简谐力激励下多组件结构系统的整体优化设计
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摘要
多组件结构系统整体优化设计通过协同优化支撑结构拓扑构型和组件布局来使结构系统的位移响应最小。本文提出通过模态加速度法(MAM)求解多组件结构系统的位移响应,并以位移响应值最小作为优化目标;引入多点约束(MPC)方法模拟组件与设计域间的铆钉或螺栓连接形式;采用有限包络圆法(FCM)来避免组件之间及组件与设计域边界产生干涉。建立了多组件结构系统整体优化问题的数学模型,并对动响应目标函数关于设计变量的灵敏度进行了推导。最后,通过几个算例验证了整体优化方法在简谐力激励下求解问题的可行性及其在实际问题中的有效性。
This paper presents an integrated layout and topology optimization of the multi-component structure system under harmonic force excitation.The configuration of the supporting structure and the component layout are simultaneously optimized to minimize the displacement responses that are obtained by using the Mode Acceleration Method(MAM).The MultiPoint Constraint(MPC)scheme is employed to simulate the rivets and bolts connecting components and supporting structures.The Finite Circle Method(FCM)is used to avoid overlaps among different components and boundaries of supporting structures.The mathematical model for the integrated layout and topology optimization of multi-component structure system is established,and the sensitivities of the objective function to design variables are deduced.Numerical examples are presented to demonstrate the effectiveness and validity of the proposed method for solving problems under harmonic force excitation.
This paper presents an integrated layout and topology optimization of the multi-component structure system under harmonic force excitation.The configuration of the supporting structure and the component layout are simultaneously optimized to minimize the displacement responses that are obtained by using the Mode Acceleration Method(MAM).The MultiPoint Constraint(MPC)scheme is employed to simulate the rivets and bolts connecting components and supporting structures.The Finite Circle Method(FCM)is used to avoid overlaps among different components and boundaries of supporting structures.The mathematical model for the integrated layout and topology optimization of multi-component structure system is established,and the sensitivities of the objective function to design variables are deduced.Numerical examples are presented to demonstrate the effectiveness and validity of the proposed method for solving problems under harmonic force excitation.
引文
[1]BENDSOE M P,KIKUCHI N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71(2):197-224.
[2]HOU J,ZHU J,HE F,et al.Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads[J].Chinese Journal of Aeronautics,2017,30(4):1441-1450.
[3]GUO X,CHENG G D.Recent development in structural design and optimization[J].Acta Mechanica Sinica,2010,26(6):807-823.
[4]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.
[5]JIANG T,CHIREHDAST M.A systems approach to structural topology optimization:Designing optimal connections[J].Journal of Mechanical Design,1997,119(1):40-47.
[6]LI Q,STEVEN G P,XIE Y M.Evolutionary structural optimization for connection topology design of,multi-component systems[J].Engineering Computations,2001,18(3/4):460-479.
[7]ZHU J H,ZHANG W H,BECKERS P.Integrated layout design of multi-component system[J].International Journal for Numerical Methods in Engineering,2009,78(6):631-651.
[8]QIAN Z,ANANTHASURESH G K.Optimal embedding of rigid objects in the topology design of structures[J].Mechanics Based Design of Structures and Machines,2004,32(2):165-193.
[9]KANG Z,WANG Y.Integrated topology optimization with embedded movable holes based on combined description by material density and level sets[J].Computer Methods in Applied Mechanics&Engineering,2013,255:1-13.
[10]ZHANG W,ZHONG W,GUO X.Explicit layout control in optimal design of structural systems with multiple embedding components[J].Computer Methods in Applied Mechanics&Engineering,2015,290:290-313.
[11]ZHU J H,GAO H H,ZHANG W H,et al.A multipoint constraints based integrated layout and topology optimization design of multi-component systems[J].Structural&Multidisciplinary Optimization,2015,51(2):397-407.
[12]PEDERSEN N L.Maximization of eigenvalues using topology optimization[J].Structural&Multidisciplinary Optimization,2000,20(1):2-11.
[13]DU J,OLHOFF N.Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps[J].Structural&Multidisciplinary Optimization,2007,34(2):91-110.
[14]TSAI T D,CHENG C C.Structural design for desired eigenfrequencies and mode shapes using topology optimization[J].Structural&Multidisciplinary Optimization,2013,47(5):673-686.
[15]MA Z D,KIKUCHI N,CHENG H C.Topological design for vibrating structures[J].Computer Methods in Applied Mechanics&Engineering,1995,121(1-4):259-280.
[16]JOG C S.Topology design of structures subjected to periodic loading[J].Journal of Sound&Vibration,2002,253(3):687-709.
[17]SHU L,WANG M Y,FANG Z,et al.Level set based structural topology optimization for minimizing frequency response[J].Journal of Sound&Vibration,2011,330(24):5820-5834.
[18]YOON G H.Structural topology optimization for frequency response problem using model reduction schemes[J].Computer Methods in Applied Mechanics&Engineering,2010,199(25-28):1744-1763.
[19]BESSELINK B,TABAK U,LUTOWSKA A,et al.A comparison of model reduction techniques from structural dynamics,numerical mathematics and systems and control[J].Journal of Sound&Vibration,2013,332(19):4403-4422.
[20]LIU H,ZHANG W H,GAO T.A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations[J].Structural&Multidisciplinary Optimization,2015,51(6):1321-1333.
[21]刘虎,朱继宏,张卫红.简谐载荷作用下连续体结构位移响应拓扑优化[J].机械制造,2012,50(7):27-30.LIU H,ZHU J H,ZHANG W H.Topological optimization of continuue structures with displacement response under harmonic load[J].Machinary,2012,50(7):27-30(in Chinese).
[22]张卫红,郭文杰,朱继宏.部件级多组件结构系统的整体式拓扑布局优化[J].航空学报,2015,36(8):2662-2669.ZHANG W H,GUO W J,ZHU J H.Integrated layout and topology optimization design of multi-component systems with assembly units[J].Acta Aeronautica et Astronautica Sinica,2015,36(8):2662-2669(in Chinese).
[23]ZHANG Q,ZHANG W H,ZHU J H,et al.Layout optimization of multi-component structures under static loads and random excitations[J].Engineering Structures,2012,43(43):120-128.
[24]LIU G R,QUEK S S.The finite element method:A practical course[M].Oxford:Butterworth-Heinemann,2003:271-277.
[25]CLOUGH R W,PENZIEN J,GRIFFIN D S.结构动力学[M].陈嘉炜,译.台北:科技图书股份有限公司,1981:271-284.CLOUGH R W,PENZIEN J,GRIFFIN D S.Dynamics of structures[M].CHEN J W,translated.Taipei:Technology Books Co.Ltd.,1981:271-284(in Chinese).
[26]BENDSOE M P,SIGMUND O.Material interpolation schemes in topology optimization[J].Archive of Applied Mechanics,1999,69(9):635-654.
[27]朱继宏,张卫红,邱克鹏.结构动力学拓扑优化局部模态现象分析[J].航空学报,2006,27(4):619-623.ZHU J H,ZHANG W H,QIU K P.Investigation of localized modes in topology optimization of dynamic structures[J].Acta Aeronautica et Astronautica Sinica,2006,27(4):619-623(in Chinese).
[28]STOLPE M,SVANBERG K.An alternative interpolation scheme for minimum compliance topology optimization[J].Structural&Multidisciplinary Optimization,2001,22(2):116-124.
[29]ZHU J H,BECKERS P,ZHANG W H.On the multicomponent layout design with inertial force[J].Journal of Computational&Applied Mathematics,2010,234(7):2222-2230.
[30]BENDSOE M P,SIGMUND O.Topology optimization:Theory,methods,and applications[M].Berlin:Springer Science&Business Media,2013:16-17.
[31]OLHOFF N,DU J.Topological design of continuum structures subjected to forced vibration[C]∥Proceedings of 6th World Congresses of Structural and Multidisciplinary Optimization.Rio de Janeiro:Engopt Orgnization,2005:1-8.
[32]OLHOFF N,DU J.Generalized incremental frequency method for topological design of continuum structures for minimum dynamic compliance subject to forced vibration at aprescribed low or high value of the excitation frequency[J].Structural and Multidisciplinary Optimization,2016,5(54):1113-1141.
[2]HOU J,ZHU J,HE F,et al.Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads[J].Chinese Journal of Aeronautics,2017,30(4):1441-1450.
[3]GUO X,CHENG G D.Recent development in structural design and optimization[J].Acta Mechanica Sinica,2010,26(6):807-823.
[4]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.
[5]JIANG T,CHIREHDAST M.A systems approach to structural topology optimization:Designing optimal connections[J].Journal of Mechanical Design,1997,119(1):40-47.
[6]LI Q,STEVEN G P,XIE Y M.Evolutionary structural optimization for connection topology design of,multi-component systems[J].Engineering Computations,2001,18(3/4):460-479.
[7]ZHU J H,ZHANG W H,BECKERS P.Integrated layout design of multi-component system[J].International Journal for Numerical Methods in Engineering,2009,78(6):631-651.
[8]QIAN Z,ANANTHASURESH G K.Optimal embedding of rigid objects in the topology design of structures[J].Mechanics Based Design of Structures and Machines,2004,32(2):165-193.
[9]KANG Z,WANG Y.Integrated topology optimization with embedded movable holes based on combined description by material density and level sets[J].Computer Methods in Applied Mechanics&Engineering,2013,255:1-13.
[10]ZHANG W,ZHONG W,GUO X.Explicit layout control in optimal design of structural systems with multiple embedding components[J].Computer Methods in Applied Mechanics&Engineering,2015,290:290-313.
[11]ZHU J H,GAO H H,ZHANG W H,et al.A multipoint constraints based integrated layout and topology optimization design of multi-component systems[J].Structural&Multidisciplinary Optimization,2015,51(2):397-407.
[12]PEDERSEN N L.Maximization of eigenvalues using topology optimization[J].Structural&Multidisciplinary Optimization,2000,20(1):2-11.
[13]DU J,OLHOFF N.Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps[J].Structural&Multidisciplinary Optimization,2007,34(2):91-110.
[14]TSAI T D,CHENG C C.Structural design for desired eigenfrequencies and mode shapes using topology optimization[J].Structural&Multidisciplinary Optimization,2013,47(5):673-686.
[15]MA Z D,KIKUCHI N,CHENG H C.Topological design for vibrating structures[J].Computer Methods in Applied Mechanics&Engineering,1995,121(1-4):259-280.
[16]JOG C S.Topology design of structures subjected to periodic loading[J].Journal of Sound&Vibration,2002,253(3):687-709.
[17]SHU L,WANG M Y,FANG Z,et al.Level set based structural topology optimization for minimizing frequency response[J].Journal of Sound&Vibration,2011,330(24):5820-5834.
[18]YOON G H.Structural topology optimization for frequency response problem using model reduction schemes[J].Computer Methods in Applied Mechanics&Engineering,2010,199(25-28):1744-1763.
[19]BESSELINK B,TABAK U,LUTOWSKA A,et al.A comparison of model reduction techniques from structural dynamics,numerical mathematics and systems and control[J].Journal of Sound&Vibration,2013,332(19):4403-4422.
[20]LIU H,ZHANG W H,GAO T.A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations[J].Structural&Multidisciplinary Optimization,2015,51(6):1321-1333.
[21]刘虎,朱继宏,张卫红.简谐载荷作用下连续体结构位移响应拓扑优化[J].机械制造,2012,50(7):27-30.LIU H,ZHU J H,ZHANG W H.Topological optimization of continuue structures with displacement response under harmonic load[J].Machinary,2012,50(7):27-30(in Chinese).
[22]张卫红,郭文杰,朱继宏.部件级多组件结构系统的整体式拓扑布局优化[J].航空学报,2015,36(8):2662-2669.ZHANG W H,GUO W J,ZHU J H.Integrated layout and topology optimization design of multi-component systems with assembly units[J].Acta Aeronautica et Astronautica Sinica,2015,36(8):2662-2669(in Chinese).
[23]ZHANG Q,ZHANG W H,ZHU J H,et al.Layout optimization of multi-component structures under static loads and random excitations[J].Engineering Structures,2012,43(43):120-128.
[24]LIU G R,QUEK S S.The finite element method:A practical course[M].Oxford:Butterworth-Heinemann,2003:271-277.
[25]CLOUGH R W,PENZIEN J,GRIFFIN D S.结构动力学[M].陈嘉炜,译.台北:科技图书股份有限公司,1981:271-284.CLOUGH R W,PENZIEN J,GRIFFIN D S.Dynamics of structures[M].CHEN J W,translated.Taipei:Technology Books Co.Ltd.,1981:271-284(in Chinese).
[26]BENDSOE M P,SIGMUND O.Material interpolation schemes in topology optimization[J].Archive of Applied Mechanics,1999,69(9):635-654.
[27]朱继宏,张卫红,邱克鹏.结构动力学拓扑优化局部模态现象分析[J].航空学报,2006,27(4):619-623.ZHU J H,ZHANG W H,QIU K P.Investigation of localized modes in topology optimization of dynamic structures[J].Acta Aeronautica et Astronautica Sinica,2006,27(4):619-623(in Chinese).
[28]STOLPE M,SVANBERG K.An alternative interpolation scheme for minimum compliance topology optimization[J].Structural&Multidisciplinary Optimization,2001,22(2):116-124.
[29]ZHU J H,BECKERS P,ZHANG W H.On the multicomponent layout design with inertial force[J].Journal of Computational&Applied Mathematics,2010,234(7):2222-2230.
[30]BENDSOE M P,SIGMUND O.Topology optimization:Theory,methods,and applications[M].Berlin:Springer Science&Business Media,2013:16-17.
[31]OLHOFF N,DU J.Topological design of continuum structures subjected to forced vibration[C]∥Proceedings of 6th World Congresses of Structural and Multidisciplinary Optimization.Rio de Janeiro:Engopt Orgnization,2005:1-8.
[32]OLHOFF N,DU J.Generalized incremental frequency method for topological design of continuum structures for minimum dynamic compliance subject to forced vibration at aprescribed low or high value of the excitation frequency[J].Structural and Multidisciplinary Optimization,2016,5(54):1113-1141.