有效提高了自由曲面的相似性、网格流畅性以及网格规整性。

Abstract:

To effectively increase the performance of free-form grid structures, the multi-objective optimization method of free-form grid structures was improved. The free-form surface was generated based on the non-uniform rational B-spline (NURBS) technology. The height of control points was taken as the optimization variable and structural strain energy as the optimization objective of the static behavior. The geometric comprehensive quantitative index was proposed to be taken as the geometric optimization objective, which comprehensively considers the similarity of the surface and the fluency and regularity of the free-form grids. Combined the sensitivity of the objective function with the NSGA-II algorithm, the sensitivity-NSGA-II hybrid algorithm (referred to as SH-NSGA-II) was proposed. The multi-objective optimization of free-form cable-braced grid shell and free-form spatial grid structures was carried out. Results show that compared with other three algorithms, the proposed algorithm not only achieved the Pareto optimal solution set with better accuracy and uniformity, but also had higher computational efficiency. The strain energy of the two optimized structures decreased by 21.2% and 60.9% respectively, and the geometric comprehensive quantitative index decreased by 15.4% and 30.9% respectively. The mechanical performance of the structures was improved, and the similarity of the surface as well as the fluency and regularity of the free-form grids was effectively improved by taking the geometric comprehensive quantitative index as the geometric objective function.