基于功能截面分解的大型横梁拓扑优化
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摘要
针对复杂载荷工况下横梁等大型三维结构件拓扑优化结果可读性差、无法对结构优化提供有效指导的问题,提出基于功能截面分解的拓扑优化方法。基于力的分解与等效原理,将三维实体分解为三个平面内的二维功能截面,根据各功能截面的受力方式确定其抗弯或抗扭属性;在此基础上,分别对两个主要承载的功能截面进行二维拓扑优化分析,并综合二维功能截面分析结果完成三维实体的整体拓扑优化,实现了将三维实体拓扑优化问题转化为二维功能截面的拓扑优化问题。以CXK5463车铣加工中心横梁为例,对结构拓扑优化效果进行了验证,仿真实验结果表明,功能截面分解方法可以得到清晰的应力传递路径,在保证横梁静动态特性基本稳定的基础上,横梁减重12.67%,优化效果较为明显。提出的方法可为大型、重型复杂结构件的拓扑优化研究提供借鉴与参考。
According to the poor readability of a three-dimensional structural topology optimization model for crossbeam with complex load conditions and the difficulty to get an effective guidance on structure optimization,a decomposition of the functional sections topology optimization method was proposed.Based on the principles of decomposition and equivalence of forces,the three-dimensional solid was decomposed into two-dimensional functional sections in three planes.The properties of resistance to bend or torsion were determined according the stress modes of each functional section;then the two-dimensional topology optimization of each of the two main functional sections was analyzed.The topology optimization of the three-dimensional solid might be accomplished by integrating the results of the analysis.At last,the goal that converting 3Dtopology optimization into 2Dtopology optimization might be completed.The crossbeam of turning-milling machining center CXK5463 was used as an example to verify the effect of the proposed method.The simulation results show that:a clear stress transfer path may be got,keeping the static and a dynamic characteristics of the crossbeam stable.The total weight is reduced by 12.67%.The results of the topology optimization are obvious and the helpful instruction and reference may be provided for the topology optimization of large?heavy complex machinery by this method.
According to the poor readability of a three-dimensional structural topology optimization model for crossbeam with complex load conditions and the difficulty to get an effective guidance on structure optimization,a decomposition of the functional sections topology optimization method was proposed.Based on the principles of decomposition and equivalence of forces,the three-dimensional solid was decomposed into two-dimensional functional sections in three planes.The properties of resistance to bend or torsion were determined according the stress modes of each functional section;then the two-dimensional topology optimization of each of the two main functional sections was analyzed.The topology optimization of the three-dimensional solid might be accomplished by integrating the results of the analysis.At last,the goal that converting 3Dtopology optimization into 2Dtopology optimization might be completed.The crossbeam of turning-milling machining center CXK5463 was used as an example to verify the effect of the proposed method.The simulation results show that:a clear stress transfer path may be got,keeping the static and a dynamic characteristics of the crossbeam stable.The total weight is reduced by 12.67%.The results of the topology optimization are obvious and the helpful instruction and reference may be provided for the topology optimization of large?heavy complex machinery by this method.
引文
[1]张氢,高倩,秦仙蓉,等.一种由整体到局部的机械结构分层优化模型[J].机械科学与技术,2010,29(11):1433-1437.Zhang Qing,Gao Qian,Qin Xianrong,et al.A Global to Local Hierarchical Optimization Model of Mechanical Structures[J].Mechanical Science and Technology for Aerospace Engineering,2010,29(11):1433-1437.
[2]王欣,黄琳,高媛,等.起重机伸缩臂截面拓扑优化[J].大连理工大学学报,2009,49(3):374-379.Wang Xin,Huang Lin,Gao Yuan,et al.Topological Optimization for Crane Telescopic Boom-section[J].Journal of Dalian University of Technology,2009,49(3):374-379.
[3]饶柳生,侯亮,潘勇军.基于拓扑优化的机床立柱筋板改进[J].机械设计与研究,2010,26(1):87-92.Rao Liusheng,Hou Liang,Pan Yongjun.Improvement of the Rib Plate in Machine Tools Column Based on Topology Optimization[J].Machine Design and Research,2010,26(1):87-92.
[4]隋允康,任旭春,龙连春,等.基于ICM方法的刚架拓扑优化[J].计算力学学报,2003,20(3):286-289.Sui Yunkang,Ren Xuchun,Long Lianchun,et al.Topological Optimization of Frame Based on ICM Method[J].Chinese Journal of Computational Mechanics,2003,20(3):286-289.
[5]隋允康,叶红玲,杜家政.结构拓扑优化的发展及其模型转化为独立层次的迫切性[J].工程力学,2005,22(增):107-118.Sui Yunkang,Ye Hongling,Du Jiazheng.Development of Structural Topological Optimization and Imminency of Its Model Transformation into Independent Level[J].Engineering Mechanics,2005,22(S):107-118.
[6]叶红玲,隋允康.基于ICM方法三维连续体结构拓扑优化[J].固体力学学报,2006,27(4):387-393.Ye Hongling,Sui Yunkang.ICM-based Topological Optimization of Three-dimensional Continuum Structure[J].Acta Mechanica Solida Sinica,2006,27(4):387-393.
[7]朱润,隋允康.基于ICM方法的多工况位移约束下板壳结构拓扑优化设计[J].固体力学学报,2012,33(1):81-90.Zhu Run,Sui Yunkang.Topological Optimization of Plate-and Shell-like Structures with Displacement Constraints under Multi-state Loadings Based on ICM Method[J].Chinese Journal of Solid Mechanics,2012,33(1):81-90.
[8]满佳,张连洪,陈永亮.基于元结构的机床结构可适应优化设计方法[J].中国机械工程,2010,21(1):51-54.Man Jia,Zhang Lianhong,Chen Yongliang.An Adaptable Optimization Design Method of Machine Tool Structures Based on Unit Structure[J].China Mechanical Engineering,2010,21(1):51-54.
[9]汪列隆,朱壮瑞,张建润.基于APDL的机床大件筋板结构尺寸的优化设计[J].轻工机械,2006,24(4):60-62.Wang Lielong,Zhu Zhuangrui,Zhang Jianrun.Study on Design for Structure and Size Optimization of Beamsheet on Big Part in Machine Tool Based on APDL[J].Light Industry Machinery,2006,24(4):60-62.
[10]梅莉,孙智孝,姬鹏博,等.基于拓扑和尺寸优化的翼肋类结构设计研究[J].飞机设计,2013,33(2):8-12.Mei Li,Sun Zhixiao,Ji Pengbo,et al.The Design Study of the Rib-Like Structure Based on Topology and Size Optimization[J].Aircraft Design,2013,33(2):8-12.
[11]邢晓辉,王洪川,王贵飞,等.基于灵敏度分析的数控机床床身尺寸优化设计[J].组合机床与自动化加工技术,2013(11):5-8.Xing Xiaohui,Wang Hongchuan,Wang Guifei,et al.Size Optimization Design of the Lathe Bed of CNC Machine Based on Sensitivity Analysis[J].Modular Machine Tool&Automatic Manufacturing Technique,2013(11):5-8.
[12]王晓煜,贾振元,杨帆,等.龙门加工中心横梁部件的拓扑优化设计与分析[J].制造技术与机床,2009(11):64-68.Wang Xiaoyu,Jia Zhenyuan,Yang Fan,et al.The Topological Optimization of Design and Analysis for Gantry Machine Tool Crossbeam Component[J].Design and Research,2009(11):64-68.
[13]Querin O M,Young V,Steven G P,et al.Computational Efficiency and Validation of Bi-directional Evolutionary Structural Optimization[J].Computer Methods in Applied Mechanics and Engineering,2000,189(2):559-573.
[14]荣见华,姜节胜,胡德文,等.基于应力及其灵敏度的结构拓扑渐进优化方法[J].力学学报,2003,35(5):584-591.Rong Jianhua,Jiang Jiesheng,Hu Dewen,et al.A Structural Topology Evolutionary Optimization Method Based on Stresses and Their Sensitivity[J].Acta Mechanica Sinica,2003,35(5):584-591.
[15]Chen Tingyu,Lin Chiayang.Determination of Optimum Design Spaces for Topology Optimization[J].Finite Elements in Analysis and Design,2000,36:1-16.
[16]荣见华,姜节胜,徐飞鸿,等.一种基于应力的双方向结构拓扑优化算法[J].计算力学学报,2004,21(3):322-329.Rong Jianhua,Jiang Jiesheng,Xu Feihong,et al.A Bi-directional Algorithm of Structural Topology Optimization[J].Chinese Journal of Computational Mechanics,2004,21(3):322-329.
[17]荣见华,唐国金,杨振兴,等.一种三维结构拓扑优化设计方法[J].固体力学学报,2005,26(3):289-296.Rong Jianhua,Tang Guojin,Yang Zhenxing,et al.A Three-dimension Structural Topology Optimization Design Method[J].Acta Mechanica Solida Sinica,2005,26(3):289-296.
[18]荣见华,姜节胜,颜东煌,等.基于人工材料的结构拓扑渐进优化设计[J].工程力学,2004,21(5):64-71.Rong Jianhua,Jiang Jiesheng,Yan Donghuang,et al.Evolutionary Optimization Design of Structural Topology Based on Man-made Material[J].Engineering Mechanics,2004,21(5):64-71.
[19]荣见华,郑健龙,徐飞鸿.结构动力修改及优化设计[M].北京:人民交通出版社,2002.
[20]孔文秦.连续体结构双向渐进优化方法研究[D].南京:南京航空航天大学,2005.
[2]王欣,黄琳,高媛,等.起重机伸缩臂截面拓扑优化[J].大连理工大学学报,2009,49(3):374-379.Wang Xin,Huang Lin,Gao Yuan,et al.Topological Optimization for Crane Telescopic Boom-section[J].Journal of Dalian University of Technology,2009,49(3):374-379.
[3]饶柳生,侯亮,潘勇军.基于拓扑优化的机床立柱筋板改进[J].机械设计与研究,2010,26(1):87-92.Rao Liusheng,Hou Liang,Pan Yongjun.Improvement of the Rib Plate in Machine Tools Column Based on Topology Optimization[J].Machine Design and Research,2010,26(1):87-92.
[4]隋允康,任旭春,龙连春,等.基于ICM方法的刚架拓扑优化[J].计算力学学报,2003,20(3):286-289.Sui Yunkang,Ren Xuchun,Long Lianchun,et al.Topological Optimization of Frame Based on ICM Method[J].Chinese Journal of Computational Mechanics,2003,20(3):286-289.
[5]隋允康,叶红玲,杜家政.结构拓扑优化的发展及其模型转化为独立层次的迫切性[J].工程力学,2005,22(增):107-118.Sui Yunkang,Ye Hongling,Du Jiazheng.Development of Structural Topological Optimization and Imminency of Its Model Transformation into Independent Level[J].Engineering Mechanics,2005,22(S):107-118.
[6]叶红玲,隋允康.基于ICM方法三维连续体结构拓扑优化[J].固体力学学报,2006,27(4):387-393.Ye Hongling,Sui Yunkang.ICM-based Topological Optimization of Three-dimensional Continuum Structure[J].Acta Mechanica Solida Sinica,2006,27(4):387-393.
[7]朱润,隋允康.基于ICM方法的多工况位移约束下板壳结构拓扑优化设计[J].固体力学学报,2012,33(1):81-90.Zhu Run,Sui Yunkang.Topological Optimization of Plate-and Shell-like Structures with Displacement Constraints under Multi-state Loadings Based on ICM Method[J].Chinese Journal of Solid Mechanics,2012,33(1):81-90.
[8]满佳,张连洪,陈永亮.基于元结构的机床结构可适应优化设计方法[J].中国机械工程,2010,21(1):51-54.Man Jia,Zhang Lianhong,Chen Yongliang.An Adaptable Optimization Design Method of Machine Tool Structures Based on Unit Structure[J].China Mechanical Engineering,2010,21(1):51-54.
[9]汪列隆,朱壮瑞,张建润.基于APDL的机床大件筋板结构尺寸的优化设计[J].轻工机械,2006,24(4):60-62.Wang Lielong,Zhu Zhuangrui,Zhang Jianrun.Study on Design for Structure and Size Optimization of Beamsheet on Big Part in Machine Tool Based on APDL[J].Light Industry Machinery,2006,24(4):60-62.
[10]梅莉,孙智孝,姬鹏博,等.基于拓扑和尺寸优化的翼肋类结构设计研究[J].飞机设计,2013,33(2):8-12.Mei Li,Sun Zhixiao,Ji Pengbo,et al.The Design Study of the Rib-Like Structure Based on Topology and Size Optimization[J].Aircraft Design,2013,33(2):8-12.
[11]邢晓辉,王洪川,王贵飞,等.基于灵敏度分析的数控机床床身尺寸优化设计[J].组合机床与自动化加工技术,2013(11):5-8.Xing Xiaohui,Wang Hongchuan,Wang Guifei,et al.Size Optimization Design of the Lathe Bed of CNC Machine Based on Sensitivity Analysis[J].Modular Machine Tool&Automatic Manufacturing Technique,2013(11):5-8.
[12]王晓煜,贾振元,杨帆,等.龙门加工中心横梁部件的拓扑优化设计与分析[J].制造技术与机床,2009(11):64-68.Wang Xiaoyu,Jia Zhenyuan,Yang Fan,et al.The Topological Optimization of Design and Analysis for Gantry Machine Tool Crossbeam Component[J].Design and Research,2009(11):64-68.
[13]Querin O M,Young V,Steven G P,et al.Computational Efficiency and Validation of Bi-directional Evolutionary Structural Optimization[J].Computer Methods in Applied Mechanics and Engineering,2000,189(2):559-573.
[14]荣见华,姜节胜,胡德文,等.基于应力及其灵敏度的结构拓扑渐进优化方法[J].力学学报,2003,35(5):584-591.Rong Jianhua,Jiang Jiesheng,Hu Dewen,et al.A Structural Topology Evolutionary Optimization Method Based on Stresses and Their Sensitivity[J].Acta Mechanica Sinica,2003,35(5):584-591.
[15]Chen Tingyu,Lin Chiayang.Determination of Optimum Design Spaces for Topology Optimization[J].Finite Elements in Analysis and Design,2000,36:1-16.
[16]荣见华,姜节胜,徐飞鸿,等.一种基于应力的双方向结构拓扑优化算法[J].计算力学学报,2004,21(3):322-329.Rong Jianhua,Jiang Jiesheng,Xu Feihong,et al.A Bi-directional Algorithm of Structural Topology Optimization[J].Chinese Journal of Computational Mechanics,2004,21(3):322-329.
[17]荣见华,唐国金,杨振兴,等.一种三维结构拓扑优化设计方法[J].固体力学学报,2005,26(3):289-296.Rong Jianhua,Tang Guojin,Yang Zhenxing,et al.A Three-dimension Structural Topology Optimization Design Method[J].Acta Mechanica Solida Sinica,2005,26(3):289-296.
[18]荣见华,姜节胜,颜东煌,等.基于人工材料的结构拓扑渐进优化设计[J].工程力学,2004,21(5):64-71.Rong Jianhua,Jiang Jiesheng,Yan Donghuang,et al.Evolutionary Optimization Design of Structural Topology Based on Man-made Material[J].Engineering Mechanics,2004,21(5):64-71.
[19]荣见华,郑健龙,徐飞鸿.结构动力修改及优化设计[M].北京:人民交通出版社,2002.
[20]孔文秦.连续体结构双向渐进优化方法研究[D].南京:南京航空航天大学,2005.