基于重分析加速的SIMP方法及在桥梁选型中的应用  

Reanalysis Accelerated SIMP Method and Its Application in Bridge Type Selection

作　　者：黄京龙 熊枫 曹鸿猷[1] 杨宏印 HUANG Jing-long;XIONG Feng;CAO Hong-you;YANG Hong-yin(School of Civil Engineering and Architecture,Wuhan University of Technology,Wuhan 430070,China;The First Construction Engineering Co,Ltd of China Construction Third Engineering Bureau,Wuhan 430040,China;School of Civil Engineering and Architecture,Wuhan Institute of Technology,Wuhan 430205,China)

机构地区：[1]武汉理工大学土木工程与建筑学院,武汉430070 [2]中建三局第一建设工程有限责任公司,武汉430040 [3]武汉工程大学土木工程与建筑学院,武汉430205

出　　处：《武汉理工大学学报》2023年第3期101-108,共8页Journal of Wuhan University of Technology

摘　　要：针对拓扑优化中固体各向同性惩罚(SIMP)方法在优化循环中需反复进行有限元分析而导致计算效率低下的不足,提出了基于组合近似重分析(CA)与SIMP方法相结合的拓扑优化加速算法。为避免迭代过程中重分析误差对最终拓扑结果的影响,采用引入自适应CA算法并采用序列级数收敛性估计近似误差,并提出了一种基于误差控制的重分析更新准则。通过数值算例对比了标准SIMP和改进SIMP方法的拓扑优化结果及计算效率。结果表明,改进的SIMP方法在得到相近拓扑构型的条件下减少了83.6%~91.8%的有限元分析次数,说明所提出的基于CA加速的SIMP方法能显著提高拓扑优化的计算效率。最后将改进SIMP方法应用于一座人行桥的选型,发现该方法优化的人行桥拓扑构型清晰,计算效率高,相比初始构型,拓扑构型可以降低结构的应力、提升人行桥的舒适性。Aiming at the disadvantage that the solid isotropic material with penalization model(SIMP)method requires repeated finite element analysis in the optimization cycle,which leads to low computational efficiency,an accelerated topology optimization algorithm based on the combination of combined approximate reanalysis(CA)and SIMP method was proposed.In order to avoid the influence of the reanalysis errors on the final topological results during the iterative process,an adaptive CA algorithm was introduced and the approximate errors were estimated by the convergence of sequence series,and a reanalysis update criterion based on error control was proposed.Some numerical examples were given to compare the results of topology optimization and computational efficiency between the standard SIMP and the improved SIMP.The results show that the improved SIMP method reduces the number of finite element analysis by 83.6%~91.8%under the condition of obtaining similar topological configurations,indicating that the proposed CA-based acceleration method can significantly improve the computational efficiency of the SIMP method.Finally,the improved SIMP method was applied to the selection of a pedestrian bridge.The results show that the topological configuration of the pedestrian bridge optimized by this method is clear and the calculation efficiency is high.Compared with the initial configuration,the topological configuration can reduce the stress of the structure and improve the comfort of the pedestrian bridge.

关 键 词：桥梁工程 拓扑优化 变密度法 重分析 结构选型 

分 类 号：U442.5[建筑科学—桥梁与隧道工程]