The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously.Nodal displacement of macrostructure and effective thermal ...The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously.Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the loadcarrying capabilities and the thermal insulation properties.The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.展开更多
The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of ...The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.展开更多
为了进一步研究连续体结构拓扑优化模型的合理性和可行性,基于独立、连续、映射(independent continuous mapping,ICM)方法,在满足结构位移约束的条件下,通过引入复合指数形式过滤函数对位移约束下质量最小化(minimum weight with a dis...为了进一步研究连续体结构拓扑优化模型的合理性和可行性,基于独立、连续、映射(independent continuous mapping,ICM)方法,在满足结构位移约束的条件下,通过引入复合指数形式过滤函数对位移约束下质量最小化(minimum weight with a displacement constraint,MWDC)模型进行了改进,建立了基于独立连续变量和复合指数函数的位移约束平面连续体结构拓扑优化模型,并进行了优化求解.同时,利用M语言,基于Matlab软件平台,开发了相应的拓扑优化计算程序,并针对4种典型平面连续体结构进行了数值验证,分别比较分析了体积约束下的柔顺度最小化(minimum compliance with a volume constraint,MCVC)模型、MWDC模型以及改进的MWDC模型所得到的最优拓扑结构.数值结果表明:采用复合指数形式过滤函数改进的MWDC优化模型迭代次数更少,优化求解计算效率更高.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11202078, 51405123)the Fundamental Research Funds for the Central Universities (Grant 2017MS077)
文摘The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously.Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the loadcarrying capabilities and the thermal insulation properties.The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.
基金Sponsored by the Ministerial Level Advanced Research Foundation (010896367)
文摘The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.
文摘为了进一步研究连续体结构拓扑优化模型的合理性和可行性,基于独立、连续、映射(independent continuous mapping,ICM)方法,在满足结构位移约束的条件下,通过引入复合指数形式过滤函数对位移约束下质量最小化(minimum weight with a displacement constraint,MWDC)模型进行了改进,建立了基于独立连续变量和复合指数函数的位移约束平面连续体结构拓扑优化模型,并进行了优化求解.同时,利用M语言,基于Matlab软件平台,开发了相应的拓扑优化计算程序,并针对4种典型平面连续体结构进行了数值验证,分别比较分析了体积约束下的柔顺度最小化(minimum compliance with a volume constraint,MCVC)模型、MWDC模型以及改进的MWDC模型所得到的最优拓扑结构.数值结果表明:采用复合指数形式过滤函数改进的MWDC优化模型迭代次数更少,优化求解计算效率更高.
基金Supported by the National Natural Science Foundation of China(10472003)Beijing Natural Science Foundation (3002002)Beijing Educational Committee and the American MSC Company(KM200410005019)
