带有区域性惩罚因子的双向渐进结构优化方法
|
摘要
针对传统的拓扑优化方法欠缺考虑增材制造工艺约束,如果优化模型存在大面积悬垂、封闭空腔等工艺几何特征将增加打印及后处理操作的复杂度的问题,提出带有区域性惩罚因子的双向渐进拓扑优化方法.首先考虑增材制造工艺特征约束,使得优化结果具有良好的可打印性;然后对模型进行网格划分,根据单元体所在的区域定义区域性惩罚因子,保证区域性惩罚因子由外表面向内核逐渐增大;最后结合有限元分析,以区域性惩罚因子对单元体的计算应力进行惩罚,决策单元体的保留与删减.通过数值实验,与传统的双向渐进结构拓扑优化算法对比的结果表明,该方法可以改变空腔形貌特征、减少垂悬面积、均衡模型应力分布,提升了拓扑优化模型的可打印效果.
Traditional structural optimization methods do not take full account of the process constraints from additive manufacturing. Manufacturing process and post-processing will become more difficult if the optimized model has process geometric characteristics such as large overhangs and closed cavities. This paper presents bidirectional evolutionary structural optimization method with regional penalty factor. It makes optimized results printable by considering process feature constraints. Regional penalty factors were defined according to the region where elements belonged to. Factors should gradually increase from outer toward inner core while meshing. Stress of the element would be penalized with the factor to decide its retention or deletion after finite element analysis. Compared with traditional bidirectional evolutionary structural optimization method by numeric experiments, the method can change the morphology of cavity, reduce overhang area, balance the stress distribution of the model, and improve the printable effect of the topology optimization model.
Traditional structural optimization methods do not take full account of the process constraints from additive manufacturing. Manufacturing process and post-processing will become more difficult if the optimized model has process geometric characteristics such as large overhangs and closed cavities. This paper presents bidirectional evolutionary structural optimization method with regional penalty factor. It makes optimized results printable by considering process feature constraints. Regional penalty factors were defined according to the region where elements belonged to. Factors should gradually increase from outer toward inner core while meshing. Stress of the element would be penalized with the factor to decide its retention or deletion after finite element analysis. Compared with traditional bidirectional evolutionary structural optimization method by numeric experiments, the method can change the morphology of cavity, reduce overhang area, balance the stress distribution of the model, and improve the printable effect of the topology optimization model.
引文
[1]Song B,Zhao X,Li S,et al.Differences in microstructure and properties between selective laser melting and traditional manufacturing for fabrication of metal parts:a review[J].Frontiers of Mechanical Engineering,2015,10(2):111-125
[2]Zhu J H,Zhang W H,Xia L.Topology optimization in aircraft and aerospace structures design[J].Archives of Computational Methods in Engineering,2016,23(4):595-622
[3]Michell A G M.The limits of economy of material in frame structure[J].The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1904,8(47):589-597
[4]Bendsoe M P,Kijuchi N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering.1988,71(2):197-224
[5]Mlejnek H P,Schirrmacher R.An engineer’s approach to optimal material distribution and shape finding[J].Computer Methods in Applied Mechanics and Engineering,1993,106(1/2):1-26
[6]Xie Y M,Steven G P.A simple evolutionary procedure for structural optimization[J].Computers&Structures,1993,49(5):885-896
[7]Querin O M,Steven G P,Xie Y M.Evolutionary structural optimisation(ESO)using a bidirectional algorithm[J].Engineering Computations,1998,15(8):1031-1048
[8]Hinton E,Sienz J.Fully stressed topological design of structures using an evolutionary procedure[J].Engineering Computations,1995,12(3):229-244
[9]Sigmund O.Design of material structures using topology optimization[D].Lyngby:Technical University of Denmark,1994
[10]Wu Yifan,Zheng Bailin,He Lyuyang,et al.Equivalent conversion method of gray-scale elements for SIMP in structures topology optimization[J].Journal of Computer-Aided Design&Computer Graphics,2017,29(4):759-767(in Chinese)(吴一帆,郑百林,何旅洋,等.结构拓扑优化变密度法的灰度单元等效转换方法[J].计算机辅助设计与图形学学报,2017,29(4):759-767)
[11]Qin Haoxing,An Zongwen,Sun Daoming.Improved guide-weight method on solving topology optimization problems and gray-scale filtering method[J].Journal of Computer-Aided Design&Computer Graphics,2015,27(10):2001-2007(in Chinese)(秦浩星,安宗文,孙道明.改进的导重法求解拓扑优化问题及灰度过滤技术[J].计算机辅助设计与图形学学报,2015,27(10):2001-2007)
[12]Nha Chu D,Xie Y M,Hira A,et al.Evolutionary structural optimization for problems with stiffness constraints[J].Finite Elements in Analysis and Design,1996,21(4):239-251
[13]Xie Y M,Steven G P.Optimal design of multiple load case structures using an evolutionary procedure[J].Engineering Computations,1994,11(4):295-302
[14]Zhu J H,Zhang W H,Qiu K P.Bi-directional evolutionary topology optimization using element replaceable method[J].Computational Mechanics,2007,40(1):97-109
[15]Yang X Y,Xie Y M,Steven G P,et al.Topology optimization for frequencies using an evolutionary method[J].Journal of Structural Engineering,1999,125(12):1432-1438
[16]Vicente W M,Picelli R,Pavanello R,et al.Topology optimization of frequency responses of fluid-structure interaction systems[J].Finite Elements in Analysis and Design,2015,98:1-13
[17]Picelli R,Vicente W M,Pavanello R,et al.Evolutionary topology optimization for natural frequency maximization problems considering acoustic-structure interaction[J].Finite Elements in Analysis and Design,2015,106:56-64
[18]Du J B,Olhoff N.Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps[J].Structural and Multidisciplinary Optimization,2007,34(2):91-110
[19]Yang Zhenxing,Rong Jianhua,Fu Jianlin.Frequency topology opimal design of three-dimensional structures[J].Journal of Vibration and Shock,2006,25(3):44-47(in Chinese)(杨振兴,荣见华,傅建林.三维结构的频率拓扑优化设计[J].振动与冲击,2006,25(3):44-47)
[20]Ye Hongling,Shen Jingxian,Sui Yunkang.Dynamic tological optimal design of three-dimensional continuum structures with frequencies constraints[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(6):1037-1045(in Chinese)(叶红玲,沈静娴,隋允康.频率约束的三维连续体结构动力拓扑优化设计[J].力学学报,2012,44(6):1037-1045)
[21]Seyranian A P,Lund E,Olhoff N.Multiple eigenvalues in structural optimization problems[J].Structural Optimization,1994,8(4):207-227
[22]Zhao J,Liu W J,Wu J H B.Determination of optimal build orientation based on satisfactory degree theory for RPT[J].International Journal of CAD/CAM,2006,6(1):51-58
[23]Das P,Chandran R,Samant R,et al.Optimum part build orientation in additive manufacturing for minimizing part errors and support structures[J].Procedia Manufacturing,2015,1:343-354
[24]Wu J,Wang C C L,Zhang X T,et al.Self-supporting rhombic infill structures for additive manufacturing[J].Computer-Aided Design,2016,80:32-42
[25]Leary M,Merli L,Torti F,et al.Optimal topology for additive manufacture:a method for enabling additive manufacture of support-free optimal structures[J].Materials&Design,2014,63:678-690
[26]Leary M,Babaee M,Brandt M,et al.Feasible build orientations for self-supporting fused deposition manufacture:a novel approach to space-filling tesselated geometries[J].Advanced Materials Research,2013,633:148-168
[27]Vanek J,Galicia J A G,Benes B.Clever support:efficient support structure generation for digital fabrication[J].Computer Graphics Forum,2014,33(5):117-125
[28]Mirzendehdel A M,Suresh K.Support structure constrained topology optimization for additive manufacturing[J].Computer-Aided Design,2016,81:1-13
[29]Langelaar M.Topology optimization of 3D self-supporting structures for additive manufacturing[J].Additive Manufacturing,2016,12:60-70
[30]Liu S,Li Q H,Chen W J,et al.An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures[J].Frontiers of Mechanical Engineering,2015,10(2):126-137
[2]Zhu J H,Zhang W H,Xia L.Topology optimization in aircraft and aerospace structures design[J].Archives of Computational Methods in Engineering,2016,23(4):595-622
[3]Michell A G M.The limits of economy of material in frame structure[J].The London,Edinburgh,and Dublin Philosophical Magazine and Journal of Science,1904,8(47):589-597
[4]Bendsoe M P,Kijuchi N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering.1988,71(2):197-224
[5]Mlejnek H P,Schirrmacher R.An engineer’s approach to optimal material distribution and shape finding[J].Computer Methods in Applied Mechanics and Engineering,1993,106(1/2):1-26
[6]Xie Y M,Steven G P.A simple evolutionary procedure for structural optimization[J].Computers&Structures,1993,49(5):885-896
[7]Querin O M,Steven G P,Xie Y M.Evolutionary structural optimisation(ESO)using a bidirectional algorithm[J].Engineering Computations,1998,15(8):1031-1048
[8]Hinton E,Sienz J.Fully stressed topological design of structures using an evolutionary procedure[J].Engineering Computations,1995,12(3):229-244
[9]Sigmund O.Design of material structures using topology optimization[D].Lyngby:Technical University of Denmark,1994
[10]Wu Yifan,Zheng Bailin,He Lyuyang,et al.Equivalent conversion method of gray-scale elements for SIMP in structures topology optimization[J].Journal of Computer-Aided Design&Computer Graphics,2017,29(4):759-767(in Chinese)(吴一帆,郑百林,何旅洋,等.结构拓扑优化变密度法的灰度单元等效转换方法[J].计算机辅助设计与图形学学报,2017,29(4):759-767)
[11]Qin Haoxing,An Zongwen,Sun Daoming.Improved guide-weight method on solving topology optimization problems and gray-scale filtering method[J].Journal of Computer-Aided Design&Computer Graphics,2015,27(10):2001-2007(in Chinese)(秦浩星,安宗文,孙道明.改进的导重法求解拓扑优化问题及灰度过滤技术[J].计算机辅助设计与图形学学报,2015,27(10):2001-2007)
[12]Nha Chu D,Xie Y M,Hira A,et al.Evolutionary structural optimization for problems with stiffness constraints[J].Finite Elements in Analysis and Design,1996,21(4):239-251
[13]Xie Y M,Steven G P.Optimal design of multiple load case structures using an evolutionary procedure[J].Engineering Computations,1994,11(4):295-302
[14]Zhu J H,Zhang W H,Qiu K P.Bi-directional evolutionary topology optimization using element replaceable method[J].Computational Mechanics,2007,40(1):97-109
[15]Yang X Y,Xie Y M,Steven G P,et al.Topology optimization for frequencies using an evolutionary method[J].Journal of Structural Engineering,1999,125(12):1432-1438
[16]Vicente W M,Picelli R,Pavanello R,et al.Topology optimization of frequency responses of fluid-structure interaction systems[J].Finite Elements in Analysis and Design,2015,98:1-13
[17]Picelli R,Vicente W M,Pavanello R,et al.Evolutionary topology optimization for natural frequency maximization problems considering acoustic-structure interaction[J].Finite Elements in Analysis and Design,2015,106:56-64
[18]Du J B,Olhoff N.Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps[J].Structural and Multidisciplinary Optimization,2007,34(2):91-110
[19]Yang Zhenxing,Rong Jianhua,Fu Jianlin.Frequency topology opimal design of three-dimensional structures[J].Journal of Vibration and Shock,2006,25(3):44-47(in Chinese)(杨振兴,荣见华,傅建林.三维结构的频率拓扑优化设计[J].振动与冲击,2006,25(3):44-47)
[20]Ye Hongling,Shen Jingxian,Sui Yunkang.Dynamic tological optimal design of three-dimensional continuum structures with frequencies constraints[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(6):1037-1045(in Chinese)(叶红玲,沈静娴,隋允康.频率约束的三维连续体结构动力拓扑优化设计[J].力学学报,2012,44(6):1037-1045)
[21]Seyranian A P,Lund E,Olhoff N.Multiple eigenvalues in structural optimization problems[J].Structural Optimization,1994,8(4):207-227
[22]Zhao J,Liu W J,Wu J H B.Determination of optimal build orientation based on satisfactory degree theory for RPT[J].International Journal of CAD/CAM,2006,6(1):51-58
[23]Das P,Chandran R,Samant R,et al.Optimum part build orientation in additive manufacturing for minimizing part errors and support structures[J].Procedia Manufacturing,2015,1:343-354
[24]Wu J,Wang C C L,Zhang X T,et al.Self-supporting rhombic infill structures for additive manufacturing[J].Computer-Aided Design,2016,80:32-42
[25]Leary M,Merli L,Torti F,et al.Optimal topology for additive manufacture:a method for enabling additive manufacture of support-free optimal structures[J].Materials&Design,2014,63:678-690
[26]Leary M,Babaee M,Brandt M,et al.Feasible build orientations for self-supporting fused deposition manufacture:a novel approach to space-filling tesselated geometries[J].Advanced Materials Research,2013,633:148-168
[27]Vanek J,Galicia J A G,Benes B.Clever support:efficient support structure generation for digital fabrication[J].Computer Graphics Forum,2014,33(5):117-125
[28]Mirzendehdel A M,Suresh K.Support structure constrained topology optimization for additive manufacturing[J].Computer-Aided Design,2016,81:1-13
[29]Langelaar M.Topology optimization of 3D self-supporting structures for additive manufacturing[J].Additive Manufacturing,2016,12:60-70
[30]Liu S,Li Q H,Chen W J,et al.An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures[J].Frontiers of Mechanical Engineering,2015,10(2):126-137