基于虚拟样机技术的某车悬架K&C特性仿真分析及硬点优化
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摘要
悬架系统作为汽车系统总成之一,对汽车操纵稳定性和平顺性有重要影响。本文以研究汽车操纵稳定性为切入点,结合某车底盘开发项目建立了原型车的悬架虚拟样机模型,并且与目标车实测K&C特性进行了仿真对比分析,找出原型车与目标车存在的特性差异。
然后根据自己设计的灵敏度计算方法找到影响悬架特性的关键点硬点坐标,通过响应面方法建立了悬架特性与悬架关键点硬点坐标之间的回归模型,分别进行单目标和多目标优化,并对优化后的结果与目标车悬架特性进行对比,说明优化方法的可行性,为悬架正向开发流程中合理布置硬点坐标提供了参考。
Vehicle suspension system as an important part of vehicle chassis system plays an important role in the influence of whole vehicle handling and riding characteristic, as a result the research of vehicle suspension system becomes an important field in the study of vehicle. Suspension K&C characteristic as an important research direction of suspension system, plays a decisive role in the influence of vehicle handling characteristic. The paper mainly does the research on the model building of suspension system and simulation while making optimization of suspension hardpoints based on a vehicle chassis system developing project.
Traditional chassis developing process does not consider the influence of hardpoints on the suspension K&C characteristic at the beginning while solely considering whole vehicle assemble based on which make car models, and then making adjustment and whole vehicle tuning. This flow not only costs much time and money but also tolerates small changes in the hardpoints coordinates, as a result we mainly adjust suspension characteristic through bushing tuning and the effect is not so well. With the development of computer tech and virtual prototyping tech, vehicle companies try to develop new chassis development flow, building suspension virtual prototype based on vehicle assemble firstly and then making simulation. Comparing the difference between prototype and target vehicle and making optimization of suspension hardpoints can guarantee the characteristic of suspension system before car model building and decrease the period of chassis development. The main contents of the paper are as following:
Firstly, build the front and rear suspension system of prototype vehicle while building flexible bodies of stabilizing bar and longitudinal arm for the purpose of guaranteeing the model precision. And confirm the stiffness of springs in the front and rear suspension system based on designed frequency of prototype vehicle.
Secondly, evaluation guide lines and simulation analysis means of vehicle suspension K&C characteristic are proposed. The target vehicle K&C characteristic is made on the Lotus suspension testrig and then a comparison is made between prototype vehicle simulation results and target vehicle experiment results which help find the difference between both vehicles such as the characteristic of toe angle in the front suspension under wheel parallel travel circumstance.
Thirdly, key hardpoints which have great influence on the front and rear suspension K&C characteristic are obtained by using a sensitivity calculation mean developed by the author and the paper prove the exactness of the mean through geometry analysis.
Fourthly, using front suspension toe angle characteristic as an example, single target optimization is made utilizing the key hardpoints obtained by sensitivity analysis. A regression model is obtained through using RSM mean which is optimized in hard points adjustable scope. By optimization, the toe angle of prototype vehicle is about the same as target vehicle while the other characteristic changes a little, which proves the feasibility of single target optimization.
Fifthly, the paper obtains the regression model between toe angle, base change, track change and suspension key hardpoints aiming at solving the problem of multi objective optimization in the tuning of vehicle. A comparison is made between prototype vehicle and target vehicle suspension characteristic, though not all the characteristic of prototype vehicle is the same as that of target vehicle, but a great improvement is obtained after optimization which proves multi objective optimization mean usable for the improvement of suspension K&C characteristic.
Finally, the paper probes into the confirmation of power coefficient used in multi objective optimization for the purpose of decreasing the complexity of multi objective optimization. A radar picture is made based on multi objective optimization feasible scope according to engineering practice, which facilitates engineers making suspension characteristic matches. The paper proposeαsuper plane based mean to help confirm the power coefficients according to engineering practice.
Suspension K&C characteristic is not only influenced by hard points but also influenced by bushing stiffness, especially the C characteristic of suspension is always adjusted by bushing tuning. The paper does not do research on the influence of bushing, and also as a result of the chassis long development period, the paper does not make a comparison between prototype practical vehicle characteristic and the simulation results. In multi objective optimization, the confirmation of the power coefficients is need to be studied deeper, how to obtain favorable results which are much nearer to engineering practice will be the pivot of the next period of research. The sensitivity analysis mean, optimization mean, the confirmation of multi objective optimization power coefficients and radar picture of multi objective optimization feasible scope are achievements in practical vehicle chassis development which can be the reference of chassis development.
然后根据自己设计的灵敏度计算方法找到影响悬架特性的关键点硬点坐标,通过响应面方法建立了悬架特性与悬架关键点硬点坐标之间的回归模型,分别进行单目标和多目标优化,并对优化后的结果与目标车悬架特性进行对比,说明优化方法的可行性,为悬架正向开发流程中合理布置硬点坐标提供了参考。
Vehicle suspension system as an important part of vehicle chassis system plays an important role in the influence of whole vehicle handling and riding characteristic, as a result the research of vehicle suspension system becomes an important field in the study of vehicle. Suspension K&C characteristic as an important research direction of suspension system, plays a decisive role in the influence of vehicle handling characteristic. The paper mainly does the research on the model building of suspension system and simulation while making optimization of suspension hardpoints based on a vehicle chassis system developing project.
Traditional chassis developing process does not consider the influence of hardpoints on the suspension K&C characteristic at the beginning while solely considering whole vehicle assemble based on which make car models, and then making adjustment and whole vehicle tuning. This flow not only costs much time and money but also tolerates small changes in the hardpoints coordinates, as a result we mainly adjust suspension characteristic through bushing tuning and the effect is not so well. With the development of computer tech and virtual prototyping tech, vehicle companies try to develop new chassis development flow, building suspension virtual prototype based on vehicle assemble firstly and then making simulation. Comparing the difference between prototype and target vehicle and making optimization of suspension hardpoints can guarantee the characteristic of suspension system before car model building and decrease the period of chassis development. The main contents of the paper are as following:
Firstly, build the front and rear suspension system of prototype vehicle while building flexible bodies of stabilizing bar and longitudinal arm for the purpose of guaranteeing the model precision. And confirm the stiffness of springs in the front and rear suspension system based on designed frequency of prototype vehicle.
Secondly, evaluation guide lines and simulation analysis means of vehicle suspension K&C characteristic are proposed. The target vehicle K&C characteristic is made on the Lotus suspension testrig and then a comparison is made between prototype vehicle simulation results and target vehicle experiment results which help find the difference between both vehicles such as the characteristic of toe angle in the front suspension under wheel parallel travel circumstance.
Thirdly, key hardpoints which have great influence on the front and rear suspension K&C characteristic are obtained by using a sensitivity calculation mean developed by the author and the paper prove the exactness of the mean through geometry analysis.
Fourthly, using front suspension toe angle characteristic as an example, single target optimization is made utilizing the key hardpoints obtained by sensitivity analysis. A regression model is obtained through using RSM mean which is optimized in hard points adjustable scope. By optimization, the toe angle of prototype vehicle is about the same as target vehicle while the other characteristic changes a little, which proves the feasibility of single target optimization.
Fifthly, the paper obtains the regression model between toe angle, base change, track change and suspension key hardpoints aiming at solving the problem of multi objective optimization in the tuning of vehicle. A comparison is made between prototype vehicle and target vehicle suspension characteristic, though not all the characteristic of prototype vehicle is the same as that of target vehicle, but a great improvement is obtained after optimization which proves multi objective optimization mean usable for the improvement of suspension K&C characteristic.
Finally, the paper probes into the confirmation of power coefficient used in multi objective optimization for the purpose of decreasing the complexity of multi objective optimization. A radar picture is made based on multi objective optimization feasible scope according to engineering practice, which facilitates engineers making suspension characteristic matches. The paper proposeαsuper plane based mean to help confirm the power coefficients according to engineering practice.
Suspension K&C characteristic is not only influenced by hard points but also influenced by bushing stiffness, especially the C characteristic of suspension is always adjusted by bushing tuning. The paper does not do research on the influence of bushing, and also as a result of the chassis long development period, the paper does not make a comparison between prototype practical vehicle characteristic and the simulation results. In multi objective optimization, the confirmation of the power coefficients is need to be studied deeper, how to obtain favorable results which are much nearer to engineering practice will be the pivot of the next period of research. The sensitivity analysis mean, optimization mean, the confirmation of multi objective optimization power coefficients and radar picture of multi objective optimization feasible scope are achievements in practical vehicle chassis development which can be the reference of chassis development.
引文
[1]陈家瑞.汽车构造第二版(下册)[M].机械工业出版社,2005.1.
[2]余志生.汽车理论第三版[M].机械工业出版社,2000.10.
[3]王望宇.汽车设计第四版[M].机械工业出版社,2004.8.
[4]郭孔辉.汽车操纵动力学[M].吉林科学技术出版社,1991.
[5]魏道高.汽车前轮定位参数研究与展望[J].合肥工业大学学报,2004年12月.
[6] JORNSEN REIMPELL, HERUTSTOLL. Automotive Chassis: Engineering Principles [M]. London: Arnold,1996.
[7] M. MARCACCI, C. LIMONE, P. BRUTTINI, F. CARATELLI AND W. ROSELLINI. Development of Scooter Suspensions for Comfort Optimization[C]. SAE,2003-32-0070.
[8]姬鹏,杨树凯,朱天军.导向机构对悬架定位参数影响的仿真分析.拖拉机与农用运输车[J].200802,1(35).
[9]王爽.悬架运动学及弹性运动学建模分析与评价[D].吉林大学硕士学位论文,2004.5.
[10] XIAOBO YANG, SUDHAKAR MEDEPALLI. Sensitivities of Suspension Bushings on Vehicle Impact Harshness Performances[C].SAE,2005-01-0827.
[11] STAWOMIR DZIERZEK. Experiment-Based Modeling of Cylindrical Rubber Bushings for the Simulation of Wheel Suspension Dynamic Behavior[C].SAE,2000-01-0095.
[12]雷雨成,李峰.橡胶衬套刚度对悬架系统影响的研究[J].上海汽车,2004.11.
[13] M.B.GERRARD. Kinematic Suspension Linkages-A Model for Their Behavior and a Procedure for Their Design[C].SAE,2002-01-0281.
[14]赵振东.汽车悬架橡胶衬套刚度的改进设计[J].机械科学与技术,2006.2.
[15] XUTING WU AND SUBHASH RAKHEJA. Dynamic Performance of Suspension Seats Under Vehicular Vibration and Shock Excitations[C].SAE,1999-01-1304.
[16] S. RAKHEJA, A. K. W. AHMED and X. YANG. Optimal Suspension Damping for Improved Driver- and Road-Friendliness of Urban Buses[C].SAE,1999-01-3728.
[17]阿达姆.措莫托[著],黄锡朋,解春阳[译].汽车行驶性能[M].北京:科学普及出版社,1992.9.
[18]安部正人[著],陈幸波[译].汽车的运动与操纵[M].北京:机械工业出版社,1998.
[19] CAPUTO and M.SPINA. Sensitivity of Suspension System Performance to Bushing Stiffness Variation-An Evaluation Methodology[C].SAE,2003-01-0237.
[20] M.B.GERRARD. The Equivalent Elastic Mechanism: A Tool for the Analysis and the Design of Compliant Suspension Linkages[C].SAE,2005-01-1719.
[21]陈欣,林逸,王焕明,等.弹性元件对悬架性能的影响[J] .长春:汽车技术,1996.5.
[22]林逸.轿车悬架系统空间多体弹性运动学研究[J].中国公路学报,2000.7.
[23]林逸,陈欣,王望予.独立悬架中的橡胶减振元件对汽车性能的影响[J].吉林工业大学学报,1993.3.
[24]张越今.汽车多体动力学及计算机仿真[M] .吉林科学技术出版社,1998.
[25] [德]耶尔森?赖姆帕尔著,张洪欣,余卓平译.汽车底盘基础[M].科学普及出版社,1992.
[26]凌雯.桑塔纳轿车悬架运动学/弹性运动学ADAMS仿真分析[D].同济大学,1999.5.
[27]吕振华.五连杆悬架的刚体运动学和弹性运动学分析[J].汽车技术,2002.11.
[28] LEE UNKOO and AHN BYEONGEUI. A Method to Analyze“The Imaginary Kingpin Axis”in Multi-Link Type Suspension Systems[C]. SAE,930262.
[29]祁宏钟,雷雨成,沈浩.确定五连杆悬架虚主销轴线的近似数值方法[J].机械设计与制造.
[30]王爽.某微车悬架KnC特性研究及其对整车操纵稳定性的影响[D],吉林大学博士学位论文,2008.12.
[31]林逸.带有非完整约束的汽车多刚体系统动力学研究[D].长春:吉林工业大学,1989.
[32]上官文斌,黄虎,刘德清.多刚体系统动力学在汽车独立悬架运动分析中的应用[J].汽车工程,1992.
[33] RAMESH EDARA and SHAN SHIH. Effective Use of Multibody Dynamics Simulation in Vehicle Suspension System Development[C].SAE,2004-01-1547.
[34]乔明侠.基于多体动力学的汽车平顺性仿真分析及悬架参数优化.合肥工业大学硕士论文[D],200504.
[35]刘红军,明平顺,等.ADAMS在汽车操纵稳定性中的应用研究[J].武汉理工大学学报,2003年04期.
[36]凌雯.ADAMS在悬架运动学和弹性运动学仿真中的应用[J].上海铁道大学,2001.5.
[37]宋传学,蔡章林.基于ADAMS/CAR的双横臂独立悬架建模与仿真[J].吉林大学学报(工学版),2004.10.
[38] ROBERT A.JONES. Understanding vehicle roll Using Mechanism Simulation software[C].SAE,199-01-0030.
[39] MARCELO MEIRA, DOURADO NUNES. Dynamic Suspension Simulation[C].SAE,2003-01-3648.
[40] FERNANDO BUARQUE. Experimental and Numerical Analysis of an Off-road Vehicle Suspension[C].SAE,2003-01-3650.
[41] JOONHONG PARK , JOONMO YI and DAEHYEONG LEE. Investigation into Suspension Dynamic Compliance Characteristics Using Direct Measurement and Simulation[C].SAE,2004-01-1065.
[42] DAVID E. WOODS, BADIH A. JAWAD. Numerical Design of Racecar Suspension Parameters[C]. SAE,1999-01-2257.
[43] MEHDI AHMADIAN. On-Vehicle Evaluation of Heavy Truck Suspension Kinematics[C].SAE,2003-01-3394.
[44] HIROYUKI SHIMATANI, SATOSHI MURATA, KEI WATANABE,TAKAYUKI KANEKO AND HIDEKI SAKAI. Development of Torsion Beam Rear Suspension with Toe Control Links[C].SAE,1999-01-0045.
[45] KEUM-SHIK HONG, DONG-SEOP JEON and WAN-SUK YOO. A New Model and an Optimal Pole-Placement Control of the Macpherson Suspension System[C].SAE,1999-01-1331.
[46] PHILLIP MORSE. Using K&C Measurements for Practical Suspension Tuning and Development[C].SAE,2004-01-3547.
[47] JEFF WARFFORD and NORMAN FREY. A Facility for the Measurement of HeavyTruck Chassis and Suspension Kinematics and Elastokinematics[C].SAE,2004-01-2609.
[48]张云清,陈宏,项俊,陈立平.麦克弗逊前悬架参数灵敏度分析及优化[J].机械设计与制造,200504
[49]任露泉.优化技术[M].北京:机械工业出版社,1987.
[50] REZA KAZEMI and KAVEH SOLTANI. The Effects of Important Parameters on Vehicle Rollover with Sensitivity Analysis[C].SAE,2003-01-0170.
[51]张云清.麦克弗逊前悬架参数灵敏度分析及改进[J].机械设计与制造,2005.4.
[52]逄淑一.某汽车悬架运动学及弹性运动学灵敏度分析及改进[D].吉林大学硕士论文,2007.05.
[53] TAEOH TAK and SUNGHUN CHUNG, HYUNGHO CHUN. An Optimal Design Software For Vehicle Suspension Systems[C].SAE,2000-01-1618.
[54] YI LIN, WENZHANG ZHAN, YAN LIU AND XIN ZHONG. Dynamics Simulation Research on Rigid-Elastic Coupling System of Car Suspension[C].SAE,2000-01-1622.
[55]夏长高,邵跃华,丁华.麦弗逊悬架运动学分析与结构参数优化[J].农业机械学报,2005年12月.
[56] Using ADAMS/Insight. 2002.
[57]邵建敏,张学昌,阎玉光.机械多目标优化设计中的权值确定[J].郑州轻工业学院学报,200106,2:32-33.
[58]李治多,王明强.多工况载荷下连续体结构拓扑优化设计研究[J].现代制造工程,2008,9:70-73.
[2]余志生.汽车理论第三版[M].机械工业出版社,2000.10.
[3]王望宇.汽车设计第四版[M].机械工业出版社,2004.8.
[4]郭孔辉.汽车操纵动力学[M].吉林科学技术出版社,1991.
[5]魏道高.汽车前轮定位参数研究与展望[J].合肥工业大学学报,2004年12月.
[6] JORNSEN REIMPELL, HERUTSTOLL. Automotive Chassis: Engineering Principles [M]. London: Arnold,1996.
[7] M. MARCACCI, C. LIMONE, P. BRUTTINI, F. CARATELLI AND W. ROSELLINI. Development of Scooter Suspensions for Comfort Optimization[C]. SAE,2003-32-0070.
[8]姬鹏,杨树凯,朱天军.导向机构对悬架定位参数影响的仿真分析.拖拉机与农用运输车[J].200802,1(35).
[9]王爽.悬架运动学及弹性运动学建模分析与评价[D].吉林大学硕士学位论文,2004.5.
[10] XIAOBO YANG, SUDHAKAR MEDEPALLI. Sensitivities of Suspension Bushings on Vehicle Impact Harshness Performances[C].SAE,2005-01-0827.
[11] STAWOMIR DZIERZEK. Experiment-Based Modeling of Cylindrical Rubber Bushings for the Simulation of Wheel Suspension Dynamic Behavior[C].SAE,2000-01-0095.
[12]雷雨成,李峰.橡胶衬套刚度对悬架系统影响的研究[J].上海汽车,2004.11.
[13] M.B.GERRARD. Kinematic Suspension Linkages-A Model for Their Behavior and a Procedure for Their Design[C].SAE,2002-01-0281.
[14]赵振东.汽车悬架橡胶衬套刚度的改进设计[J].机械科学与技术,2006.2.
[15] XUTING WU AND SUBHASH RAKHEJA. Dynamic Performance of Suspension Seats Under Vehicular Vibration and Shock Excitations[C].SAE,1999-01-1304.
[16] S. RAKHEJA, A. K. W. AHMED and X. YANG. Optimal Suspension Damping for Improved Driver- and Road-Friendliness of Urban Buses[C].SAE,1999-01-3728.
[17]阿达姆.措莫托[著],黄锡朋,解春阳[译].汽车行驶性能[M].北京:科学普及出版社,1992.9.
[18]安部正人[著],陈幸波[译].汽车的运动与操纵[M].北京:机械工业出版社,1998.
[19] CAPUTO and M.SPINA. Sensitivity of Suspension System Performance to Bushing Stiffness Variation-An Evaluation Methodology[C].SAE,2003-01-0237.
[20] M.B.GERRARD. The Equivalent Elastic Mechanism: A Tool for the Analysis and the Design of Compliant Suspension Linkages[C].SAE,2005-01-1719.
[21]陈欣,林逸,王焕明,等.弹性元件对悬架性能的影响[J] .长春:汽车技术,1996.5.
[22]林逸.轿车悬架系统空间多体弹性运动学研究[J].中国公路学报,2000.7.
[23]林逸,陈欣,王望予.独立悬架中的橡胶减振元件对汽车性能的影响[J].吉林工业大学学报,1993.3.
[24]张越今.汽车多体动力学及计算机仿真[M] .吉林科学技术出版社,1998.
[25] [德]耶尔森?赖姆帕尔著,张洪欣,余卓平译.汽车底盘基础[M].科学普及出版社,1992.
[26]凌雯.桑塔纳轿车悬架运动学/弹性运动学ADAMS仿真分析[D].同济大学,1999.5.
[27]吕振华.五连杆悬架的刚体运动学和弹性运动学分析[J].汽车技术,2002.11.
[28] LEE UNKOO and AHN BYEONGEUI. A Method to Analyze“The Imaginary Kingpin Axis”in Multi-Link Type Suspension Systems[C]. SAE,930262.
[29]祁宏钟,雷雨成,沈浩.确定五连杆悬架虚主销轴线的近似数值方法[J].机械设计与制造.
[30]王爽.某微车悬架KnC特性研究及其对整车操纵稳定性的影响[D],吉林大学博士学位论文,2008.12.
[31]林逸.带有非完整约束的汽车多刚体系统动力学研究[D].长春:吉林工业大学,1989.
[32]上官文斌,黄虎,刘德清.多刚体系统动力学在汽车独立悬架运动分析中的应用[J].汽车工程,1992.
[33] RAMESH EDARA and SHAN SHIH. Effective Use of Multibody Dynamics Simulation in Vehicle Suspension System Development[C].SAE,2004-01-1547.
[34]乔明侠.基于多体动力学的汽车平顺性仿真分析及悬架参数优化.合肥工业大学硕士论文[D],200504.
[35]刘红军,明平顺,等.ADAMS在汽车操纵稳定性中的应用研究[J].武汉理工大学学报,2003年04期.
[36]凌雯.ADAMS在悬架运动学和弹性运动学仿真中的应用[J].上海铁道大学,2001.5.
[37]宋传学,蔡章林.基于ADAMS/CAR的双横臂独立悬架建模与仿真[J].吉林大学学报(工学版),2004.10.
[38] ROBERT A.JONES. Understanding vehicle roll Using Mechanism Simulation software[C].SAE,199-01-0030.
[39] MARCELO MEIRA, DOURADO NUNES. Dynamic Suspension Simulation[C].SAE,2003-01-3648.
[40] FERNANDO BUARQUE. Experimental and Numerical Analysis of an Off-road Vehicle Suspension[C].SAE,2003-01-3650.
[41] JOONHONG PARK , JOONMO YI and DAEHYEONG LEE. Investigation into Suspension Dynamic Compliance Characteristics Using Direct Measurement and Simulation[C].SAE,2004-01-1065.
[42] DAVID E. WOODS, BADIH A. JAWAD. Numerical Design of Racecar Suspension Parameters[C]. SAE,1999-01-2257.
[43] MEHDI AHMADIAN. On-Vehicle Evaluation of Heavy Truck Suspension Kinematics[C].SAE,2003-01-3394.
[44] HIROYUKI SHIMATANI, SATOSHI MURATA, KEI WATANABE,TAKAYUKI KANEKO AND HIDEKI SAKAI. Development of Torsion Beam Rear Suspension with Toe Control Links[C].SAE,1999-01-0045.
[45] KEUM-SHIK HONG, DONG-SEOP JEON and WAN-SUK YOO. A New Model and an Optimal Pole-Placement Control of the Macpherson Suspension System[C].SAE,1999-01-1331.
[46] PHILLIP MORSE. Using K&C Measurements for Practical Suspension Tuning and Development[C].SAE,2004-01-3547.
[47] JEFF WARFFORD and NORMAN FREY. A Facility for the Measurement of HeavyTruck Chassis and Suspension Kinematics and Elastokinematics[C].SAE,2004-01-2609.
[48]张云清,陈宏,项俊,陈立平.麦克弗逊前悬架参数灵敏度分析及优化[J].机械设计与制造,200504
[49]任露泉.优化技术[M].北京:机械工业出版社,1987.
[50] REZA KAZEMI and KAVEH SOLTANI. The Effects of Important Parameters on Vehicle Rollover with Sensitivity Analysis[C].SAE,2003-01-0170.
[51]张云清.麦克弗逊前悬架参数灵敏度分析及改进[J].机械设计与制造,2005.4.
[52]逄淑一.某汽车悬架运动学及弹性运动学灵敏度分析及改进[D].吉林大学硕士论文,2007.05.
[53] TAEOH TAK and SUNGHUN CHUNG, HYUNGHO CHUN. An Optimal Design Software For Vehicle Suspension Systems[C].SAE,2000-01-1618.
[54] YI LIN, WENZHANG ZHAN, YAN LIU AND XIN ZHONG. Dynamics Simulation Research on Rigid-Elastic Coupling System of Car Suspension[C].SAE,2000-01-1622.
[55]夏长高,邵跃华,丁华.麦弗逊悬架运动学分析与结构参数优化[J].农业机械学报,2005年12月.
[56] Using ADAMS/Insight. 2002.
[57]邵建敏,张学昌,阎玉光.机械多目标优化设计中的权值确定[J].郑州轻工业学院学报,200106,2:32-33.
[58]李治多,王明强.多工况载荷下连续体结构拓扑优化设计研究[J].现代制造工程,2008,9:70-73.