结构动力重分析算法研究与应用
|
摘要
随着中国航空航天、造船和汽车工业及土木工程的高速发展,结构设计趋向复杂化,针对复杂结构的力学分析和优化设计问题,已经远远超出传统经验设计方法所能解决的能力范畴。CAE技术的诞生在很大程度上弥补了经验设计的不足。目前,CAE分析已经成为结构设计的必需过程和步骤。随着人们对CAE技术的广泛应用和对计算精度要求的提高,计算模型变得越来越庞大。为了提高计算速度,人们在进行高性能计算机研究的同时,也在进行着改进求解算法,缩短计算时间的工作。
结合2009年国家自然科学基金面上项目《基于重分析理论的简化车身多单元框架结构截面参数快速优化研究》(项目编号:50975121)、2009年教育部高等学校博士点基金项目《亏损振动系统自适应重分析算法研究》(项目编号:20090061110022)和2008年度一汽集团科技创新项目《车身性能多目标优化平台建立》(项目编号:0837与093715),本文对结构动力重分析技术进行了研究,并对重分析算法与结构动力修改、结构优化的结合应用进行了讨论。
针对模态重分析问题,本文首次提出FSCA ( Frequency-Shift Combined Approximations)重分析方法,并与现有CA(Combined Approximations)和MCA(Modified Combined Approximations)重分析方法进行了对比分析。FSCA算法在对修改后结构进行模态分析的过程中,基于修改前的模态分析结果和矩阵分解信息,引入移频因子和Epsilon算法,通过移频基向量的线性组合加速,快速求解修改后结构的模态信息。FSCA算法解决了CA算法计算高阶模态误差较大的问题,并与MCA算法比较,计算量明显减少,并且计算精度得到提高。
基于预条件Lanczos静态重分析算法,提出了一种动力响应重分析的直接积分法。本方法对修改后结构的动力响应重分析问题,将直接积分法中的等效静力学问题应用预条件Lanczos算法进行重分析计算。本文针对结构动力响应分析的中心差分法、Houbolt方法、Wilson-θ方法和Newmark方法,分别给出重分析计算的方法,并以卡车车身左前轮激励下驾驶员座椅固定点的动力响应重分析问题为例,验证了算法的准确性。
基于本文提出的FSCA模态重分析算法,求解修改后结构动力响应重分析问题,提出了一种模态迭加重分析方法,通过FSCA算法进行修改后结构的模态计算,提高模态迭加法求解结构动力响应的计算效率。以卡车车身左后轮激励下驾驶员座椅固定点的动力响应重分析为例,验证了算法的正确性。
在重分析算法研究的基础上,分别讨论了结构修改和优化过程中常用的静力学灵敏度、模态灵敏度和动力响应灵敏度分析问题,并给出了应用重分析算法求解灵敏度问题的公式。基于结构灵敏度信息,结合结构动力修改的一阶、二阶Taylor展开表达式,给出求解结构动力修改逆问题的算法和算例。算例表明:在结构模态小修改时,一阶和二阶Taylor展开式均可确定合理的设计参数;当模态修改较大时,二阶Taylor展开式的优势更为明显。
基于SIMP(Solid Isotropic Material with Penalization model)加权应变能和准则法的拓扑优化方法,针对车身接头结构的静刚度约束,讨论了不同单元类型下的加强板结构设计问题,给出修改方案,并进行了验证分析。在某卡车车身多工况试验设计的基础上,采用结构重分析算法,快速计算不同试验点的刚度、模态和动力学特性,提取各响应参数,应用最小二乘技术构建结构优化的数学模型;在优化数学模型的基础上,应用外点罚函数法进行结构的优化设计,并讨论了不同罚因子下的结构优化结果。
With the rapid development of space, shipbuilding, automotive industry and civil engineering in China, the structural design is becoming more and more complex. The analysis and optimization of complex structures can not be solved by the traditional design method any more. The generation of CAE technology has made up this contribution. CAE is becoming a necessary process and step in structural design, and it is becoming more and more useful and common. With the structural model growing, the cost of the CAE computations is increasing. In order to improve the computational efficiency, some researchers devote themselves to the development of the HPC (High Performance Computer), while others are researching into the improved algorithm for fast computations.
This thesis is supported by National Natural Science Foundation of China“Fast Optimization of Cross-Sectional Parameters for Simplified Car Body Multi-Elements Frame Structure Based on Reanalysis Theory”(No.50975121), Specialized Research Fund for the Doctoral Program of Higher Education“The Research of Adaptive Reanalysis Algorithm of the Defective Vibration System”(No.20090061110022) and FAW Group Science and Technology Innovation Project“The Multi-Optimization Platform for Car-Body Performance”(No.0837and093715). The structural dynamic reanalysis algorithm is generated, and the applications of the reanalysis method in structural dynamic modifications and structural optimizations have been discussed in this thesis.
The Frequency-Shift Combined Approximations (FSCA) reanalysis method is first developed for structural vibration, and is compared with the Combined Approximations (CA) method and the Modified Combined Approximations (MCA) method. The FSCA method treats the modal reanalysis with frequency-shift factor and Epsilon algorithm, which have reduced the high mode calculation errors in CA method successfully. Compared to the MCA method, the cost of computations in FSCA method is reduced obviously.
Based on the Preconditioning Lanczos algorithm for static reanalysis, a method for dynamic response reanalysis is developed using immediate integration method. The Preconditioning Lanczos method is used for solving the equivalent static equations in the immediate integration. Based on the Central Difference method, Houbolt method, Wilson-θmethod and Newmark method, the dynamic response reanalysis algorithms are developed, respectively. A truck-body dynamic response reanalysis example is demonstrated for the accuracy of algorithms.
Based on the FSCA modal reanalysis, a dynamic response reanlysis method is developed using modal superposition method. The truck-body dynamic response reanalysis example is demonstrated for the accuracy.
Based on the research of reanalysis method, effective procedures for repeated sensitivity analysis of static problems, vibration problems and dynamic problems in structural modifications are developed. With the sensitivity information, the first order and second order Taylor expansions are used for solving the inverse problems of structural dynamic modification. Equations and examples are given to demonstrate the effect for the modal modifications.
Based on the Solid Isotropic Material with Penalization model (SIMP) method for topology optimization and the Optimization Criterion(OC) method, static stiffness problems of car-body joints are solved by using shell and solid finite elements, and schemes for the reinforcing plate are given for the joints structure, respectively. A truck-body size optimization is brought out using the experimental design, structural reanalysis method, least square regression and penalty function. The stiffness, modal frequency and dynamic parameters are calculated with the reanalysis method. Different penalty factors are introduced for testing the optimization process.
结合2009年国家自然科学基金面上项目《基于重分析理论的简化车身多单元框架结构截面参数快速优化研究》(项目编号:50975121)、2009年教育部高等学校博士点基金项目《亏损振动系统自适应重分析算法研究》(项目编号:20090061110022)和2008年度一汽集团科技创新项目《车身性能多目标优化平台建立》(项目编号:0837与093715),本文对结构动力重分析技术进行了研究,并对重分析算法与结构动力修改、结构优化的结合应用进行了讨论。
针对模态重分析问题,本文首次提出FSCA ( Frequency-Shift Combined Approximations)重分析方法,并与现有CA(Combined Approximations)和MCA(Modified Combined Approximations)重分析方法进行了对比分析。FSCA算法在对修改后结构进行模态分析的过程中,基于修改前的模态分析结果和矩阵分解信息,引入移频因子和Epsilon算法,通过移频基向量的线性组合加速,快速求解修改后结构的模态信息。FSCA算法解决了CA算法计算高阶模态误差较大的问题,并与MCA算法比较,计算量明显减少,并且计算精度得到提高。
基于预条件Lanczos静态重分析算法,提出了一种动力响应重分析的直接积分法。本方法对修改后结构的动力响应重分析问题,将直接积分法中的等效静力学问题应用预条件Lanczos算法进行重分析计算。本文针对结构动力响应分析的中心差分法、Houbolt方法、Wilson-θ方法和Newmark方法,分别给出重分析计算的方法,并以卡车车身左前轮激励下驾驶员座椅固定点的动力响应重分析问题为例,验证了算法的准确性。
基于本文提出的FSCA模态重分析算法,求解修改后结构动力响应重分析问题,提出了一种模态迭加重分析方法,通过FSCA算法进行修改后结构的模态计算,提高模态迭加法求解结构动力响应的计算效率。以卡车车身左后轮激励下驾驶员座椅固定点的动力响应重分析为例,验证了算法的正确性。
在重分析算法研究的基础上,分别讨论了结构修改和优化过程中常用的静力学灵敏度、模态灵敏度和动力响应灵敏度分析问题,并给出了应用重分析算法求解灵敏度问题的公式。基于结构灵敏度信息,结合结构动力修改的一阶、二阶Taylor展开表达式,给出求解结构动力修改逆问题的算法和算例。算例表明:在结构模态小修改时,一阶和二阶Taylor展开式均可确定合理的设计参数;当模态修改较大时,二阶Taylor展开式的优势更为明显。
基于SIMP(Solid Isotropic Material with Penalization model)加权应变能和准则法的拓扑优化方法,针对车身接头结构的静刚度约束,讨论了不同单元类型下的加强板结构设计问题,给出修改方案,并进行了验证分析。在某卡车车身多工况试验设计的基础上,采用结构重分析算法,快速计算不同试验点的刚度、模态和动力学特性,提取各响应参数,应用最小二乘技术构建结构优化的数学模型;在优化数学模型的基础上,应用外点罚函数法进行结构的优化设计,并讨论了不同罚因子下的结构优化结果。
With the rapid development of space, shipbuilding, automotive industry and civil engineering in China, the structural design is becoming more and more complex. The analysis and optimization of complex structures can not be solved by the traditional design method any more. The generation of CAE technology has made up this contribution. CAE is becoming a necessary process and step in structural design, and it is becoming more and more useful and common. With the structural model growing, the cost of the CAE computations is increasing. In order to improve the computational efficiency, some researchers devote themselves to the development of the HPC (High Performance Computer), while others are researching into the improved algorithm for fast computations.
This thesis is supported by National Natural Science Foundation of China“Fast Optimization of Cross-Sectional Parameters for Simplified Car Body Multi-Elements Frame Structure Based on Reanalysis Theory”(No.50975121), Specialized Research Fund for the Doctoral Program of Higher Education“The Research of Adaptive Reanalysis Algorithm of the Defective Vibration System”(No.20090061110022) and FAW Group Science and Technology Innovation Project“The Multi-Optimization Platform for Car-Body Performance”(No.0837and093715). The structural dynamic reanalysis algorithm is generated, and the applications of the reanalysis method in structural dynamic modifications and structural optimizations have been discussed in this thesis.
The Frequency-Shift Combined Approximations (FSCA) reanalysis method is first developed for structural vibration, and is compared with the Combined Approximations (CA) method and the Modified Combined Approximations (MCA) method. The FSCA method treats the modal reanalysis with frequency-shift factor and Epsilon algorithm, which have reduced the high mode calculation errors in CA method successfully. Compared to the MCA method, the cost of computations in FSCA method is reduced obviously.
Based on the Preconditioning Lanczos algorithm for static reanalysis, a method for dynamic response reanalysis is developed using immediate integration method. The Preconditioning Lanczos method is used for solving the equivalent static equations in the immediate integration. Based on the Central Difference method, Houbolt method, Wilson-θmethod and Newmark method, the dynamic response reanalysis algorithms are developed, respectively. A truck-body dynamic response reanalysis example is demonstrated for the accuracy of algorithms.
Based on the FSCA modal reanalysis, a dynamic response reanlysis method is developed using modal superposition method. The truck-body dynamic response reanalysis example is demonstrated for the accuracy.
Based on the research of reanalysis method, effective procedures for repeated sensitivity analysis of static problems, vibration problems and dynamic problems in structural modifications are developed. With the sensitivity information, the first order and second order Taylor expansions are used for solving the inverse problems of structural dynamic modification. Equations and examples are given to demonstrate the effect for the modal modifications.
Based on the Solid Isotropic Material with Penalization model (SIMP) method for topology optimization and the Optimization Criterion(OC) method, static stiffness problems of car-body joints are solved by using shell and solid finite elements, and schemes for the reinforcing plate are given for the joints structure, respectively. A truck-body size optimization is brought out using the experimental design, structural reanalysis method, least square regression and penalty function. The stiffness, modal frequency and dynamic parameters are calculated with the reanalysis method. Different penalty factors are introduced for testing the optimization process.
引文
[1] Kodiyalam. S., Sobieszczanski-Sobieski. J. Multidisciplinary design optimization - some formal methods, framework requirements, and application to vehicle design[J]. International Journal of Vehicle Design, 2001, 25(1-2): 3-22.
[2] Duddeck. F., Heiserer. D., Lescheticky. J. Stochastic methods for optimization of crash and NVH problems[J]. Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings, 2003: 2265-2268.
[3] Duddeck. F. Multidisciplinary optimization of car bodies[J]. Structural and Multidisciplinary Optimization, 2008, 35(4): 375-389.
[4]李晖.高性能计算机若干关键问题研究[D]:博士学位论文.合肥:中国科学技术大学,2009.
[5]王顺绪.特征值问题的并行计算[D]:南京:南京航空航天大学,2008.
[6]刘海峰.结构静力重分析中若干问题的研究[D]:长春:吉林大学,2010.
[7]张美艳.复杂结构的动力重分析方法研究[D]:上海:复旦大学,2007.
[8] Abu Kassim. A. M., Topping. B. H. V. Static reanalysis: a review[J]. Journal of structural engineering, 1987, 113(5): 1029-1045.
[9] Jasbir S. Arora. Survey of structural reanalysis techniques[J]. Journal of the Structure Division, ASCE, 1976, 102(4): 783-802.
[10] Chen. S. H., Huang. C., Liu. Z. S., et al. Static reanalysis for topological modifications of structures[J]. Acta Mechanica Solida Sinica, 1999, 12(2): 155-164.
[11] Cheikh. M., Loredo. A. Static reanalysis of discrete elastic structures with reflexive inverse[J]. Applied Mathematical Modelling, 2002, 26(9): 877-891.
[12] Chen. S. H., Yang. X. W. Extended Kirsch combined method for eigenvalue reanalysis[J]. AIAA Journal, 2000, 38(5): 927-930.
[13] Yang. X. W., Chen. S. H., Wu. B. S. Eigenvalue reanalysis of structures using perturbations and Padéapproximation[J]. Mechanical Systems and Signal Processing, 2001, 15(2): 257-263.
[14] Cacciola. P., Impollonia. N., Muscolino. G. A dynamic reanalysis technique for general structural modifications under deterministic or stochastic input[J]. Computers & Structures, 2005, 83(14): 1076-1085.
[15]陈德成,贺向东,王泉, et al.复杂结构快速动力重分析的计算方法[J].北京大学学报(自然科学版), 1992, 28(05): 575-582.
[16]黄传奇.一种精确结构静力重分析方法[J].计算结构力学及其应用, 1996, 13(3): 295-302.
[17]黄诚.结构拓扑修改的重分析理论[D]:长春:吉林工业大学,1999.
[18] Kirsch. U., Kocvara. M., Zowe. J. Accurate reanalysis of structures by a preconditioned conjugate gradient method[J]. International Journal for Numerical Methods in Engineering, 2002, 55(2): 233-251.
[19] Sobieszczansk I J. Structuralmodification by perturbation method[J]. Journal. of the Structural Division, ASCE, 1968, 94(12): 2799-2816.
[20] Sobieszczansk I J. Matrix algorithm for structural modification based upon the parallel element concept[J]. AIAA Journal, 1969, 7(1): 2132-2139.
[21] Akgun. M. A., Garcelon. J. H., Haftka. R. T. Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas[J]. International Journal for Numerical Methods in Engineering, 2001, 50(7): 1587-1606.
[22] Impollonia. N. A method to derive approximate explicit solutions for structural mechanics problems[J]. International Journal of Solids and Structures, 2006, 43(22-23): 7082-7098.
[23] Kolakowski. P., Wiklo. M., Holnicki-Szulc. J. The virtual distortion method - a versatile reanalysis tool for structures and systems[J]. Structural and Multidisciplinary Optimization, 2008, 36(3): 217-234.
[24] Majid K. I., Saka M. P., Celik T. The theorem of structural variation generalized for rigidly jointed frames[C], Proceedings of the Institution of Civil Engineers. London, 1978.
[25] Topping B. H. V., Abu, Kassim. The application of the theorems of structural variation to finite element problems[J]. International Journal for Numerical Methods in Engineering 1983, 19(1): 141-151.
[26] Topping B. H. V., Kassim A. M. A. The use and the efficiency of the theorems of structural variation to finite element analysis[J]. International Journal for Numerical Methods in Engineering 1987, 24(10): 1901-1920.
[27]梁平,王树范,王永利, et al.轴对称结构拓扑变化重分析的新方法[J].吉林大学学报(工学版), 2006, 36(3): 26-29.
[28] Barthelemy. J, R. T. Haftka. Appriximation concepts for optimum structural design - a review[J]. Structural and Multidisciplinary Optimization, 1993, 5(3): 129-144.
[29] Romstad. K. M, Huntchinson. J. R, Runge. K. H. Design parameter variation and structural response[J]. International journal of Nunerical Methods in Engineering, 1973, 5(3): 337-349.
[30] Svanberg. K. The method of moving asymptotes - a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373.
[31] Fleury. C. Efficient approximation concepts using second order information[J]. International Journal for Numerical Methods in Engineering, 1989, 28(9): 2041-2058.
[32] Fleury. C. First and second order convex approximation strategies in structural optimization[J]. Structural and Multidisciplinary Optimization, 1989, 1(1): 3-10.
[33] Melosh. R. J, Luik. R. Multiple configuration analysis of structures[J]. Journal of the Structure Division, ASCE, 1968, 94(11): 2581-2596.
[34] Fox. R. L, Miura. H. An approximate analysis technique for design calculations[J]. AIAA Journal, 1971, 9(1): 177-179.
[35] Kirsch. U., Rubinstein. M. F. Structural reanalysis by iteration[J]. Computers & Structures, 1972, 2(4): 497-510.
[36] Kirsch. U., Toledano. G. Approximate reanalysis for modifications of structural geomrtry[J]. Computers & Structures, 1983, 16(1): 269-279.
[37] Kirsch. U. Reduced basis approximations of structural displacements for optimal design[J]. AIAA Journal, 1991, 29(10): 1751-1758.
[38] Kirsch. U., Eisenberger. M. Approximate interactive design of large structures[J]. Computing Systems in Engineering, 1991, 2(1): 67-73.
[39] Kirsch. U. Improved stiffness-based first-order approximations for structural optimization[J]. AIAA Journal, 1995, 33(1): 143-150.
[40] Kirsch. U., Liu. S. Structural reanalysis for general layout modifications[J]. AIAA Journal, 1997, 35(2): 382-388.
[41] Chen. S., Huang. C., Liu. Z. Structural approximate reanalysis for topological modifications of finite element systems[J]. AIAA Journal, 1998, 36(9): 1760-1762.
[42] Kirsch. U., Moses. F. An improved reanalysis method for grillage-type structures[J]. Computers and Structures, 1998, 68(1-3): 79-88.
[43] Kirsch. U., Papalambros. P. Y. Structural reanalysis for topological modifications - a unified approach[J]. Structural and Multidisciplinary Optimization, 2001, 21(5): 333-344.
[44] Kirsch. U., Papalambros. P. Y. Exact and accurate solutions in the approximate reanalysis of structures[J]. AIAA Journal, 2001, 39(11): 2198-2205.
[45] Chen. S. H., Yang. Z. J. A universal method for structural static reanalysis of topological modifications[J]. International Journal for Numerical Methods in Engineering, 2004, 61(5): 673-686.
[46]陈塑寰吴晓明杨志军.结构静态拓扑重分析的迭代组合近似方法[J].力学学报, 2004, 36(05): 611-616.
[47] Wu. B. S., Lim. C. W., Li. Z. G. A finite element algorithm for reanalysis of structures with added degrees of freedom[J]. Finite Elements in Analysis and Design, 2004, 40(13-14): 1791-1801.
[48] Wu. B. S., Li. Z. G. Static reanalysis of structures with added degrees of freedom[J]. Communications in Numerical Methods in Engineering, 2006, 22(4): 269-281.
[49] Liu. H. F., Wu. B. S., Li. Z. G. Simple iteration method for structural static reanalysis[J]. Canadian Journal of Civil Engineering, 2009, 36(9): 1535-1538.
[50]孙睿珩,徐涛,张昊, et al.组合近似重分析方法的ANASYS二次开发[J].吉林大学学报(工学版), 2009, 29(s2): 396-400.
[51] Bae. H. R., Grandhi. R. V. Successive matrix inversion method for reanalysis of engineering structural systems[J]. AIAA Journal, 2004, 42(8): 1529-1535.
[52] Bae. H. R., Grandhi. R. V., Canfield. R. A. Accelerated engineering design optimization using successive matrix inversion method[J]. International Journal for Numerical Methods in Engineering, 2006, 66(9): 1361-1377.
[53] Bae. H. R., Grandhi. R. V., Canfield. R. A. Efficient successive reanalysis technique for engineering structures[J]. AIAA Journal, 2006, 44(8): 1883-1889.
[54]陈塑寰.结构振动分析的矩阵摄动理论[M].重庆:重庆出版社,1989.
[55] Chen. S. H., Yang. X. W., Wu. B. S. Static displacement reanalysis of structures using perturbation and Padéapproximation[J]. Communications in Numerical Methods in Engineering, 2000, 16(2): 75-82.
[56]陈塑寰孟光黄海.摄动法结合Padé逼近在结构拓扑重分析中的应用[J].应用力学学报, 2005, 22(02): 155-158.
[57]陈塑寰孟光郭克尖黄海.结构静态拓扑重分析的摄动-Padé逼近法[J].固体力学学报, 2005, 26(03): 321-324.
[58]吴晓明,陈塑寰,黄志东. Epsilon算法在汽车结构设计分析中的应用[J].吉林大学学报(工学版), 2006, 36(3): 8-11.
[59] Wu. X. M., Chen. S. H., Yang. Z. J. Static displacement reanalysis of modified structues using the epsilon algorithm[J]. AIAA Journal, 2007, 45(8): 2083-2086.
[60] Yang. Z. J., Chen. X., Kelly. R. An Adaptive Static Reanalysis Method for Structural Modifications Using Epsilon Algorithm[J]. International Joint Conference on Computational Sciences and Optimization, Vol 2, Proceedings, 2009: 897-899 1051.
[61]徐涛,程飞,于澜, et al.基于预条件Lanczos算法的结构拓扑修改静态重分析方法[J].吉林大学学报(工学版), 2007, 37(05): 1214-1219.
[62]徐涛,程飞,郭桂凯, et al.结构静态重分析的改进预条件Lanczos方法[J].机械强度, 2009, 31(03): 425-431.
[63]徐涛,程飞,宋广才, et al.结构拓扑修改静态重分析的BFGS方法[J].吉林大学学报(工学版), 2009, 39(01): 103-107.
[64] Level. P., Moraux0. D., Drazetic. P., et al. On a direct inversion of the impedance matrix in response reanalysis[J]. Communications in Numerical Methods in Engineering, 1996, 12(3): 151-159.
[65] Weissenberger. J. T. Effect of local modifications on the vibration characteristics of linear systems[J]. Journal of Applied Mechanics, 1968, 35(6): 327-332.
[66] Wittrick. W. H. Rates of change of eigenvalues with reference to buckling and vibration problems[J]. Journal of the Royal Aeronautical Society, 1962, 66: 590-590.
[67] Zarghamee. M. S. Optimum frequency of structures[J]. AIAA Journal, 1968, 6(4): 749-750.
[68] Zarghamee. M. S. Minimum weight design with stability constraint[J]. Journal of the Structure Division, ASCE, 1970, 96(8): 1697-1710.
[69] Fox. R. L., Kapoor. M. P. Rates of change of eigenvalues and eigenvectors[J]. AIAA Journal, 1969, 6(12): 2426-2429.
[70] Goldman. R. L. Vibration analysis by dynamic partitioning[J]. AIAA Journal, 1969, 6(6): 1152-1154.
[71] Hou. S. N. Review of modal synthesis techniques and a new approach[J]. The Shock and Vibration Bulletin, 1969, 40(4): 25-39.
[72] Hunn. B. A. A method of calculating the normal modes of an aircraft[J]. Quarterly Journal of Mechanics, 1955, 8(1): 38-58.
[73] Gladwell. G. M. Branch mode analysis of vibrating systems[J]. journal of Sound and Vibration, 1964, 1(1): 41-59.
[74] Hurty. W. C. Dynamic analysis of structures using component modes[J]. AIAA Journal, 1965, 3(4): 678-685.
[75] Kirsch. U. Approximate vibration reanalysis of structures[J]. AIAA Journal, 2003, 41(3): 504-511.
[76] Kirsch. U., Bogomolni. M. Error evaluation in approximate reanalysis of structures[J]. Structural and Multidisciplinary Optimization, 2004, 28(2-3): 77-86.
[77] Kirsch. U., Bogomolni. M. Procedures for approximate eigenproblem reanalysis of structures[J]. International Journal for Numerical Methods in Engineering, 2004, 60(12): 1969-1986.
[78] He. J. J., Jiang. J. S., Xu. B. Modal reanalysis methods for structural large topological modifications with added degrees of freedom and non-classical damping[J]. Finite Elements in Analysis and Design, 2007, 44(1-2): 75-85.
[79] Bogomolni. M., Kirsch. U., Sheinman. I. Efficient design sensitivities of structures subjected to dynamic loading[J]. International Journal of Solids and Structures, 2006, 43(18-19): 5485-5500.
[80] Kirsch. U., Bogomolni. M., Sheinman. I. Efficient procedures for repeated calculations of the structural response using combined approximations[J]. Structural and Multidisciplinary Optimization, 2006, 32(6): 435-446.
[81] Rong. F., Chen. S. H., Chen. Y. D. Structural modal reanalysis for topological modifications with extended Kirsch method[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(5-6): 697-707.
[82] Chen. S. H., Yang. X. W., Lian. H. D. Comparison of several eigenvalue reanalysis methods for modified structures[J]. Structural and Multidisciplinary Optimization, 2000, 20(4): 253-259.
[83] Ma. L., Chen. S. H., Meng. G. W. Combined approximation for reanalysis of complex eigenvalues[J]. Computers & Structures, 2009, 87(7-8): 502-506.
[84] Yang. Z. J, Chen. S. H, Wu. X. M. A method for modal reanalysis of topological modifications of structures[J]. International Journal for Numerical Methods in Engineering, 2006, 65(13): 2203-2220.
[85] Chen. S. H., Rong. F. A new method of structural modal reanalysis for topological modifications[J]. Finite Elements in Analysis and Design, 2002, 38(11): 1015-1028.
[86] Zhang. G., Nikolaidis. E., Mourelatos. Z. P. An Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures[J]. Journal of Mechanical Design, 2009, 131(5): 1-13.
[87]孙亮,李顺华,李正光, et al.结构动力重分析的向量值有理逼近方法[J].吉林大学学报(理学版), 2005, 43(03): 258-261.
[88]何建军,姜节胜.结构拓扑修改动力学重分析的单步摄动逆迭代法[J].西北工业大学学报, 2006, 24(03): 313-316.
[89]张美艳,韩平畴.基于有理逼近和灵敏度分析的结构动力重分析方法[J].振动与冲击, 2006, 25(04): 50-52.
[90]张美艳,韩平畴.结构动力重分析的子结构有理逼近[J].计算力学学报, 2008, 25(06): 878-881.
[91]张美艳,韩平畴,唐国安.子结构灵敏度综合在结构动力重分析中的应用[J].振动与冲击, 2008, 27(04): 27-29.
[92]杨荣,王乐,徐涛, et al.具有不完全特征向量系的状态向量摄动的快速算法[J].吉林大学学报(工学版), 2008, 38(05): 1101-1104.
[93] Liu. X. L., Oliveira. C. S. Iterative modal perturbation and reanalysis of eigenvalue problem[J]. Communications in Numerical Methods in Engineering, 2003, 19(4): 263-274.
[94]吴晓明,陈塑寰. Epsilon算法在结构模态重分析中的应用[J].吉林大学学报(工学版), 2006, 36(04): 447-450.
[95] Chen. S. H., Wu. X. M., Yang. Z. J. Eigensolution reanalysis of modified structures using epsilon-algorithm[J]. International Journal for Numerical Methods in Engineering, 2006, 66(13): 2115-2130.
[96] Chen. S. H., Ma. L., Meng. G. W. Dynamic response reanalysis for modified structures under arbitrary excitation using epsilon-algorithm[J]. Computers & Structures, 2008, 86(23-24): 2095-2101.
[97]曹文钢,曲令晋,白迎春.基于灵敏度分析的客车车身质量优化研究[J].汽车工程, 2009, 31(03): 278-281.
[98]张武,陈剑,夏海.基于灵敏度分析的发动机悬置系统稳健优化设计[J].汽车工程, 2009, 31(08): 728-732.
[99]张代胜,张林涛,谭继锦, et al.基于刚度灵敏度分析的客车车身轻量化研究[J].汽车工程, 2008, 30(08): 718-720.
[100] D'Vari. R., Baker. M. Aeroelastic loads and sensitivity analysis for structural loads optimization[J]. Journal of Aircraft, 1999, 36(1): 156-166.
[101]唐明裴,阎贵平.结构灵敏度分析及计算方法概述[J].中国铁道科学, 2003, 24(01): 74-79.
[102] Pandey. P. C., Bakshi. P. Analytical response sensitivity computation using hybrid finite elements[J]. Computers and Structures, 1999, 71(5): 525-534.
[103] Haftka. Raphael T. Semi-analytical static nonlinear structural sensitivity analysis[J]. AIAA Journal, 1993, 31(7): 1307-1312.
[104] Haftka. R. T., Adelman. H. M. Recent developments in structural sensitivity analysis[J]. Structural Optimization, 1989, 1(3): 137-151.
[105] Barthelemy. B., Chon. C. T., Haftka. R. T. Accuracy problems associted with semi-analytical derivatives of static response[J]. Finite Elements in Analysis and Design, 1988, 4(3): 249-265.
[106] Bugeda. G., Onate. E. Optimum aerodynamic shape design including mesh adaptivity[J]. International Journal for Numerical Methods in Fluids, 1995, 20(8-9): 915-934.
[107] Choi. K. K., Twu. S. L. Equivalence of continuum and discrete methods of shape design sensitivity analysis[J]. AIAA Journal, 1989, 27(10): 1418-1424.
[108] Barthelemy. B., Haftka. R. T. Accuracy analysis of the semi-analytical method for shape sensitivity[J]. Mechanics Based Design of Structures and Machines, 1990, 18(3): 407-432.
[109] Mlejnek. H. P. Accuracy of semi-analytical sensitivities and its improvement by the "natural method"[J]. Structural Optimization, 1992, 4(2): 128-131.
[110] Olhoff. N., Rasmussen. J., Lund. E. A method of exact numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analysis[J]. Mechanics of Structures and Machines, 1993, 21(1): 1-66.
[111] Van. K. F., De. B. H. Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions[J]. International Journal for Numerical Methods in Engineering, 1998, 42(1): 71-91.
[112] De. B. H., Van. K. F. Refined semi-analytical design sensitivities[J]. International Journal of Solids and Structures, 2000, 37(46): 6961-6980.
[113] Kibsgaard. S. Sensitivity analysis - the basis for optimization[J]. International Journal for Numerical Methods in Engineering, 1992, 34(3): 901-932.
[114] Lund. E., Olhoff. N. Shape design sensitivity analysis of eigenvalues using "exact" numerical differentiation of finite element matrices[J]. Structural Optimization, 1994, 8(1): 52-59.
[115] Friswell. M. I. Calculation of second and higher order eigenvector derivatives[J]. Journal of Guidance, Control, and Dynamics, 1995, 18(4): 919-921.
[116] Andrew. A. L., Tan. R. C. E. Computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration[J]. AIAA Journal, 1996, 34(10): 2214-2216.
[117] Andrew. A. L., Tan. R. C. E. Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration[J]. Communications in Numerical Methods in Engineering, 1999, 15(9): 641-649.
[118] Chen. T. Y. Design sensitivity analysis for repeated eigenvalues in structural design[J]. AIAA Journal, 1993, 31(12): 2347-2350.
[119] Choi. K. K., Haug. E. J., Seong. H. G. Iterative method for finite dimensional structural optimization problems with repeated eigenvalues[J]. International Journal for Numerical Methods in Engineering, 1983, 19(1): 93-112.
[120] Dailey. R. L. Eigenvector derivatives with repeated eigenvalues[J]. AIAA Journal, 1989, 27(4): 486-491.
[121] Xu. T, Chen. S. H., Liu. Z. S. Perturbation sensitivity of generalized modes of defective systems[J]. Computers & Structures, 1994, 52(2): 179-185.
[122]徐涛,于澜,鞠伟, et al.计算亏损系统模态灵敏度的逐层递推演算方法[J].力学学报, 2008, 40(02): 281-288.
[123] Xu. T., Xu. T. S., Zuo. W. J., et al. Fast sensitivity analysis of defective system[J]. Applied Mathematics and Computation, 2010, 217(7): 3248-3256.
[124] Poldneff. M. J., Arora. J. S. Design sensitivity analysis in dynamic thermoviscoelasticlty with implicit integration[J]. International Journal of Solids and Structures, 1996, 33(4): 577-594.
[125] Cho. S., Choi. K. K. Design sensitivity analysis and optimization of non-linear transient dynamics. Part I - Sizing design[J]. International Journal for Numerical Methods in Engineering, 2000, 48(3): 351-373.
[126] Kim. N. H., Choi. K. K. Design sensitivity analysis and optimization of nonlinear transient dynamics[J]. Mechanics of Structures and Machines, 2001, 29(3): 351-371.
[127] Kirsch. U. Efficient sensitivity analysis for structural optimization[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 117(1-2): 143-156.
[128] Kirsch. U., Papalambros. P. Y. Accurate displacement derivatives for structural optimization using approximate reanalysis[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(31): 3945-3956.
[129] Kirsch. U., Bogomolni. M., Sheinman. I. Efficient procedures for repeated calculations of structural sensitivities[J]. Engineering Optimization, 2007, 39(3): 307-325.
[130] Kirsch. U., Bogomolni. M., van Keulen. F. Efficient finite difference design sensitivities[J]. AIAA Journal, 2005, 43(2): 399-405.
[131] Bogomolni. M., Kirsch. U., Sheinman. I. Nonlinear dynamic sensitivities of structures using combined approximations[J]. AIAA Journal, 2006, 44(11): 2765-2772.
[132]廖伯瑜,周新民,尹志宏.现代机械动力学及其工程应用[M].北京:机械工业出版社,2004.
[133] Stetson. K. A., Palma. G. E. Inversion of first-order perturbation theory and its application to structural design[J]. AIAA J, 1976, 14(4): 454-460.
[134] Chen. J.C., Wade. B.K. Matrix Perturbation for Structural Dynamic Analysis[J]. AIAA J, 1977, 15(8): 1095-1100.
[135] Berman. A. Mass matrix correction using an incomplete set of measured modes[J]. AIAA J, 1979, 17(10): 1147-1148.
[136] Wei. F. S. Stiffness matrix correction from incomplete test data [J]. AIAA J, 1980, 18(10): 1274-1275.
[137] Liu. S. Improvement of analytical dynamic models using complex modal test data[J]. International Journal of Mechanical Sciences, 1992, 34(10): 817-829.
[138]彭晓洪,丁锡洪,周建功.用模态参数识别结果对实际结构有限元动力模型的修正[J].振动与冲击, 1984, (03): 8-15.
[139]王朝永,张令弥.利用试验模态参数修正有限元模型的再正交拉格朗日乘子法[J].振动工程学报, 1986, (2): 54-58.
[140] Liu. J. K., Chan. H. C. A universal matrix perturbation technique for structural dynamic modification using singular value decomposition[J]. Journal of Sound and Vibration, 1999, 228(2): 265-274.
[141] Blaldvdn. J. F., Hutton. S. G. Natural Modes of Modified Structures[J]. AIAA J, 1985, 23(11): 1737-1743.
[142] Kundra. T. K. Structural dynamic modifications via models[J]. Sadhana-Academy Proceedings in Engineering Sciences, 2000, 25: 261-276.
[143] Nakra. B. C. Structural dynamic modification using additive damping[J]. Sadhana-Academy Proceedings in Engineering Sciences, 2000, 25: 277-289.
[144] Sestieri. A. Structural dynamic modification[J]. Sadhana-Academy Proceedings in Engineering Sciences, 2000, 25: 247-259.
[145] Li. T., He. J. M. Modification of truss structures using linear modification method[J]. Inverse Problems in Engineering, 2001, 9(3): 217-234.
[146] Yap. K. C., Zimmerman. D. C. A comparative study of structural dynamic modification and sensitivity method approximation[J]. Mechanical Systems and Signal Processing, 2002, 16(4): 585-597.
[147] Chen. H. P. Efficient methods for determining modal parameters of dynamic structures with large modifications[J]. Journal of Sound and Vibration, 2006, 298(1-2): 462-470.
[148] Hang. H. J., Shankar. K., Lai. J. C. S. Prediction of the effects on dynamic response due to distributed structural modification with additional degrees of freedom[J]. Mechanical Systems and Signal Processing, 2008, 22(8): 1809-1825.
[149] Hang. H. J., Shankar. K., Lai. J. C. S. Effects of distributed structural dynamic modification with reduced degrees of freedom[J]. Mechanical Systems and Signal Processing, 2009, 23(7): 2154-2177.
[150] Hang. H. J., Shankar. K., Lai. J. C. S. Effects of distributed structural dynamic modification with additional degrees of freedom on 3D structure[J]. Mechanical Systems and Signal Processing, 2010, 24(5): 1349-1368.
[151] Papalambros. P. Y., Wilde. D. J. Principles of Optimal Design: Modeling and Computation[M]. Cambridge:Cambridge University Press,1988.
[152] Zhou. M., Pagaldipti. N., Thomas. H. L., et al. An integrated approach to topology, sizing, and shape optimization[J]. Structural and Multidisciplinary Optimization, 2004, 26(5): 308-317.
[153] Pedersen. N. L., Nielsen. A. K. Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling[J]. Structural and Multidisciplinary Optimization, 2003, 25(5-6): 436-445.
[154] Fourie. P. C., Groenwold. A. A. The particle swarm optimization algorithm in size and shape optimization[J]. Structural and Multidisciplinary Optimization, 2002, 23(4): 259-267.
[155] Bhavikatti. S. S., Ramakrishnan. C. V. Optimum design of fillets in flat and round tension bars[C], Proceedings of the ASME 1977 Design Engineering Technical Conference. Chicago, 1977.
[156] Prasad. B., Emerson. J. F. Optimal structural remodeling of multi-objective systems[J]. Computers and Structures, 1984, 18(4): 619-628.
[157] Bennett. J. A., Botkin. M. E. Structural shape optimization with geometric description and adaptive mesh refinement[J]. AIAA J, 1985, 23(3): 458-464.
[158] Braibant. V., Fleury. C. Shape optimal design using B-splines[J]. Computer Methods in Applied Mechanics and Engineering, 1984, 44(3): 247-267.
[159] Imam. M. H. Three-dimensional shape optimization[J]. International Journal for Numerical Methods in Engineering, 1982, 18(5): 661-673.
[160] Braibant. V., Fleury. C. An approximation-concepts approach to shape optimal design[J]. Computer Methods in Applied Mechanics and Engineering, 1985, 53(2): 119-148.
[161] Belegundu. A. D., Rajan. S. D. A shape optimization approach based on natural design variables and shape functions[J]. Comput. Methods Appl. Mech. Engrg., 1988, 66(1): 89-106.
[162] H. Azegami, M. Shimoda, E. Katamine, et al. A domain optimization technique for elliptic boundary value problems[C], Computer Aided Optimization Design of Structures IV, Structural Optimization. Southampton, 1995.
[163] Inzarulfaisham. A. R., Azegami. H. Solution to boundary shape optimization problem of linear elastic continua with prescribed natural vibration mode shapes[J]. Structural and Multidisciplinary Optimization, 2004, 27(3): 210-217.
[164]荣见华,郑健龙,徐飞鸿.结构动力修改与优化设计[M].长沙:人民交通出版社,2002.
[165] Michell. A. G. M. The limits of economy of material in frame-structures[J]. Phil. Mag., 1904, 8(47): 589-597.
[166] Bends?e. M. P., Ben-Tal. A., Zowe. J. Optimization methods for truss geometry and topology design[J]. Structural Optimization, 1994, 7(3): 141-159.
[167] Gil. L., Andreu. A. Shape and cross-section optimization of a truss structure[J]. Computers and Structures, 2001, 79(7): 681-689.
[168] Duda. J. W., Jakiela. M. J. Generation and classification of structural topologies with genetic algorithm speciation[J]. Journal of Mechanical Design, Transactions Of the ASME, 1997, 119(1): 127-131.
[169] Chapman. C. D., Saitou. K., Jakiela. M. J. Genetic algorithms as an approach to configuration and topology design[J]. Journal of Mechanical Design, Transactions Of the ASME, 1994, 116(4): 1005-1012.
[170] Harasaki. H., Arora. J. S. A new class of evolutionary methods based on the concept of Transferred Force for structural design[J]. Structural and Multidisciplinary Optimization, 2001, 22(1): 35-56.
[171] Kita. E., Toyoda. T. Structural design using cellular automata[J]. Structural and Multidisciplinary Optimization, 2000, 19(1): 64-73.
[172] Abdalla. M. M., Gürdal. Z. Structural design using cellular automata for eigenvalue problems[J]. Structural and Multidisciplinary Optimization, 2004, 26(3-4): 200-208.
[173] Bends?e. 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.
[174] Bends(?)e. M. P. Optimal shape design as a material distribution problem[J]. Structural Optimization, 1989, 1(4): 193-202.
[175] Yang. R. J., Chahande. A. I. Automotive applications of topology optimization[J]. Structural Optimization, 1995, 9(3-4): 245-249.
[176] Bends(?)e. M. P., Sigmund. O. Material interpolation schemes in topology optimization[J]. Archive of Applied Mechanics, 1999, 69(9-10): 635-654.
[177] Suzuki. K., Kikuchi. N. A homogenization method for shape and topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 1991, 93(3): 291-318.
[178] Diaz. A. R., Kikuchi. N. Solutions to shape and topology eigenvalue optimization problems using a homogenization method[J]. International Journal for Numerical Methods in Engineering, 1992, 35: 1487-1502.
[179] Pedersen. N. L. Maximization of eigenvalues using topology optimization[J]. Structural and Multidisciplinary Optimization, 2000, 20(1): 2-11.
[180] Mayer. R. R., Kikuchi. N., Scott. A. Application of topological optimization techniques to structural crashworthiness[J]. International Journal for Numerical Methods in Engineering, 1996, 39(8): 1383-1403.
[181] Mayer. R. R., Maurer. D., Bottcher. C. Application of Topological Optimization Program to the Danner Test Simulation[C], Proceedings of the ASME 2000 Design Engineering and Technical Conferences. Maryland, 2000.
[182] Kharmanda. G., Olhoff. N., Mohamed. A., et al. Reliability-based topology optimization[J]. Structural and Multidisciplinary Optimization, 2004, 26(5): 295-307.
[183] Bremicker. M., Chirehdast. M., Kikuchi. N., et al. Integrated topology and shape optimization in structural design[J]. Mech. Struct. Mach., 1991, 19(4): 551-587.
[184]龙江启,兰凤崇,陈吉清.车身轻量化与钢铝一体化结构新技术的研究进展[J].机械工程学报, 2008, 44(06): 27-35.
[185] Avalle. M., Peroni. L., Peroni. M., et al. Bi-Material Joining for Car Body Structures: Experimental and Numerical Analysis[J]. Journal of Adhesion, 2010, 86(5-6): 539-560.
[186] Carle. D., Blount. G. The suitability of aluminium as an alternative material for car bodies[J]. Materials & Design, 1999, 20(5): 267-272.
[187]高云凯,姜欣,彭和东, et al.轿车车身轻量化结构[J].现代零部件, 2004, (05): 34,36,38.
[188] Sun. H. T., Shen. G. Z., Hu. P., et al. Study on Lightweight Optimization of Car Body Based on Crash[C], Icicta: 2009 Second International Conference on Intelligent Computation Technology and Automation, Vol Ii, Proceedings. Changsha, 2009.
[189] Zhang. H. Z., Zhang. S. R., Hu. P., et al. An Intelligent System Based on Optimization for Car Body Design[C], 2009 Ieee Intelligent Vehicles Symposium, Vols 1 and 2. Symposium, 2009.
[190] X. W. Zhang, Z. Tao. A Study on Shape Optimization of Bus Body Structure Based on Stiffness Sensitivity Analysis[C], 2009 Ieee 10th International Conference on Computer-Aided Industrial Design & Conceptual Design, Vols 1-3. Wenzhou, 2009.
[191] Zhu. P., Zhang. Y., Chen. G. L. Metamodel-based lightweight design of an automotive front-body structure using robust optimization[C], Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering. 2009.
[192] Wennhage. P. Weight optimization of large scale sandwich structures with acoustic and mechanical constraints[J]. Journal of Sandwich Structures & Materials, 2003, 5(3): 253-266.
[193] Azadi. M., Azadi. S., Zahedi. F., et al. Multidisciplinary Optimization of a Car Component under Nvh and Weight Constraints Using Rsm[J]. International Journal of Vehicle Noise and Vibration, 2009, 5(3): 261-270.
[194]崔玲,高云凯.基于正交试验设计的客车车身结构优化研究[J].制造业自动化, 2010, 32(11): 142-147.
[195]宋凯,成艾国,胡朝辉, et al.基于真实接头车身概念模型的结构优化[J].中国机械工程, 2010, 21(22): 2764-2770.
[196] Kim. M. H., Suh. M. W., Bae. D. H. Development of an optimum design technique for the bus window pillar member[J]. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, 2001, 215(D1): 11-20.
[197] Suh. M. W., Yang. W. H., Suhr. J. Analysis of the joint structure of the vehicle body by condensed joint matrix method[J]. Ksme International Journal, 2001, 15(12): 1639-1646.
[198] Suh. M. W., Suhr. J., Yang. W. H. Condensed joint matrix method for the joint structure of a vehicle body[J]. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, 2002, 216(D1): 35-41.
[199] Kirsch. U. A unified reanalysis approach for structural analysis, design, and optimization[J]. Structural and Multidisciplinary Optimization, 2003, 25(2): 67-85.
[200]刘长学.超大规模稀疏矩阵计算方法[M].上海:上海科学技术出版社,1991.
[201] Roberts. D. E. On the convergence of rows of vector padéapproximants[J]. Journal of Computational and Applied Mathematics, 1996, 70(1): 95-109.
[202]陈塑寰.结构振动分析的数值方法[M].长春:吉林科学技术出版社,1996.
[203] Bathe. K. J. Finite elemente method[M]. Berlin:Springer,2002.
[204] Houbolt. J. C. A recurrence matrix solution for the dynamic response of elastic aircraft[J]. Aeronautical Journal, 1950, 17: 540-550.
[205] Bathe. K. J., Wilson. E. L. Numerical methods in finite analysis[M]. New Jersey:Prentice Hall Inc,1976.
[206] Newmark. N. M. A method of computation for structural dynamics[J]. Journal of Engineering Mechanics, 1959, 85(3): 249-260.
[207]黄明游,刘播,徐涛.数值计算方法[M].北京:科学出版社,2005.
[208] Carpentieri. B., Duff. I. S., Giraud. L. A Class of Spectral Two-Level Preconditioners[J]. Journal on Scientific Computing, SIAM, 2003, 25(2): 749-765.
[209] Giraud. L., Gratton. S., Martin. E. Incremental spectral preconditioners for sequences of linear systems[J]. 2007, 57(11-12): 1164-1180.
[210]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[211] Curran. R., Castagne. S., Rothwell. A., et al. Uncertainty and Sensitivity Analysis in Aircraft Operating Costs in Structural Design Optimization[J]. Journal of Aircraft, 2009, 46(6): 2145-2155.
[212] Van K. F., Haftka. R. T., Kim. N. H. Review of options for structural design sensitivity analysis. Part 1: Linear systems[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(30-33): 3213-3243.
[213]李亦文,徐涛,左文杰, et al.基于相对灵敏度的车身结构模型修改[J].吉林大学学报(工学版), 2009, 39(06): 1435-1440.
[214] Guo. G. K, Xu. T., Li. Y. W., et al. Optimization of Joints Stiffness on the Autobody Based on Minimization of Strain Energy[C], Proceedings of the 3rd International Conference on Mechanical Engineering and Mechanics. Beijing, 2009.
[215]黄金陵.汽车车身设计[M].北京:机械工业出版社,2007.
[216]黄金陵,娄永强,龚礼洲.轿车车身结构概念模型中接头的模拟[J].机械工程学报, 2000, 36(3): 78-81.
[217]钱令希.工程结构优化设计[M].北京:水利水电出版社,1983.
[218]任露泉.试验优化设计与分析[M].长春:吉林科学技术出版社,2001.
[219]李董辉,童小娇.数值最优化[M].北京:科学出版社,2005.
[220] Dai. Y. H. Convergence properties of the BFGS algoritm[J]. Siam Journal on Optimization, 2003, 13(3): 693-701.
[2] Duddeck. F., Heiserer. D., Lescheticky. J. Stochastic methods for optimization of crash and NVH problems[J]. Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings, 2003: 2265-2268.
[3] Duddeck. F. Multidisciplinary optimization of car bodies[J]. Structural and Multidisciplinary Optimization, 2008, 35(4): 375-389.
[4]李晖.高性能计算机若干关键问题研究[D]:博士学位论文.合肥:中国科学技术大学,2009.
[5]王顺绪.特征值问题的并行计算[D]:南京:南京航空航天大学,2008.
[6]刘海峰.结构静力重分析中若干问题的研究[D]:长春:吉林大学,2010.
[7]张美艳.复杂结构的动力重分析方法研究[D]:上海:复旦大学,2007.
[8] Abu Kassim. A. M., Topping. B. H. V. Static reanalysis: a review[J]. Journal of structural engineering, 1987, 113(5): 1029-1045.
[9] Jasbir S. Arora. Survey of structural reanalysis techniques[J]. Journal of the Structure Division, ASCE, 1976, 102(4): 783-802.
[10] Chen. S. H., Huang. C., Liu. Z. S., et al. Static reanalysis for topological modifications of structures[J]. Acta Mechanica Solida Sinica, 1999, 12(2): 155-164.
[11] Cheikh. M., Loredo. A. Static reanalysis of discrete elastic structures with reflexive inverse[J]. Applied Mathematical Modelling, 2002, 26(9): 877-891.
[12] Chen. S. H., Yang. X. W. Extended Kirsch combined method for eigenvalue reanalysis[J]. AIAA Journal, 2000, 38(5): 927-930.
[13] Yang. X. W., Chen. S. H., Wu. B. S. Eigenvalue reanalysis of structures using perturbations and Padéapproximation[J]. Mechanical Systems and Signal Processing, 2001, 15(2): 257-263.
[14] Cacciola. P., Impollonia. N., Muscolino. G. A dynamic reanalysis technique for general structural modifications under deterministic or stochastic input[J]. Computers & Structures, 2005, 83(14): 1076-1085.
[15]陈德成,贺向东,王泉, et al.复杂结构快速动力重分析的计算方法[J].北京大学学报(自然科学版), 1992, 28(05): 575-582.
[16]黄传奇.一种精确结构静力重分析方法[J].计算结构力学及其应用, 1996, 13(3): 295-302.
[17]黄诚.结构拓扑修改的重分析理论[D]:长春:吉林工业大学,1999.
[18] Kirsch. U., Kocvara. M., Zowe. J. Accurate reanalysis of structures by a preconditioned conjugate gradient method[J]. International Journal for Numerical Methods in Engineering, 2002, 55(2): 233-251.
[19] Sobieszczansk I J. Structuralmodification by perturbation method[J]. Journal. of the Structural Division, ASCE, 1968, 94(12): 2799-2816.
[20] Sobieszczansk I J. Matrix algorithm for structural modification based upon the parallel element concept[J]. AIAA Journal, 1969, 7(1): 2132-2139.
[21] Akgun. M. A., Garcelon. J. H., Haftka. R. T. Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas[J]. International Journal for Numerical Methods in Engineering, 2001, 50(7): 1587-1606.
[22] Impollonia. N. A method to derive approximate explicit solutions for structural mechanics problems[J]. International Journal of Solids and Structures, 2006, 43(22-23): 7082-7098.
[23] Kolakowski. P., Wiklo. M., Holnicki-Szulc. J. The virtual distortion method - a versatile reanalysis tool for structures and systems[J]. Structural and Multidisciplinary Optimization, 2008, 36(3): 217-234.
[24] Majid K. I., Saka M. P., Celik T. The theorem of structural variation generalized for rigidly jointed frames[C], Proceedings of the Institution of Civil Engineers. London, 1978.
[25] Topping B. H. V., Abu, Kassim. The application of the theorems of structural variation to finite element problems[J]. International Journal for Numerical Methods in Engineering 1983, 19(1): 141-151.
[26] Topping B. H. V., Kassim A. M. A. The use and the efficiency of the theorems of structural variation to finite element analysis[J]. International Journal for Numerical Methods in Engineering 1987, 24(10): 1901-1920.
[27]梁平,王树范,王永利, et al.轴对称结构拓扑变化重分析的新方法[J].吉林大学学报(工学版), 2006, 36(3): 26-29.
[28] Barthelemy. J, R. T. Haftka. Appriximation concepts for optimum structural design - a review[J]. Structural and Multidisciplinary Optimization, 1993, 5(3): 129-144.
[29] Romstad. K. M, Huntchinson. J. R, Runge. K. H. Design parameter variation and structural response[J]. International journal of Nunerical Methods in Engineering, 1973, 5(3): 337-349.
[30] Svanberg. K. The method of moving asymptotes - a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373.
[31] Fleury. C. Efficient approximation concepts using second order information[J]. International Journal for Numerical Methods in Engineering, 1989, 28(9): 2041-2058.
[32] Fleury. C. First and second order convex approximation strategies in structural optimization[J]. Structural and Multidisciplinary Optimization, 1989, 1(1): 3-10.
[33] Melosh. R. J, Luik. R. Multiple configuration analysis of structures[J]. Journal of the Structure Division, ASCE, 1968, 94(11): 2581-2596.
[34] Fox. R. L, Miura. H. An approximate analysis technique for design calculations[J]. AIAA Journal, 1971, 9(1): 177-179.
[35] Kirsch. U., Rubinstein. M. F. Structural reanalysis by iteration[J]. Computers & Structures, 1972, 2(4): 497-510.
[36] Kirsch. U., Toledano. G. Approximate reanalysis for modifications of structural geomrtry[J]. Computers & Structures, 1983, 16(1): 269-279.
[37] Kirsch. U. Reduced basis approximations of structural displacements for optimal design[J]. AIAA Journal, 1991, 29(10): 1751-1758.
[38] Kirsch. U., Eisenberger. M. Approximate interactive design of large structures[J]. Computing Systems in Engineering, 1991, 2(1): 67-73.
[39] Kirsch. U. Improved stiffness-based first-order approximations for structural optimization[J]. AIAA Journal, 1995, 33(1): 143-150.
[40] Kirsch. U., Liu. S. Structural reanalysis for general layout modifications[J]. AIAA Journal, 1997, 35(2): 382-388.
[41] Chen. S., Huang. C., Liu. Z. Structural approximate reanalysis for topological modifications of finite element systems[J]. AIAA Journal, 1998, 36(9): 1760-1762.
[42] Kirsch. U., Moses. F. An improved reanalysis method for grillage-type structures[J]. Computers and Structures, 1998, 68(1-3): 79-88.
[43] Kirsch. U., Papalambros. P. Y. Structural reanalysis for topological modifications - a unified approach[J]. Structural and Multidisciplinary Optimization, 2001, 21(5): 333-344.
[44] Kirsch. U., Papalambros. P. Y. Exact and accurate solutions in the approximate reanalysis of structures[J]. AIAA Journal, 2001, 39(11): 2198-2205.
[45] Chen. S. H., Yang. Z. J. A universal method for structural static reanalysis of topological modifications[J]. International Journal for Numerical Methods in Engineering, 2004, 61(5): 673-686.
[46]陈塑寰吴晓明杨志军.结构静态拓扑重分析的迭代组合近似方法[J].力学学报, 2004, 36(05): 611-616.
[47] Wu. B. S., Lim. C. W., Li. Z. G. A finite element algorithm for reanalysis of structures with added degrees of freedom[J]. Finite Elements in Analysis and Design, 2004, 40(13-14): 1791-1801.
[48] Wu. B. S., Li. Z. G. Static reanalysis of structures with added degrees of freedom[J]. Communications in Numerical Methods in Engineering, 2006, 22(4): 269-281.
[49] Liu. H. F., Wu. B. S., Li. Z. G. Simple iteration method for structural static reanalysis[J]. Canadian Journal of Civil Engineering, 2009, 36(9): 1535-1538.
[50]孙睿珩,徐涛,张昊, et al.组合近似重分析方法的ANASYS二次开发[J].吉林大学学报(工学版), 2009, 29(s2): 396-400.
[51] Bae. H. R., Grandhi. R. V. Successive matrix inversion method for reanalysis of engineering structural systems[J]. AIAA Journal, 2004, 42(8): 1529-1535.
[52] Bae. H. R., Grandhi. R. V., Canfield. R. A. Accelerated engineering design optimization using successive matrix inversion method[J]. International Journal for Numerical Methods in Engineering, 2006, 66(9): 1361-1377.
[53] Bae. H. R., Grandhi. R. V., Canfield. R. A. Efficient successive reanalysis technique for engineering structures[J]. AIAA Journal, 2006, 44(8): 1883-1889.
[54]陈塑寰.结构振动分析的矩阵摄动理论[M].重庆:重庆出版社,1989.
[55] Chen. S. H., Yang. X. W., Wu. B. S. Static displacement reanalysis of structures using perturbation and Padéapproximation[J]. Communications in Numerical Methods in Engineering, 2000, 16(2): 75-82.
[56]陈塑寰孟光黄海.摄动法结合Padé逼近在结构拓扑重分析中的应用[J].应用力学学报, 2005, 22(02): 155-158.
[57]陈塑寰孟光郭克尖黄海.结构静态拓扑重分析的摄动-Padé逼近法[J].固体力学学报, 2005, 26(03): 321-324.
[58]吴晓明,陈塑寰,黄志东. Epsilon算法在汽车结构设计分析中的应用[J].吉林大学学报(工学版), 2006, 36(3): 8-11.
[59] Wu. X. M., Chen. S. H., Yang. Z. J. Static displacement reanalysis of modified structues using the epsilon algorithm[J]. AIAA Journal, 2007, 45(8): 2083-2086.
[60] Yang. Z. J., Chen. X., Kelly. R. An Adaptive Static Reanalysis Method for Structural Modifications Using Epsilon Algorithm[J]. International Joint Conference on Computational Sciences and Optimization, Vol 2, Proceedings, 2009: 897-899 1051.
[61]徐涛,程飞,于澜, et al.基于预条件Lanczos算法的结构拓扑修改静态重分析方法[J].吉林大学学报(工学版), 2007, 37(05): 1214-1219.
[62]徐涛,程飞,郭桂凯, et al.结构静态重分析的改进预条件Lanczos方法[J].机械强度, 2009, 31(03): 425-431.
[63]徐涛,程飞,宋广才, et al.结构拓扑修改静态重分析的BFGS方法[J].吉林大学学报(工学版), 2009, 39(01): 103-107.
[64] Level. P., Moraux0. D., Drazetic. P., et al. On a direct inversion of the impedance matrix in response reanalysis[J]. Communications in Numerical Methods in Engineering, 1996, 12(3): 151-159.
[65] Weissenberger. J. T. Effect of local modifications on the vibration characteristics of linear systems[J]. Journal of Applied Mechanics, 1968, 35(6): 327-332.
[66] Wittrick. W. H. Rates of change of eigenvalues with reference to buckling and vibration problems[J]. Journal of the Royal Aeronautical Society, 1962, 66: 590-590.
[67] Zarghamee. M. S. Optimum frequency of structures[J]. AIAA Journal, 1968, 6(4): 749-750.
[68] Zarghamee. M. S. Minimum weight design with stability constraint[J]. Journal of the Structure Division, ASCE, 1970, 96(8): 1697-1710.
[69] Fox. R. L., Kapoor. M. P. Rates of change of eigenvalues and eigenvectors[J]. AIAA Journal, 1969, 6(12): 2426-2429.
[70] Goldman. R. L. Vibration analysis by dynamic partitioning[J]. AIAA Journal, 1969, 6(6): 1152-1154.
[71] Hou. S. N. Review of modal synthesis techniques and a new approach[J]. The Shock and Vibration Bulletin, 1969, 40(4): 25-39.
[72] Hunn. B. A. A method of calculating the normal modes of an aircraft[J]. Quarterly Journal of Mechanics, 1955, 8(1): 38-58.
[73] Gladwell. G. M. Branch mode analysis of vibrating systems[J]. journal of Sound and Vibration, 1964, 1(1): 41-59.
[74] Hurty. W. C. Dynamic analysis of structures using component modes[J]. AIAA Journal, 1965, 3(4): 678-685.
[75] Kirsch. U. Approximate vibration reanalysis of structures[J]. AIAA Journal, 2003, 41(3): 504-511.
[76] Kirsch. U., Bogomolni. M. Error evaluation in approximate reanalysis of structures[J]. Structural and Multidisciplinary Optimization, 2004, 28(2-3): 77-86.
[77] Kirsch. U., Bogomolni. M. Procedures for approximate eigenproblem reanalysis of structures[J]. International Journal for Numerical Methods in Engineering, 2004, 60(12): 1969-1986.
[78] He. J. J., Jiang. J. S., Xu. B. Modal reanalysis methods for structural large topological modifications with added degrees of freedom and non-classical damping[J]. Finite Elements in Analysis and Design, 2007, 44(1-2): 75-85.
[79] Bogomolni. M., Kirsch. U., Sheinman. I. Efficient design sensitivities of structures subjected to dynamic loading[J]. International Journal of Solids and Structures, 2006, 43(18-19): 5485-5500.
[80] Kirsch. U., Bogomolni. M., Sheinman. I. Efficient procedures for repeated calculations of the structural response using combined approximations[J]. Structural and Multidisciplinary Optimization, 2006, 32(6): 435-446.
[81] Rong. F., Chen. S. H., Chen. Y. D. Structural modal reanalysis for topological modifications with extended Kirsch method[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(5-6): 697-707.
[82] Chen. S. H., Yang. X. W., Lian. H. D. Comparison of several eigenvalue reanalysis methods for modified structures[J]. Structural and Multidisciplinary Optimization, 2000, 20(4): 253-259.
[83] Ma. L., Chen. S. H., Meng. G. W. Combined approximation for reanalysis of complex eigenvalues[J]. Computers & Structures, 2009, 87(7-8): 502-506.
[84] Yang. Z. J, Chen. S. H, Wu. X. M. A method for modal reanalysis of topological modifications of structures[J]. International Journal for Numerical Methods in Engineering, 2006, 65(13): 2203-2220.
[85] Chen. S. H., Rong. F. A new method of structural modal reanalysis for topological modifications[J]. Finite Elements in Analysis and Design, 2002, 38(11): 1015-1028.
[86] Zhang. G., Nikolaidis. E., Mourelatos. Z. P. An Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures[J]. Journal of Mechanical Design, 2009, 131(5): 1-13.
[87]孙亮,李顺华,李正光, et al.结构动力重分析的向量值有理逼近方法[J].吉林大学学报(理学版), 2005, 43(03): 258-261.
[88]何建军,姜节胜.结构拓扑修改动力学重分析的单步摄动逆迭代法[J].西北工业大学学报, 2006, 24(03): 313-316.
[89]张美艳,韩平畴.基于有理逼近和灵敏度分析的结构动力重分析方法[J].振动与冲击, 2006, 25(04): 50-52.
[90]张美艳,韩平畴.结构动力重分析的子结构有理逼近[J].计算力学学报, 2008, 25(06): 878-881.
[91]张美艳,韩平畴,唐国安.子结构灵敏度综合在结构动力重分析中的应用[J].振动与冲击, 2008, 27(04): 27-29.
[92]杨荣,王乐,徐涛, et al.具有不完全特征向量系的状态向量摄动的快速算法[J].吉林大学学报(工学版), 2008, 38(05): 1101-1104.
[93] Liu. X. L., Oliveira. C. S. Iterative modal perturbation and reanalysis of eigenvalue problem[J]. Communications in Numerical Methods in Engineering, 2003, 19(4): 263-274.
[94]吴晓明,陈塑寰. Epsilon算法在结构模态重分析中的应用[J].吉林大学学报(工学版), 2006, 36(04): 447-450.
[95] Chen. S. H., Wu. X. M., Yang. Z. J. Eigensolution reanalysis of modified structures using epsilon-algorithm[J]. International Journal for Numerical Methods in Engineering, 2006, 66(13): 2115-2130.
[96] Chen. S. H., Ma. L., Meng. G. W. Dynamic response reanalysis for modified structures under arbitrary excitation using epsilon-algorithm[J]. Computers & Structures, 2008, 86(23-24): 2095-2101.
[97]曹文钢,曲令晋,白迎春.基于灵敏度分析的客车车身质量优化研究[J].汽车工程, 2009, 31(03): 278-281.
[98]张武,陈剑,夏海.基于灵敏度分析的发动机悬置系统稳健优化设计[J].汽车工程, 2009, 31(08): 728-732.
[99]张代胜,张林涛,谭继锦, et al.基于刚度灵敏度分析的客车车身轻量化研究[J].汽车工程, 2008, 30(08): 718-720.
[100] D'Vari. R., Baker. M. Aeroelastic loads and sensitivity analysis for structural loads optimization[J]. Journal of Aircraft, 1999, 36(1): 156-166.
[101]唐明裴,阎贵平.结构灵敏度分析及计算方法概述[J].中国铁道科学, 2003, 24(01): 74-79.
[102] Pandey. P. C., Bakshi. P. Analytical response sensitivity computation using hybrid finite elements[J]. Computers and Structures, 1999, 71(5): 525-534.
[103] Haftka. Raphael T. Semi-analytical static nonlinear structural sensitivity analysis[J]. AIAA Journal, 1993, 31(7): 1307-1312.
[104] Haftka. R. T., Adelman. H. M. Recent developments in structural sensitivity analysis[J]. Structural Optimization, 1989, 1(3): 137-151.
[105] Barthelemy. B., Chon. C. T., Haftka. R. T. Accuracy problems associted with semi-analytical derivatives of static response[J]. Finite Elements in Analysis and Design, 1988, 4(3): 249-265.
[106] Bugeda. G., Onate. E. Optimum aerodynamic shape design including mesh adaptivity[J]. International Journal for Numerical Methods in Fluids, 1995, 20(8-9): 915-934.
[107] Choi. K. K., Twu. S. L. Equivalence of continuum and discrete methods of shape design sensitivity analysis[J]. AIAA Journal, 1989, 27(10): 1418-1424.
[108] Barthelemy. B., Haftka. R. T. Accuracy analysis of the semi-analytical method for shape sensitivity[J]. Mechanics Based Design of Structures and Machines, 1990, 18(3): 407-432.
[109] Mlejnek. H. P. Accuracy of semi-analytical sensitivities and its improvement by the "natural method"[J]. Structural Optimization, 1992, 4(2): 128-131.
[110] Olhoff. N., Rasmussen. J., Lund. E. A method of exact numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analysis[J]. Mechanics of Structures and Machines, 1993, 21(1): 1-66.
[111] Van. K. F., De. B. H. Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions[J]. International Journal for Numerical Methods in Engineering, 1998, 42(1): 71-91.
[112] De. B. H., Van. K. F. Refined semi-analytical design sensitivities[J]. International Journal of Solids and Structures, 2000, 37(46): 6961-6980.
[113] Kibsgaard. S. Sensitivity analysis - the basis for optimization[J]. International Journal for Numerical Methods in Engineering, 1992, 34(3): 901-932.
[114] Lund. E., Olhoff. N. Shape design sensitivity analysis of eigenvalues using "exact" numerical differentiation of finite element matrices[J]. Structural Optimization, 1994, 8(1): 52-59.
[115] Friswell. M. I. Calculation of second and higher order eigenvector derivatives[J]. Journal of Guidance, Control, and Dynamics, 1995, 18(4): 919-921.
[116] Andrew. A. L., Tan. R. C. E. Computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration[J]. AIAA Journal, 1996, 34(10): 2214-2216.
[117] Andrew. A. L., Tan. R. C. E. Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration[J]. Communications in Numerical Methods in Engineering, 1999, 15(9): 641-649.
[118] Chen. T. Y. Design sensitivity analysis for repeated eigenvalues in structural design[J]. AIAA Journal, 1993, 31(12): 2347-2350.
[119] Choi. K. K., Haug. E. J., Seong. H. G. Iterative method for finite dimensional structural optimization problems with repeated eigenvalues[J]. International Journal for Numerical Methods in Engineering, 1983, 19(1): 93-112.
[120] Dailey. R. L. Eigenvector derivatives with repeated eigenvalues[J]. AIAA Journal, 1989, 27(4): 486-491.
[121] Xu. T, Chen. S. H., Liu. Z. S. Perturbation sensitivity of generalized modes of defective systems[J]. Computers & Structures, 1994, 52(2): 179-185.
[122]徐涛,于澜,鞠伟, et al.计算亏损系统模态灵敏度的逐层递推演算方法[J].力学学报, 2008, 40(02): 281-288.
[123] Xu. T., Xu. T. S., Zuo. W. J., et al. Fast sensitivity analysis of defective system[J]. Applied Mathematics and Computation, 2010, 217(7): 3248-3256.
[124] Poldneff. M. J., Arora. J. S. Design sensitivity analysis in dynamic thermoviscoelasticlty with implicit integration[J]. International Journal of Solids and Structures, 1996, 33(4): 577-594.
[125] Cho. S., Choi. K. K. Design sensitivity analysis and optimization of non-linear transient dynamics. Part I - Sizing design[J]. International Journal for Numerical Methods in Engineering, 2000, 48(3): 351-373.
[126] Kim. N. H., Choi. K. K. Design sensitivity analysis and optimization of nonlinear transient dynamics[J]. Mechanics of Structures and Machines, 2001, 29(3): 351-371.
[127] Kirsch. U. Efficient sensitivity analysis for structural optimization[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 117(1-2): 143-156.
[128] Kirsch. U., Papalambros. P. Y. Accurate displacement derivatives for structural optimization using approximate reanalysis[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(31): 3945-3956.
[129] Kirsch. U., Bogomolni. M., Sheinman. I. Efficient procedures for repeated calculations of structural sensitivities[J]. Engineering Optimization, 2007, 39(3): 307-325.
[130] Kirsch. U., Bogomolni. M., van Keulen. F. Efficient finite difference design sensitivities[J]. AIAA Journal, 2005, 43(2): 399-405.
[131] Bogomolni. M., Kirsch. U., Sheinman. I. Nonlinear dynamic sensitivities of structures using combined approximations[J]. AIAA Journal, 2006, 44(11): 2765-2772.
[132]廖伯瑜,周新民,尹志宏.现代机械动力学及其工程应用[M].北京:机械工业出版社,2004.
[133] Stetson. K. A., Palma. G. E. Inversion of first-order perturbation theory and its application to structural design[J]. AIAA J, 1976, 14(4): 454-460.
[134] Chen. J.C., Wade. B.K. Matrix Perturbation for Structural Dynamic Analysis[J]. AIAA J, 1977, 15(8): 1095-1100.
[135] Berman. A. Mass matrix correction using an incomplete set of measured modes[J]. AIAA J, 1979, 17(10): 1147-1148.
[136] Wei. F. S. Stiffness matrix correction from incomplete test data [J]. AIAA J, 1980, 18(10): 1274-1275.
[137] Liu. S. Improvement of analytical dynamic models using complex modal test data[J]. International Journal of Mechanical Sciences, 1992, 34(10): 817-829.
[138]彭晓洪,丁锡洪,周建功.用模态参数识别结果对实际结构有限元动力模型的修正[J].振动与冲击, 1984, (03): 8-15.
[139]王朝永,张令弥.利用试验模态参数修正有限元模型的再正交拉格朗日乘子法[J].振动工程学报, 1986, (2): 54-58.
[140] Liu. J. K., Chan. H. C. A universal matrix perturbation technique for structural dynamic modification using singular value decomposition[J]. Journal of Sound and Vibration, 1999, 228(2): 265-274.
[141] Blaldvdn. J. F., Hutton. S. G. Natural Modes of Modified Structures[J]. AIAA J, 1985, 23(11): 1737-1743.
[142] Kundra. T. K. Structural dynamic modifications via models[J]. Sadhana-Academy Proceedings in Engineering Sciences, 2000, 25: 261-276.
[143] Nakra. B. C. Structural dynamic modification using additive damping[J]. Sadhana-Academy Proceedings in Engineering Sciences, 2000, 25: 277-289.
[144] Sestieri. A. Structural dynamic modification[J]. Sadhana-Academy Proceedings in Engineering Sciences, 2000, 25: 247-259.
[145] Li. T., He. J. M. Modification of truss structures using linear modification method[J]. Inverse Problems in Engineering, 2001, 9(3): 217-234.
[146] Yap. K. C., Zimmerman. D. C. A comparative study of structural dynamic modification and sensitivity method approximation[J]. Mechanical Systems and Signal Processing, 2002, 16(4): 585-597.
[147] Chen. H. P. Efficient methods for determining modal parameters of dynamic structures with large modifications[J]. Journal of Sound and Vibration, 2006, 298(1-2): 462-470.
[148] Hang. H. J., Shankar. K., Lai. J. C. S. Prediction of the effects on dynamic response due to distributed structural modification with additional degrees of freedom[J]. Mechanical Systems and Signal Processing, 2008, 22(8): 1809-1825.
[149] Hang. H. J., Shankar. K., Lai. J. C. S. Effects of distributed structural dynamic modification with reduced degrees of freedom[J]. Mechanical Systems and Signal Processing, 2009, 23(7): 2154-2177.
[150] Hang. H. J., Shankar. K., Lai. J. C. S. Effects of distributed structural dynamic modification with additional degrees of freedom on 3D structure[J]. Mechanical Systems and Signal Processing, 2010, 24(5): 1349-1368.
[151] Papalambros. P. Y., Wilde. D. J. Principles of Optimal Design: Modeling and Computation[M]. Cambridge:Cambridge University Press,1988.
[152] Zhou. M., Pagaldipti. N., Thomas. H. L., et al. An integrated approach to topology, sizing, and shape optimization[J]. Structural and Multidisciplinary Optimization, 2004, 26(5): 308-317.
[153] Pedersen. N. L., Nielsen. A. K. Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling[J]. Structural and Multidisciplinary Optimization, 2003, 25(5-6): 436-445.
[154] Fourie. P. C., Groenwold. A. A. The particle swarm optimization algorithm in size and shape optimization[J]. Structural and Multidisciplinary Optimization, 2002, 23(4): 259-267.
[155] Bhavikatti. S. S., Ramakrishnan. C. V. Optimum design of fillets in flat and round tension bars[C], Proceedings of the ASME 1977 Design Engineering Technical Conference. Chicago, 1977.
[156] Prasad. B., Emerson. J. F. Optimal structural remodeling of multi-objective systems[J]. Computers and Structures, 1984, 18(4): 619-628.
[157] Bennett. J. A., Botkin. M. E. Structural shape optimization with geometric description and adaptive mesh refinement[J]. AIAA J, 1985, 23(3): 458-464.
[158] Braibant. V., Fleury. C. Shape optimal design using B-splines[J]. Computer Methods in Applied Mechanics and Engineering, 1984, 44(3): 247-267.
[159] Imam. M. H. Three-dimensional shape optimization[J]. International Journal for Numerical Methods in Engineering, 1982, 18(5): 661-673.
[160] Braibant. V., Fleury. C. An approximation-concepts approach to shape optimal design[J]. Computer Methods in Applied Mechanics and Engineering, 1985, 53(2): 119-148.
[161] Belegundu. A. D., Rajan. S. D. A shape optimization approach based on natural design variables and shape functions[J]. Comput. Methods Appl. Mech. Engrg., 1988, 66(1): 89-106.
[162] H. Azegami, M. Shimoda, E. Katamine, et al. A domain optimization technique for elliptic boundary value problems[C], Computer Aided Optimization Design of Structures IV, Structural Optimization. Southampton, 1995.
[163] Inzarulfaisham. A. R., Azegami. H. Solution to boundary shape optimization problem of linear elastic continua with prescribed natural vibration mode shapes[J]. Structural and Multidisciplinary Optimization, 2004, 27(3): 210-217.
[164]荣见华,郑健龙,徐飞鸿.结构动力修改与优化设计[M].长沙:人民交通出版社,2002.
[165] Michell. A. G. M. The limits of economy of material in frame-structures[J]. Phil. Mag., 1904, 8(47): 589-597.
[166] Bends?e. M. P., Ben-Tal. A., Zowe. J. Optimization methods for truss geometry and topology design[J]. Structural Optimization, 1994, 7(3): 141-159.
[167] Gil. L., Andreu. A. Shape and cross-section optimization of a truss structure[J]. Computers and Structures, 2001, 79(7): 681-689.
[168] Duda. J. W., Jakiela. M. J. Generation and classification of structural topologies with genetic algorithm speciation[J]. Journal of Mechanical Design, Transactions Of the ASME, 1997, 119(1): 127-131.
[169] Chapman. C. D., Saitou. K., Jakiela. M. J. Genetic algorithms as an approach to configuration and topology design[J]. Journal of Mechanical Design, Transactions Of the ASME, 1994, 116(4): 1005-1012.
[170] Harasaki. H., Arora. J. S. A new class of evolutionary methods based on the concept of Transferred Force for structural design[J]. Structural and Multidisciplinary Optimization, 2001, 22(1): 35-56.
[171] Kita. E., Toyoda. T. Structural design using cellular automata[J]. Structural and Multidisciplinary Optimization, 2000, 19(1): 64-73.
[172] Abdalla. M. M., Gürdal. Z. Structural design using cellular automata for eigenvalue problems[J]. Structural and Multidisciplinary Optimization, 2004, 26(3-4): 200-208.
[173] Bends?e. 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.
[174] Bends(?)e. M. P. Optimal shape design as a material distribution problem[J]. Structural Optimization, 1989, 1(4): 193-202.
[175] Yang. R. J., Chahande. A. I. Automotive applications of topology optimization[J]. Structural Optimization, 1995, 9(3-4): 245-249.
[176] Bends(?)e. M. P., Sigmund. O. Material interpolation schemes in topology optimization[J]. Archive of Applied Mechanics, 1999, 69(9-10): 635-654.
[177] Suzuki. K., Kikuchi. N. A homogenization method for shape and topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 1991, 93(3): 291-318.
[178] Diaz. A. R., Kikuchi. N. Solutions to shape and topology eigenvalue optimization problems using a homogenization method[J]. International Journal for Numerical Methods in Engineering, 1992, 35: 1487-1502.
[179] Pedersen. N. L. Maximization of eigenvalues using topology optimization[J]. Structural and Multidisciplinary Optimization, 2000, 20(1): 2-11.
[180] Mayer. R. R., Kikuchi. N., Scott. A. Application of topological optimization techniques to structural crashworthiness[J]. International Journal for Numerical Methods in Engineering, 1996, 39(8): 1383-1403.
[181] Mayer. R. R., Maurer. D., Bottcher. C. Application of Topological Optimization Program to the Danner Test Simulation[C], Proceedings of the ASME 2000 Design Engineering and Technical Conferences. Maryland, 2000.
[182] Kharmanda. G., Olhoff. N., Mohamed. A., et al. Reliability-based topology optimization[J]. Structural and Multidisciplinary Optimization, 2004, 26(5): 295-307.
[183] Bremicker. M., Chirehdast. M., Kikuchi. N., et al. Integrated topology and shape optimization in structural design[J]. Mech. Struct. Mach., 1991, 19(4): 551-587.
[184]龙江启,兰凤崇,陈吉清.车身轻量化与钢铝一体化结构新技术的研究进展[J].机械工程学报, 2008, 44(06): 27-35.
[185] Avalle. M., Peroni. L., Peroni. M., et al. Bi-Material Joining for Car Body Structures: Experimental and Numerical Analysis[J]. Journal of Adhesion, 2010, 86(5-6): 539-560.
[186] Carle. D., Blount. G. The suitability of aluminium as an alternative material for car bodies[J]. Materials & Design, 1999, 20(5): 267-272.
[187]高云凯,姜欣,彭和东, et al.轿车车身轻量化结构[J].现代零部件, 2004, (05): 34,36,38.
[188] Sun. H. T., Shen. G. Z., Hu. P., et al. Study on Lightweight Optimization of Car Body Based on Crash[C], Icicta: 2009 Second International Conference on Intelligent Computation Technology and Automation, Vol Ii, Proceedings. Changsha, 2009.
[189] Zhang. H. Z., Zhang. S. R., Hu. P., et al. An Intelligent System Based on Optimization for Car Body Design[C], 2009 Ieee Intelligent Vehicles Symposium, Vols 1 and 2. Symposium, 2009.
[190] X. W. Zhang, Z. Tao. A Study on Shape Optimization of Bus Body Structure Based on Stiffness Sensitivity Analysis[C], 2009 Ieee 10th International Conference on Computer-Aided Industrial Design & Conceptual Design, Vols 1-3. Wenzhou, 2009.
[191] Zhu. P., Zhang. Y., Chen. G. L. Metamodel-based lightweight design of an automotive front-body structure using robust optimization[C], Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering. 2009.
[192] Wennhage. P. Weight optimization of large scale sandwich structures with acoustic and mechanical constraints[J]. Journal of Sandwich Structures & Materials, 2003, 5(3): 253-266.
[193] Azadi. M., Azadi. S., Zahedi. F., et al. Multidisciplinary Optimization of a Car Component under Nvh and Weight Constraints Using Rsm[J]. International Journal of Vehicle Noise and Vibration, 2009, 5(3): 261-270.
[194]崔玲,高云凯.基于正交试验设计的客车车身结构优化研究[J].制造业自动化, 2010, 32(11): 142-147.
[195]宋凯,成艾国,胡朝辉, et al.基于真实接头车身概念模型的结构优化[J].中国机械工程, 2010, 21(22): 2764-2770.
[196] Kim. M. H., Suh. M. W., Bae. D. H. Development of an optimum design technique for the bus window pillar member[J]. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, 2001, 215(D1): 11-20.
[197] Suh. M. W., Yang. W. H., Suhr. J. Analysis of the joint structure of the vehicle body by condensed joint matrix method[J]. Ksme International Journal, 2001, 15(12): 1639-1646.
[198] Suh. M. W., Suhr. J., Yang. W. H. Condensed joint matrix method for the joint structure of a vehicle body[J]. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering, 2002, 216(D1): 35-41.
[199] Kirsch. U. A unified reanalysis approach for structural analysis, design, and optimization[J]. Structural and Multidisciplinary Optimization, 2003, 25(2): 67-85.
[200]刘长学.超大规模稀疏矩阵计算方法[M].上海:上海科学技术出版社,1991.
[201] Roberts. D. E. On the convergence of rows of vector padéapproximants[J]. Journal of Computational and Applied Mathematics, 1996, 70(1): 95-109.
[202]陈塑寰.结构振动分析的数值方法[M].长春:吉林科学技术出版社,1996.
[203] Bathe. K. J. Finite elemente method[M]. Berlin:Springer,2002.
[204] Houbolt. J. C. A recurrence matrix solution for the dynamic response of elastic aircraft[J]. Aeronautical Journal, 1950, 17: 540-550.
[205] Bathe. K. J., Wilson. E. L. Numerical methods in finite analysis[M]. New Jersey:Prentice Hall Inc,1976.
[206] Newmark. N. M. A method of computation for structural dynamics[J]. Journal of Engineering Mechanics, 1959, 85(3): 249-260.
[207]黄明游,刘播,徐涛.数值计算方法[M].北京:科学出版社,2005.
[208] Carpentieri. B., Duff. I. S., Giraud. L. A Class of Spectral Two-Level Preconditioners[J]. Journal on Scientific Computing, SIAM, 2003, 25(2): 749-765.
[209] Giraud. L., Gratton. S., Martin. E. Incremental spectral preconditioners for sequences of linear systems[J]. 2007, 57(11-12): 1164-1180.
[210]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[211] Curran. R., Castagne. S., Rothwell. A., et al. Uncertainty and Sensitivity Analysis in Aircraft Operating Costs in Structural Design Optimization[J]. Journal of Aircraft, 2009, 46(6): 2145-2155.
[212] Van K. F., Haftka. R. T., Kim. N. H. Review of options for structural design sensitivity analysis. Part 1: Linear systems[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(30-33): 3213-3243.
[213]李亦文,徐涛,左文杰, et al.基于相对灵敏度的车身结构模型修改[J].吉林大学学报(工学版), 2009, 39(06): 1435-1440.
[214] Guo. G. K, Xu. T., Li. Y. W., et al. Optimization of Joints Stiffness on the Autobody Based on Minimization of Strain Energy[C], Proceedings of the 3rd International Conference on Mechanical Engineering and Mechanics. Beijing, 2009.
[215]黄金陵.汽车车身设计[M].北京:机械工业出版社,2007.
[216]黄金陵,娄永强,龚礼洲.轿车车身结构概念模型中接头的模拟[J].机械工程学报, 2000, 36(3): 78-81.
[217]钱令希.工程结构优化设计[M].北京:水利水电出版社,1983.
[218]任露泉.试验优化设计与分析[M].长春:吉林科学技术出版社,2001.
[219]李董辉,童小娇.数值最优化[M].北京:科学出版社,2005.
[220] Dai. Y. H. Convergence properties of the BFGS algoritm[J]. Siam Journal on Optimization, 2003, 13(3): 693-701.