In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are reg...In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.展开更多
The level set method(LSM)is renowned for producing smooth boundaries and clear geometric representations,facilitating integration with CAD environments.However,its inability to autonomously generate new holes during o...The level set method(LSM)is renowned for producing smooth boundaries and clear geometric representations,facilitating integration with CAD environments.However,its inability to autonomously generate new holes during optimization makes the results highly dependent on the initial design.Although topological derivatives are often introduced to enable hole nucleation,their conversion into effective shape derivatives remains challenging,limiting topological evolution.To address this,a level set topology optimization method with autonomous hole formation(LSM-AHF)is proposed,integrating the material removal mechanism of the SIMP(Solid Isotropic Material with Penalization)method into the LSM framework.First,an initial structure is generated by adjusting the judgment threshold,and a binary thresholding algorithm is subsequently employed to obtain a clear and well-defined geometry.The structural boundaries of this geometry are then identified and used to construct a signed distance field,which serves as the initial level set function.To ensure smooth transitions across material interfaces and enhance numerical stability,Gaussian filtering is subsequently applied to the distance field.Numerical results demonstrate that LSMAHF effectively enables hole nucleation without manual initialization and improves topology change,addressing the respective limitations of conventional LSM and SIMP methods.展开更多
为获得高速动车齿轮箱最优结构设计方案,针对目前国产高速动车牵引齿轮箱箱体特点及存在的问题,基于SIMP(solid isotropic material with penalization)材料插值模型及应变能理论,利用软件HyperMesh中的拓扑优化与形状优化模块对动车齿...为获得高速动车齿轮箱最优结构设计方案,针对目前国产高速动车牵引齿轮箱箱体特点及存在的问题,基于SIMP(solid isotropic material with penalization)材料插值模型及应变能理论,利用软件HyperMesh中的拓扑优化与形状优化模块对动车齿轮箱箱体结构进行拓扑优化和局部形状优化。优化结果表明:优化后的动车齿轮箱结构的最大变形和最大应力有大幅度降低,能有效提高齿轮箱箱体的刚度和强度。文中结果可为设计性能优异的国产化高速动车齿轮箱提供数据支持。展开更多
为得到清晰的0-1拓扑分布结构,在SIMP(solid isotropic microstructures withpenalization)和SRV(the sum of the reciprocal variables)方法的基础上提出了一种新的混合方法——SIMP-SRV方法,该方法将SIMP得到的优化结果用来初始化SRV...为得到清晰的0-1拓扑分布结构,在SIMP(solid isotropic microstructures withpenalization)和SRV(the sum of the reciprocal variables)方法的基础上提出了一种新的混合方法——SIMP-SRV方法,该方法将SIMP得到的优化结果用来初始化SRV方法的设计变量,再用SRV方法得到最终的优化目标。将SIMP-SRV方法应用于柔性机构的0-1拓扑优化设计中,得到了轮廓清晰的拓扑分布结构,完全消除了中间密度单元,从而证明了该方法的有效性。展开更多
基金funded by National Nature Science Foundation of China(92266203)National Nature Science Foundation of China(52205278)+1 种基金Key Projects of Shijiazhuang Basic Research Program(241791077A)Central Guide Local Science and Technology Development Fund Project of Hebei Province(246Z1022G).
文摘In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.
基金supported by the National Natural Science Foundation of China[52475096]Guangxi Natural Science Fund for Distinguished Young Scholars[2025GXNSFFA069009]+2 种基金Bagui Outstanding Youth Program of Guangxi,ChinaNatural Science and Technology Innovation Development Doubling Plan Project of Guangxi University,China[2024BZRC010]Innovation Project of Guangxi Graduate Education,China[YCBZ2025014].
文摘The level set method(LSM)is renowned for producing smooth boundaries and clear geometric representations,facilitating integration with CAD environments.However,its inability to autonomously generate new holes during optimization makes the results highly dependent on the initial design.Although topological derivatives are often introduced to enable hole nucleation,their conversion into effective shape derivatives remains challenging,limiting topological evolution.To address this,a level set topology optimization method with autonomous hole formation(LSM-AHF)is proposed,integrating the material removal mechanism of the SIMP(Solid Isotropic Material with Penalization)method into the LSM framework.First,an initial structure is generated by adjusting the judgment threshold,and a binary thresholding algorithm is subsequently employed to obtain a clear and well-defined geometry.The structural boundaries of this geometry are then identified and used to construct a signed distance field,which serves as the initial level set function.To ensure smooth transitions across material interfaces and enhance numerical stability,Gaussian filtering is subsequently applied to the distance field.Numerical results demonstrate that LSMAHF effectively enables hole nucleation without manual initialization and improves topology change,addressing the respective limitations of conventional LSM and SIMP methods.
文摘为获得高速动车齿轮箱最优结构设计方案,针对目前国产高速动车牵引齿轮箱箱体特点及存在的问题,基于SIMP(solid isotropic material with penalization)材料插值模型及应变能理论,利用软件HyperMesh中的拓扑优化与形状优化模块对动车齿轮箱箱体结构进行拓扑优化和局部形状优化。优化结果表明:优化后的动车齿轮箱结构的最大变形和最大应力有大幅度降低,能有效提高齿轮箱箱体的刚度和强度。文中结果可为设计性能优异的国产化高速动车齿轮箱提供数据支持。
文摘为得到清晰的0-1拓扑分布结构,在SIMP(solid isotropic microstructures withpenalization)和SRV(the sum of the reciprocal variables)方法的基础上提出了一种新的混合方法——SIMP-SRV方法,该方法将SIMP得到的优化结果用来初始化SRV方法的设计变量,再用SRV方法得到最终的优化目标。将SIMP-SRV方法应用于柔性机构的0-1拓扑优化设计中,得到了轮廓清晰的拓扑分布结构,完全消除了中间密度单元,从而证明了该方法的有效性。
