自由曲面形状和拓扑联合优化研究

Combined shape and topology optimization of free-form structure

为了得到形状与拓扑这两大因素共同影响下的自由曲面形状和拓扑的最优解,以结构鲁棒性为优化目标,将自由曲面的形状和拓扑同时作为优化的变量,采用差分演化算法进行优化求解,实现了全局最优的曲面形状和网格拓扑.算例表明,与形状和拓扑优二者分开优化相比,优化得到的该结构鲁棒性更高,结构力学性能更优,求得的曲面形状和网格拓扑能够有效地抵抗所对应的荷载,体现结构的主要传力路径.

Shape and topology of free-form grid structures were simultaneously considered in order to reach the global optimum shapes and topologies.Optimum structural robustness was set to be the objective while parameters to define the structural shape and topology were taken as design variables.A differential evolution algorithm was used to solve the combined optimization problem.Global optimum shapes and topologies of free-form structures were obtained.The obtained results were compared with those achieved by optimizing solely shape or topology.Results showed that more robust structures with better mechanical properties were obtained,which implied the superiority of the method.The optimized structures were more efficient in carrying the load,and the resulted shape and topology clearly revealed the main force transferring paths.