基于Ordered-RAMP模型的热固耦合结构多材料拓扑优化方法
|
摘要
针对传统单材料热固耦合拓扑优化设计难以实现结构材料与性能综合最优的问题,提出一种基于变密度理论有序材料属性有理近似模型的多材料拓扑优化方法.该方法通过搭建比例系数与平移系数,将多种材料属性采用[0,1]连续分布的单设计变量进行描述,并研究和比较与有序固体各向同行惩罚微结构模型的优缺点;其次借助归一化加权方法定义以结构柔度最小化和散热弱度最小化为目标函数的数学模型.结合设计变量敏度分析,详细推导多材料、多目标条件下热固耦合结构拓扑优化的迭代公式.通过数值算例分析对比了不同权系数以及不同材料属性组合对优化结果的影响;结果表明,所提出的优化方法在热固耦合结构多材料多目标拓扑优化设计中具有可行性和有效性.
In general, it is difficult for single material thermo-elastic coupling topology optimization to obtain the comprehensive optimum of structural materials and properties. In this study, a multi-material topology optimization approach based on the ordered rational approximation of material properties(Ordered-RAMP) is proposed. In this method, the proportional and translation coefficients are established and the associated materials properties are described by a single design variable with [0,1] continuous distribution. The pros and cons of the proposed method were investigated and compared with the ordered solid isotropic microstructures with penalization(Ordered-SIMP). The normalized weighting method is introduced to construct the multi-objective function with minimization of structural compliance and heat dissipation, followed by sensitivity analysis of design variables. The iterative formation of thermo-elastic coupling topology optimization is derived under the multi-material and multi-objective conditions. The effects of weight coefficients and materials combination on the optimal results were analyzed through numerical examples. The results are shown that the proposed method is feasible and efficient to the multi-material-based ther-mo-elastic coupling topology optimization problems.
In general, it is difficult for single material thermo-elastic coupling topology optimization to obtain the comprehensive optimum of structural materials and properties. In this study, a multi-material topology optimization approach based on the ordered rational approximation of material properties(Ordered-RAMP) is proposed. In this method, the proportional and translation coefficients are established and the associated materials properties are described by a single design variable with [0,1] continuous distribution. The pros and cons of the proposed method were investigated and compared with the ordered solid isotropic microstructures with penalization(Ordered-SIMP). The normalized weighting method is introduced to construct the multi-objective function with minimization of structural compliance and heat dissipation, followed by sensitivity analysis of design variables. The iterative formation of thermo-elastic coupling topology optimization is derived under the multi-material and multi-objective conditions. The effects of weight coefficients and materials combination on the optimal results were analyzed through numerical examples. The results are shown that the proposed method is feasible and efficient to the multi-material-based ther-mo-elastic coupling topology optimization problems.
引文
[1]Zuo Kongtian,Qian Qin,Zhao Yudong,et al.Research on the topology optimization about thermo-structural coupling field[J].Acta Mechanica Solida Sinica,2005,26(4):447-452(in Chinese)(左孔天,钱勤,赵雨东,等.热固耦合结构的拓扑优化设计研究[J].固体力学学报,2005,26(4):447-452)
[2]Sun Shiping,Zhang Weihong.Topology optimization design of thermo-elastic structure[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(6):878-887(in Chinese)(孙士平,张卫红.热弹性结构的拓扑优化设计[J].力学学报,2009,41(6):878-887)
[3]Li Dongmei,Zhang Xianmin,Wang Nianfeng,et al.Topology optimization of thermo-mechanical coupling structures based on reliability constraint[J].Journal of South China University of Technology:Natural Science Edition,2011,39(6):42-46(in Chinese)(李冬梅,张宪民,王念峰,等.基于可靠性约束的热固耦合结构拓扑优化[J].华南理工大学学报:自然科学版,2011,39(6):42-46)
[4]Gao T,Zhang W H.Topology optimization involving thermo-elastic stress loads[J].Structural and Multidisciplinary Optimization,2010,42(5):725-738
[5]Hou J,Zhu J H,Li Q.On the topology optimization of elastic supporting structures under thermomechanical loads[J].International Journal of Aerospace Engineering,2016,2016:Article No.7372603
[6]Deng S G,Suresh K.Topology optimization under thermo-elastic buckling[J].Structural and Multidisciplinary Optimization,2017,55(5):1759-1772
[7]Sigmund O,Torquato S.Design of materials with extreme thermal expansion using a three-phase topology optimization method[J].Journal of the Mechanics and Physics of Solids,1997,45(6):1037-1067
[8]Yin L,Ananthasuresh G K.Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme[J].Structural and Multidisciplinary Optimization,2001,23(1):49-62
[9]Zhou S W,Wang M Y.Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition[J].Structural and Multidisciplinary Optimization,2007,33(2):89-111
[10]Tavakoli R,Mohseni S M.Alternating active-phase algorithm for multimaterial topology optimization problems:a 115-line MATLAB implementation[J].Structural and Multidisciplinary Optimization,2014,49(4):621-642
[11]Wang M Y,Wang X M.‘‘Color’’level sets:a multi-phase method for structural topology optimization with multiple materials[J].Computer Methods in Applied Mechanics and Engineering,2004,193(6-8):469-496
[12]Ramani A.A pseudo-sensitivity based discrete-variable approach to structural topology optimization with multiple materials[J].Structural and Multidisciplinary Optimization,2009,41(6):913-934
[13]Gao T,Xu P L,Zhang W H.Topology optimization of thermo-elastic structures with multiple materials under mass constraint[J].Computers and Structures,2016,173:150-160
[14]Bends?e M P,Sigmund O.Topology optimization-theory,methods and application[M].Heidelberg:Springer,2003
[15]Zuo W J,Saitou K.Multi-material topology optimization using ordered SIMP interpolation[J].Structural and Multidisciplinary Optimization,2017,55(2):477-491
[16]Gersborg-Hansen A,Bends?e M P,Sigmund O.Topology optimization of heat conduction problems using the finite volume method[J].Structural and Multidisciplinary Optimization,2006,31(4):251-259
[17]Chen Yongdang,Zhang Jianhua,Tong Hongjie,et al.Variable density and multi-load topology optimization method for rocket sled chassis design[J].Journal of Computer-Aided Design&Computer Graphics,2012,24(8):1108-1112(in Chinese)(陈永当,张建华,仝鸿杰,等.面向火箭滑车底盘设计的变密度多载荷拓扑优化方法[J].计算机辅助设计与图形学学报,2012,24(8):1108-1112)
[18]Luo Z,Yang J Z,Chen L P.A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures[J].Aerospace Science and Technology,2006,10(5):364-373
[19]Sigmund O.A 99 line topology optimization code written in Matlab[J].Structural and Multidisciplinary Optimization,2001,21(2):120-127
[20]Long Kai,Zhao Hongwei.A modified optimality criterion method for gray elements suppression[J].Journal of Computer-Aided Design&Computer Graphics,2010,22(12):2197-2201(in Chinese)(龙凯,赵红伟.抑制灰度单元的改进优化准则法[J].计算机辅助设计与图形学学报,2010,22(12):2197-2201)
[2]Sun Shiping,Zhang Weihong.Topology optimization design of thermo-elastic structure[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(6):878-887(in Chinese)(孙士平,张卫红.热弹性结构的拓扑优化设计[J].力学学报,2009,41(6):878-887)
[3]Li Dongmei,Zhang Xianmin,Wang Nianfeng,et al.Topology optimization of thermo-mechanical coupling structures based on reliability constraint[J].Journal of South China University of Technology:Natural Science Edition,2011,39(6):42-46(in Chinese)(李冬梅,张宪民,王念峰,等.基于可靠性约束的热固耦合结构拓扑优化[J].华南理工大学学报:自然科学版,2011,39(6):42-46)
[4]Gao T,Zhang W H.Topology optimization involving thermo-elastic stress loads[J].Structural and Multidisciplinary Optimization,2010,42(5):725-738
[5]Hou J,Zhu J H,Li Q.On the topology optimization of elastic supporting structures under thermomechanical loads[J].International Journal of Aerospace Engineering,2016,2016:Article No.7372603
[6]Deng S G,Suresh K.Topology optimization under thermo-elastic buckling[J].Structural and Multidisciplinary Optimization,2017,55(5):1759-1772
[7]Sigmund O,Torquato S.Design of materials with extreme thermal expansion using a three-phase topology optimization method[J].Journal of the Mechanics and Physics of Solids,1997,45(6):1037-1067
[8]Yin L,Ananthasuresh G K.Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme[J].Structural and Multidisciplinary Optimization,2001,23(1):49-62
[9]Zhou S W,Wang M Y.Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition[J].Structural and Multidisciplinary Optimization,2007,33(2):89-111
[10]Tavakoli R,Mohseni S M.Alternating active-phase algorithm for multimaterial topology optimization problems:a 115-line MATLAB implementation[J].Structural and Multidisciplinary Optimization,2014,49(4):621-642
[11]Wang M Y,Wang X M.‘‘Color’’level sets:a multi-phase method for structural topology optimization with multiple materials[J].Computer Methods in Applied Mechanics and Engineering,2004,193(6-8):469-496
[12]Ramani A.A pseudo-sensitivity based discrete-variable approach to structural topology optimization with multiple materials[J].Structural and Multidisciplinary Optimization,2009,41(6):913-934
[13]Gao T,Xu P L,Zhang W H.Topology optimization of thermo-elastic structures with multiple materials under mass constraint[J].Computers and Structures,2016,173:150-160
[14]Bends?e M P,Sigmund O.Topology optimization-theory,methods and application[M].Heidelberg:Springer,2003
[15]Zuo W J,Saitou K.Multi-material topology optimization using ordered SIMP interpolation[J].Structural and Multidisciplinary Optimization,2017,55(2):477-491
[16]Gersborg-Hansen A,Bends?e M P,Sigmund O.Topology optimization of heat conduction problems using the finite volume method[J].Structural and Multidisciplinary Optimization,2006,31(4):251-259
[17]Chen Yongdang,Zhang Jianhua,Tong Hongjie,et al.Variable density and multi-load topology optimization method for rocket sled chassis design[J].Journal of Computer-Aided Design&Computer Graphics,2012,24(8):1108-1112(in Chinese)(陈永当,张建华,仝鸿杰,等.面向火箭滑车底盘设计的变密度多载荷拓扑优化方法[J].计算机辅助设计与图形学学报,2012,24(8):1108-1112)
[18]Luo Z,Yang J Z,Chen L P.A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures[J].Aerospace Science and Technology,2006,10(5):364-373
[19]Sigmund O.A 99 line topology optimization code written in Matlab[J].Structural and Multidisciplinary Optimization,2001,21(2):120-127
[20]Long Kai,Zhao Hongwei.A modified optimality criterion method for gray elements suppression[J].Journal of Computer-Aided Design&Computer Graphics,2010,22(12):2197-2201(in Chinese)(龙凯,赵红伟.抑制灰度单元的改进优化准则法[J].计算机辅助设计与图形学学报,2010,22(12):2197-2201)