基于摄动法的周期性多孔结构稳健性拓扑优化设计  

Robust topology optimization of periodical cellular structures with perturbation method

作　　者：占金青 孙宇 王啸 刘敏 ZHAN Jinqing;SUN Yu;WANG Xiao;LIU Min(School of Mechatronics and Vehicle Engineering,East China Jiaotong University,Nanchang 330013,China;Key Laboratory of Conveyance Equipment,Ministry of Education,Nanchang 330013,China)

机构地区：[1]华东交通大学机电与车辆工程学院,江西南昌330013 [2]载运工具与装备教育部重点实验室,江西南昌330013

出　　处：《铁道科学与工程学报》2023年第4期1522-1532,共11页Journal of Railway Science and Engineering

基　　金：国家自然科学基金资助项目(52065019,52165002,51665011);江西省自然科学基金资助项目(20202BAB204015,20202ACBL214013)。

摘　　要：为了考虑载荷不确定性对多尺度拓扑优化结果的影响,提出一种基于摄动法的周期性多孔结构稳健性拓扑优化设计方法。假设宏观结构由材料微结构周期性排列构成,采用能量均匀化方法求解微结构的宏观等效弹性矩阵。考虑作用载荷的大小和方向不确定性,采用摄动法求解不确定性载荷条件下的周期性多孔结构响应,以宏观结构柔顺度的期望、标准差加权和最小化为目标,以宏观和微观结构体积作为约束,建立基于摄动法的周期性多孔结构稳健性多尺度拓扑优化模型,采用准则优化算法求解优化问题。数值算例结果表明提出的设计方法是有效的;与确定性拓扑优化结果相比,考虑载荷方向不确定的稳健性拓扑优化获得的宏观结构和材料微结构构型有很大不同,以抵抗水平方向载荷的作用;载荷大小不确定对稳健性多尺度拓扑优化结果影响较小。随着权重因子值增大,稳健性多尺度拓扑优化获得的宏观和微观结构构型发生变化,设计的周期性多孔材料结构柔顺度的期望增加,柔顺度的标准差减少。稳健性多尺度拓扑优化获得的结构柔顺度的标准差比确定性多尺度拓扑优化结果小,稳健性设计的周期性多孔结构具有更好的稳健性。Considering the influence of the uncertain loading on the multiscale designs,a method for robust topology optimization of periodic cellular structures with perturbation method was proposed.The macrostructure was assumed to be composed of periodic microstructures,and the effective elasticity matrix of the microscopic unit cell was calculated using the energy-based homogenization method.Considering the uncertain loading magnitudes and directions,the stochastic perturbation method was applied to solve the response of periodic cellular structures under loading uncertainty.The minimization of the weighted sum of the statistical mean and standard variance of the compliance of the macrostructure was developed as the objective function.Both the volume fractions of the macrostructure and microstructures were used as constraints.The model for robust topology optimization of periodic cellular structures with the perturbation method was established.The optimality criteria algorithm was applied to solve the topology optimization problem.Several robust topology optimization cases were presented to demonstrate the validity of the proposed method.Compared with the results of the deterministic topology optimization,the macrostructure and microstructure configurations obtained by the robust topology optimization were different by considering the uncertainties of the load direction.It can withstand the horizontal load.The uncertainties of the load magnitude have little effect on the results of the robust topology optimization of periodic cellular structures.As the weight factor increases,the macrostructure and microstructure configurations obtained by robust topology optimization change.The mean of the compliance of the periodic cellular structures increases,and the standard variance of the compliance of the structures decreases.The standard deviation of the structural compliance of the robust topology optimization is smaller than that of the results of deterministic topology optimization,and the performance of the periodic cellula

关 键 词：周期性多孔结构 材料微结构 稳健性拓扑优化 不确定性载荷 摄动法 

分 类 号：U260[机械工程—车辆工程]