薄壁结构件塑性成形技术研究
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摘要
内高压胀形工艺与先分片(段)成形再拼焊的传统制造工艺相比，具备整体成形几何形状非常复杂的中空薄壁结构件的能力。几何构形一体化程度的改善既有助于精简工序环节、降低工装成本，又有利于提高零件的比强度、比刚度与疲劳寿命。伴随着计算机数字控制技术、传感器测试技术以及液压密封技术的日益成熟与完善，内高压胀形工艺已进入实用化阶段。目前，这种先进塑性成形工艺正在世界汽车工业轻量化进程中发挥着积极作用。可以预见，内高压胀形工艺也将有力地促进航空、航天、船舶、机车等产业的制造技术水平的进步与提高。
本论文围绕管材内高压胀形工艺，针对塑性成形工艺设计方法和塑性变形稳定性等问题展开了研究。
塑性成形工艺设计所涉及的因素一般较多，而且每个因素的具体水平也比较多。基于偏差的分析表明，均匀试验设计要比正交试验设计更适合于多因素多水平复杂试验方案的优化设计问题。与传统的多元回归分析数据处理方式相比，多层前馈神经网络的隐式统计推理功能，对于建立成形结果与塑性成形工艺参数之间的内在映射关系，则更具有工程实用意义。本论文以管材无模轴压胀形的有限元数值模拟为研究平台，首次采用均匀试验设计与神经网络技术相结合的方法，就基于成形指标约束的塑性成形工艺参数设计方法的技术可行性进行了研究，以期从策略上提高塑性成形工艺参数设计的主动性和针对性，克服传统试错方式的被动性和盲目性。
塑性皱曲是管材内高压胀形工艺的一种典型失效形式。对塑性皱曲的发生和发展进行理论上的分析，不仅具有重要的学术价值，同时也有助于加深对管材内高压胀形工艺变形机理的认识，进而为确定合理的加载方案提供必要的指导。受到轴向载荷作用下的薄壁管轴对称坍塌的机构化模型的启发，在将该机构化模型的适用材料类型由理想塑性材料推广至线性强化材料之后，本论文针对管材无模轴压胀形端部皱曲的局部性特征，首次提出了一种“皱曲区—膨胀区—皱曲区”的管坯区划理论模型。在此基础上，通过将基于塑性失稳系数的薄壳塑性稳定性理论与能量准则相结合，在系统势能极小条件下，建立起管材无模轴压胀形端部
摘 要
皱曲临界载荷的理论计算方法。
此外，本论文还对内高压胀形材料的力学性能测试与建模、内高压胀形工艺
的有限元数值模拟技术以及加载控制实验系统开发等问题进行了实践与探索。
Compared with the conventional stamping plus welding approach,the Internal High Pressure Forming (IHPF) technology has the ability to entirely form hollow thin-walled components with complex configuration. Higher structural integrity will bring about less procedure amount,lower tooling cost,but higher specific strength,bigger specific stiffness and longer fatigue lifetime. Due to the great advancement of the hydraulic seal performance and the transducer control capability,the IHPF technology already reaches the practical level. Currently,this advanced plastic forming technology plays an important role on the lightweight issue in the automotive industry. It can be imagined that this technology is also significant for the manufacturing art improvement of the aircraft,shipping and locomotive.
Centering on the tube hydroforming (THF) technology,this paper studies the methodology for the plastic forming process design and the stability of the plastic deformation.
Generally,the plastic forming process design involves certain parameters,while each parameter has several cases. The discrepancy analysis demonstrates that,for the multi-factor and multi-level project design,the uniform experimental design is better than the orthogonal one. Unlike the regression analysis method,the implicit statistical inference ability of the multi-layer feedforward neural network provides a more pragmatistic way to establish the mapping relationship between the plastic deformation and the process parameters. In order to enhance the efficiency of the plastic forming process design and to overcome the drawbacks of the trial-and-error approach,on the basis of the Finite Element model of the dieless tube hydroforming under internal pressure and axial compression,this dissertation for the first time combines the uniform experimental design method with the neural network technique to design the plastic forming process parameters,which will lead to the designated deformation.
Plastic wrinkling is a typical defective mode during the THF. The theoretical study on the wrinkle's onset and growth is academically valuable and useful to understand the mechanism of the THF in depth,which will make a positive contribution to the loading design. Inspired by the symmetric collapse model of thin-walled tube under axial compression and expanding its applicable material type from the ideal plastic case to the linear hardening one,this dissertation for the first time proposes a zoning model to explore the local wrinkling characteristic of the THF. According to the thin shell plastic stability theory,which is based on the plastic instability coefficients,and under the condition of the system potential minimization,this paper formulates a method to calculate the critical wrinkling loads of the THF.
Besides,some IHPF-related topics,such as material properties evaluation,Finite Element simulation and loading control experimental system,are also included in this paper.
本论文围绕管材内高压胀形工艺，针对塑性成形工艺设计方法和塑性变形稳定性等问题展开了研究。
塑性成形工艺设计所涉及的因素一般较多，而且每个因素的具体水平也比较多。基于偏差的分析表明，均匀试验设计要比正交试验设计更适合于多因素多水平复杂试验方案的优化设计问题。与传统的多元回归分析数据处理方式相比，多层前馈神经网络的隐式统计推理功能，对于建立成形结果与塑性成形工艺参数之间的内在映射关系，则更具有工程实用意义。本论文以管材无模轴压胀形的有限元数值模拟为研究平台，首次采用均匀试验设计与神经网络技术相结合的方法，就基于成形指标约束的塑性成形工艺参数设计方法的技术可行性进行了研究，以期从策略上提高塑性成形工艺参数设计的主动性和针对性，克服传统试错方式的被动性和盲目性。
塑性皱曲是管材内高压胀形工艺的一种典型失效形式。对塑性皱曲的发生和发展进行理论上的分析，不仅具有重要的学术价值，同时也有助于加深对管材内高压胀形工艺变形机理的认识，进而为确定合理的加载方案提供必要的指导。受到轴向载荷作用下的薄壁管轴对称坍塌的机构化模型的启发，在将该机构化模型的适用材料类型由理想塑性材料推广至线性强化材料之后，本论文针对管材无模轴压胀形端部皱曲的局部性特征，首次提出了一种“皱曲区—膨胀区—皱曲区”的管坯区划理论模型。在此基础上，通过将基于塑性失稳系数的薄壳塑性稳定性理论与能量准则相结合，在系统势能极小条件下，建立起管材无模轴压胀形端部
摘 要
皱曲临界载荷的理论计算方法。
此外，本论文还对内高压胀形材料的力学性能测试与建模、内高压胀形工艺
的有限元数值模拟技术以及加载控制实验系统开发等问题进行了实践与探索。
Compared with the conventional stamping plus welding approach,the Internal High Pressure Forming (IHPF) technology has the ability to entirely form hollow thin-walled components with complex configuration. Higher structural integrity will bring about less procedure amount,lower tooling cost,but higher specific strength,bigger specific stiffness and longer fatigue lifetime. Due to the great advancement of the hydraulic seal performance and the transducer control capability,the IHPF technology already reaches the practical level. Currently,this advanced plastic forming technology plays an important role on the lightweight issue in the automotive industry. It can be imagined that this technology is also significant for the manufacturing art improvement of the aircraft,shipping and locomotive.
Centering on the tube hydroforming (THF) technology,this paper studies the methodology for the plastic forming process design and the stability of the plastic deformation.
Generally,the plastic forming process design involves certain parameters,while each parameter has several cases. The discrepancy analysis demonstrates that,for the multi-factor and multi-level project design,the uniform experimental design is better than the orthogonal one. Unlike the regression analysis method,the implicit statistical inference ability of the multi-layer feedforward neural network provides a more pragmatistic way to establish the mapping relationship between the plastic deformation and the process parameters. In order to enhance the efficiency of the plastic forming process design and to overcome the drawbacks of the trial-and-error approach,on the basis of the Finite Element model of the dieless tube hydroforming under internal pressure and axial compression,this dissertation for the first time combines the uniform experimental design method with the neural network technique to design the plastic forming process parameters,which will lead to the designated deformation.
Plastic wrinkling is a typical defective mode during the THF. The theoretical study on the wrinkle's onset and growth is academically valuable and useful to understand the mechanism of the THF in depth,which will make a positive contribution to the loading design. Inspired by the symmetric collapse model of thin-walled tube under axial compression and expanding its applicable material type from the ideal plastic case to the linear hardening one,this dissertation for the first time proposes a zoning model to explore the local wrinkling characteristic of the THF. According to the thin shell plastic stability theory,which is based on the plastic instability coefficients,and under the condition of the system potential minimization,this paper formulates a method to calculate the critical wrinkling loads of the THF.
Besides,some IHPF-related topics,such as material properties evaluation,Finite Element simulation and loading control experimental system,are also included in this paper.
引文
[1] F. Dohman, Ch. Hartl, Hydroforming: Research and Practical Application, Proceedings of the 2th International Conference on Innovations in Hydroforming Technology, Columbus, Ohio State University, 1997, pp.1-9
[2] G. Morphy, Hydroforming High Strength Steel Tube for Automotive Structural Application Using Expansion, SAE Technical PaperNo. 970373, 1997
[3] Ch. Bruggenmann, S. Shah, Hydroforming Product and Process—Requirements and Implementation, TPA 2nd Annual Automotive Tube Conference, 1997, pp.89-103
[4] M. Koc, T. Altan, An overall review of the tube hydroforming (THF) technology, Journal of Materials Processing Technology, 108 (2001), pp.384-393
[5] F.-U. Leitloff, Hydroforimg Gives the Right Shape to Hollow Components, IMPRESSION, Edition 8, 1997, SMG Sddeutsche Maschinenbau GmbH & Co, p.4
[6] Anon., Hydroforming Technology, Advanced Materials & Processes, 5/97, pp.50-53
[7] M. Ahmetoglu, K. Sutter, X. J. Li, T. Altan, Tube hydroforming: current research, applications and need for training, Journal of Materials Processing Technology, 98(2000), pp.224-231
[8] F. Klaas, Innovation in high-pressure hydroforming, Proceedings of the 2th International Conference on Innovations in Hydroforming Technology, Columbus, Ohio State University, 1997, pp. 15-19
[9] H. Cherek, Part cost reduction in the hydroforming processes, Proceedings of the 2th International Conference on Innovations in Hydroforming Technology, Columbus, Ohio State University, 1997, pp.22-26
[10] G. Morphy, Tube Hydroforming: Dimensional Capability Analysis of a High Volume Automotive Structural Component Production Process, SAE Technical Paper No. 980450, 1998
[11] Th. A. Hannibal, J. R. Dieffenbach, Hydroformed Structural Elements: An Economic Evaluation of the Technology, SAE Technical Paper No. 980451, 1998
[12] E. Doege, R. Ksters, M.-I. Rotarescu, C. Ropers, Neue Mglichkeiten der Berechnung von Prozessparametern fr die Innenhochdruckumformung von rohrfrmigen Bauteilen, Umformen Trennen Fgen, 1/2001, Seiten 4-7
[13] H.-U. Lcke, Ch. Hartl, T. Abbey, Hydroforming, Journal of Materials Processing Technology, 115 (2001), pp.87-91
[14] G. Holzinger, Mit IHU zu hochprzisen Leichtbauteilen, STAHL, 1/2000, Seiten 58-59
[15] M. Ahmetoglu, T. Altan, Tube hydroforming: state-of-the-art and future trends, Journal of Materials Processing Technology, 98 (2000), pp.25-33
[16] J. Neubert, Innenhochdruckumformung im ULSAB-Projekt, Blech Rohre Profile, 43 (1996) 1/2, Seite 62
[17] U. Herberg, Umformen von Platinen mit Innendruck, Blech Rohre Profile, 43 (1996) 1/2, Seite 57
[18] M. Geiger, P. Hein, Neue Ideen zum Innenhochdmckumformen, Blech Rohre Profile, 43 (1996) 1/2, Seiten 63-64
[19] M. Geiger, P. Hein, S. Bobbert, FE-Analysis and Process Design for the Hydroforming of Sheet Metal Pairs, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept. 1999, Besancon, France, pp.9-14
[20] M. Geiger, F. Vollertsen, P. Hein, Hydroforming of sheet metal pairs, Proceedings of SheMet'98, 1998, pp.37-51
[21] M. Kleiner, R. Kolleck, J. Rauer, Die-less forming of sheet metal parts, Proceedings of SheMet'98, 1998, pp.63-70
[22] S. Novotny, P. Hein, Hydroforming of sheet metal pairs from aluminum alloys, Proceedings ofSheMet'99, 1999, pp.591-606
[23] P. Hein, F. Vollertsen, Hydroforming of sheet metal pairs, Journal of Materials Processing Technology, 87(1999), pp.154-164
[24] O. Kreis, P. Hein, Manufacturing system for the integrated hydroforming, trimming and welding of sheet metal pairs, Journal of Materials Processing Technology, 115(2001), pp.49-54
[25] S. Novotny, P. Hein, Hydroforming of sheet metal pairs from aluminium alloys, Journal of Materials Processing Technology, 115(2001), pp.65-69
[26] A. Eichhorn, S. Motsch, Hydroforming of Tailored Tubes, Proceedings of the 21st Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor,Michigan, USA, pp.23-31
[27] K. Siegert, M. Hussermann, B. Lsch, R. Rieger, Recent developments in hydroforming technology, Journal of Materials Processing Technology, 98 (2000), pp.251-258
[28] MERCER Management Consult, IHU-Anwendungen in der Automobilindustrie, Mnchen, Mai 2000
[29] S. Lichtenberg, H.-G. Hoff, Stand der Innenhochdruckumformung in Deutschland, Blech Rohre Profile, 43 (1996) 1/2, Seiten 40-46
[30] H. Grabowski, Preface, Proceedings of the Workshop Universal Design Theory, Aachen Shaker Verlag, 1998
[31] 王同海编著，管材塑性加工技术，机械工业出版社，1998年7月
[32] 苑世剑，王仲仁，轻量化结构内高压成形技术，材料科学与工艺，1999，7(增刊)，PP．139-142
[33] 王仲仁，球形容器整体成形新工艺，压力容器，1988，5(1)，pp．78-81
[34] Z. R. Wang, T. Wang, D. C. Kang, S. H. Zhang, Y. Fang, The technology of the hydrobulging of whole spherical vessels and experimental analysis, Journal of Mechanical Working Technology, 1989, 18 (1), pp.85-94
[35] S. H. Zhang, Z. R. Wang, The stress distribution and plastic hastening-sphere effect in the integral hydrobulge forming of spherical vessels, International Journal of Materials and Product Technology, 1990, 5, pp.293-300
[36] S. H. Zhang, Z. R. Wang, Experimental research and FEM analysis of the hydroforming technology of double-layer spherical vessels, Advanced Technology of Plasticity, Proceedings of the 4th ICTP, 1993, 1, pp.49-53
[37] 王仲仁，曾元松，苑世剑，张士宏，椭球壳体液压成形的塑性变形规律的研究，固体力学学报，1998，19(3)，pp．259-264
[38] 王仲仁，苑世剑，曾元松，张士宏，董建令，王凤志，无模胀球的原理与研究进展，机械工程学报，1999，35(4)，pp．64-66
[39] J. L. Dong, Z.R. Wang, C.D. Liu, Single-curvature polyhedron hydrobuilding technology for manufacturing spherical vessels, Proceedings of the 7th International Conference on Pressure Vessel Technology, 1999, pp.128-134
[40] 苑世剑，郎利辉，王仲仁，内高压成形技术研究与应用进展，哈尔滨工业大学学报，2000，32(5)，pp．60-63
[41] 张士宏，许沂，王忠堂，郎利辉，刘钢，板材零件成对液压成形新技术，哈尔滨工业大学学报，2000，32(4)，pp．7-9
[42] 赵长财，张涛，刘国晖，刘助柏，有限长薄壁管胀形研究，塑性工程学报，1997，4(1)，pp．36-41
[43] 赵长财，薄壁管在内压，轴力作用下的初始屈服，塑性工程学报，2000，8(3)，pp．29-31
[44] 李新军，周贤宾，K．Sutter，T．Altan，薄壁管轴压胀形的加载与控制，第七届全国锻压学术年会论文集，中国机械工程学会锻压学会编，航空工业出版社，1999年10月，pp．256-260
[45] 李新军，周贤宾，李敏，W．Thomas，T．Altan，计算机仿真技术在钣料冲压成形中的应用，航空制造工程，1998，3，pp．24-26
[46] H. Tautenhahn, Anisotropie und Textur von Rohren, Blech Rohre Profile, 43(1996)5, Seiten 234-239
[47] S. D. Liu, D. Meuleman, K. Thompson, Analytical and Experimental Examination of Tubular Hydroforming Limits, SAE Technical Paper No. 980449, 1998
[48] R. Kergen, J. C. Lescart, P. Duroux, Analysis of the Tube Formability in Perspective of Tube Hydroforming, Proceedings of the 21st Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor, Michigan, USA, pp.33-41
[49] T. Yoshida, Y. Kuriyama, Effects of Material Properties and Process Parameters on Deformation Behavior of Tube in Hydroforming, Proceedings of the 21th Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor, Michigan, USA, pp.43-52
[50] B. Carleer, G. van der Kevie, L. de Winter, B. van Veldhuizen, Analysis of the effect of material properties on the hydroforming process of tubes, Journal of Materials Processing Technology, 104 (2000), pp.158-166
[51] 王仁，熊祝华，黄文彬，塑性力学基础，科学出版社，1998年3月
[52] T. Sokolowski, K. Gerke, M. Ahmetoglu, T. Altan, Evaluation of Material Characteristics in Tube Hydroforming: Hydraulic Bulge Testing of Tubes, Advanced Technology of Plasticity, Vol. Ⅱ, Proceedings of the 6th ICTP, Sept. 19-24, 1999, pp. 1217-1222
[53] T. Sokolowski, K. Gerke, M. Ahmetoglu, T. Altan, Evaluation of Tube Formability and Material Characteristics: Hydraulic Bulge Testing of Tubes, Journal of Materials Processing Technology, 98 (2000), pp.34-40
[54] Abschluβbericht: Werkstckfestigkeitsmessung dutch freies Aufweitstauchen, LUF, Universitt Paderborn, 2000.9
[55] E. Doege, D. Drmann, C. Frank, Tiefziehen mit pulsierendem Niederhalter, Blech, 5/1996, Seiten 68-74
[56] C. M. Ziegler, Schwingende Niederhalterkraft und Regelkreise beim Tiefziehen, Dissertation: Beitrtge zur Umformtechnik, IFU, Universitt Stuttgart, Band 19, 1999
[57] E. Doege, C. Frank, G. Kurz, Schwingende Niederhalterkraft verbessert die Tiefziehergebnisse, Maschinenmarkt, 37/2000, Seiten28-34
[58] DASYLab Anwenderhandbuch Version 3.5, DATALOG GmbH, 1996
[59] J. Woitschig, Diplomarbeit: Prozefioptimierung durch die Schwingungs-berlagerung beim Innenhochdruckumformen, LUF, Universitt Paderbom, 2001.4
[60] Abschluβbericht: Untersuchung der Prozeβbeeinflussung beim Innenhochdruekumformen dutch eine pulsierende Anregung, LUF, Universitt Paderborn, 2001.8
[61] 肖景容，李尚健主编，塑性成形模拟理论，华中理工大学出版社，1994年12月
[62] 马泽恩主编，计算机辅助塑性成形，西北工业大学出版社，1995年5月
[63] 李顺平，杨合，神经网络在塑性加工中的应用，航空制造工程，1998，3，pp．27-28
[64] 吴林志，’99全国固体力学学术会议简介，力学进展，2000，30(1)，pp．156-158
[65] 戴昆，何祝斌，王仲仁，管材内压液力成形的稳定性分析，塑性工程学报，2000，7(4)，pp．49-52
[66] 吴洪飞，苑世剑，王仲仁，内高压成形塑性屈曲分析，锻压技术，2001，5，pp．29-31
[67] 方开泰，均匀设计与均匀设计表，科学出版社，1994年6月
[68] 程相君，王春宁，陈生潭，神经网络原理及其应用，国防工业出版社，1995．1
[69] 楼顺天，施阳，基于MATLAB的系统分析与设计——神经网络，西安电子科技大学出版社，1998
[70] S. Haykin, Neural networks: a comprehensive foundation (second edition), Prentice-Hall Inc., 1999
[71] H. Demuth, M. Beale, User's Guide for Neural Network Toolbox Version 3.0, MathWorks Inc., 1998
[72] G. F. Page, J. B. Gomm, D. Williams, Application of Neural Networks to Modelling and Control, Chapman and Hall, 1993
[73] 张际先，宓霞，神经网络及其在工程中的应用，机械工业出版社，1998．5
[74] J. A. Freeman, D. M. Skapura, Neural networks: algorithms, applications, and programming techniques, Addison-Wesley Publishing Company, 1992
[75] J. G. Taylor, The Promise of Neural Networks, Springer-Verlag London Limited, 1993
[76] B. Widrow and S. D. Sterns, Adaptive Signal Processing, New York: Prentice-Hall Inc., 1985
[77] M.T. Hagan, H.B. Demuth, M.H. Beale, Neural Network Design, PWS Publishing Company, Boston, MA 1996
[78] D.E Rumelhart, G.E. Hinton, R.J. Williams, Learning internal representations by error propagation, Parallel Data Processing (edited by D. Rumeihart and J. McClelland), Vol.1, Chapter 8, the M.I.T.Press, Cambridge, MA 1986, pp. 318-362
[79] D. Nguyen, B. Widrow, Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights, Proceedings of the International Joint Conference on Neural Networks, vol3, pp. 21-26, 1990
[80] D. Schmoeckel, C. Hessler, B. Engel, Pressure Control in Hydraulic Tube Forming, Annals of the CIRP, 1992, 41(1), pp. 311-314
[81] S. Thiruvarudchelvan, G. L. Seet, H. E. Ang, Computer-monitored hydraulic bulging of tubes, Journal of Materials Processing Technology, 57(1996), pp. 182-188
[82] T. Altan, M. Koc, I. Aue-u-lan, K. Tibari, Umformbarkeits-und Konstruktionsgesichtspunkte bei der Innenhochdruck-Umformung, Vortragstexte des Symposiums "Internationale Konferenz Hydroumformung" in Fellbach bei Stuttgart, am 12. und 13. Oktober 1999, Hydroumformung von Rohren, Strangpreβprofilen und Blechen, MAT-INFO Werkstoff-Informationsgesellschaft mbH, 1999, Seiten 135-151
[83] Z. C. Xia, S. C. Tang, On Path Dependence of Tubular Hydroforming, Proceedings of the 21st Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor, Michigan, USA, pp. 53-59
[84] J. B. Yang, B. H. Jeon, S. I. Oh, Design sensitivity analysis and optimization of the hydroforming process, Journal of Materials Processing Technology, 113 (2001), pp. 666-672
[85] L. P. Lei, D. H. Kim, S. J. Kang, S. M. Hwang, B. S. Kang, Analysis and design of hydroforming processes by the rigid-plastic finite element method, Journal of Materials Processing Technology, 114 (2001), pp. 201-206
[86] K. Manabe, H. Nishimura, Einfluβ des Werkstoffes bei der Formgebung von Rohren, BNDER BLECHE ROHRE, 1983, 4, Seiten 92-95
[87] J. Tirosh, A. Neuberger, A. Shirizly, On Tube Expansion by Internal Fluid Pressure with Additional Compressive Stress, International Journal of Mechanical Sciences, 38(1996), pp. 839-851
[88] S. Fuchizawa, M. Narazaki, A. Shirayori, Bulge Forming of Aluminum Alloy Tubes by Internal Pressure and Axial Compression, Advanced Technology of Plasticity 1996, Vol. Ⅰ, proceedings of the 5th ICTP, Oct. 7-10, 1996, pp.497-500
[89] J. Tirosh, A. Neuberger, A. Shirizly, Tube Expansion with 'unlimited' strain, Advanced Technology of Plasticity 1996, Vol. Ⅰ , proceedings of the 5th ICTP, Oct. 7-10, 1996, pp.527-530
[90] F. Dohmann, Ch. Hartl, Entwicklungen und Anwendungen des Innenhochdruckumformens, Blech Rohre Profile, 43(1996) 1/2, Seiten 30-35
[91] F. Dohmann, Ch. Hartl, Hydroforming—a method to manufacture light-weight parts, Journal of Materials Processing Technology, 60(1996), pp.669-676
[92] F. Dohmann, Ch. Hartl, Tube hydroforming—research and practical application, Journal of Materials Processing Technology, 71(1997), pp.174-186
[93] S. Toyoda, K. Uwai, K. Suzuki, T. Saito, A. Yoshitake, T. Mori, Hydroforming Formability of Electric Resistance Welded Tubes for Automobiles, SAE Technical Paper No. 1999-01-0027, 1999
[94] D. Thuvesen, I. Rask, Simulation of a Product Engineering Process—Tube Hydroforming, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept. 1999, Besancon, France, pp.485-489
[95] S. C. Rama, J. M. Zhang, A Numerical Approach to Analyze Tubular Hydroforming, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept.1999, Besancon, France, pp.497-502
[96] L. FUice, L. Fratini, E Micari, A Simple Experiment to Characterize Material Formability in Tube Hydroforming, Annals of the CIRP, Vol. 50, 1/2001, pp. 181-184
[97] H. L. Xing, A. Makinouchi, Virtual Design for Hydroforming of Tubes, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept. 1999, Besancon, France, pp.479-484
[98] H. L. Xing, A. Makinouchi, Numerical analysis and design for tubular hydroforming, International Journal of Mechanical Sciences, 43(2001), pp. 1009-1026
[99] 郞利辉，苑世剑，王仲仁，王小松，付庄，内高压液力成形陷产生及其失效分析，塑性工程学报，2001，8 (4)，30-35
[100] E. Ore, D. Durban, Elastoplastic Buckling of Axially Compressed Circular Cylindrical Shells, International Journal of Mechanical Sciences, 34(1992), pp. 727-742
[101] S. Li, S. R. Reid, The Plastic Buckling of Axially Compressed Square Tubes, ASME Journal of Applied Mechanics, 59(1992), pp.276-282
[102] S. R. Reid, Plastic Deformation Mechanisms in Axially Compressed Metal Tubes Used as Impact Energy Absorbers, International Journal of Mechanical Sciences, 35(1993), pp. 1035-1052
[103] Seishi Yamada, J. G. A. Croll, Buckling and Post-buckling Characteristics of Pressure-Loaded Cylinders, ASME Journal of Applied Mechanics, 60(1993), pp.290-299
[104] G. A. Kardomateas, Stability Loss in Thick Transversely Isotropic Cylindrical Shells Under Axial Compression, ASME Journal of Applied Mechanics, 60(1993), pp.506-513
[105] Lars P. Mikkelsen, Elastic-viscoplastic buckling of circular cylindrical shells under axial compression, European Journal of Mechanics, A/Solids, 14(1995), pp.901-920
[106] G. A. Kardomateas, Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression, ASME Journal of Applied Mechanics, 62(1995), pp.43-52
[107] A. A. Singace, Axial crushing analysis of tubes deforming in the multi-lobe mode, International Journal of Mechanical Sciences, 41(1999), pp. 865-890
[108] Seishi Yamada, J. G. A. Croll, Contributions to Understanding the Behavior of Axially Compressed Cylinders, ASME Journal of Applied Mechanics, 66(1999), pp.299-309
[109] S. R. Guillow, G. Lu, R. H. Grzebieta, Quasi-static axial compression of thin-walled circular aluminium tubes, International Journal of Mechanical Sciences, 43(2001), pp. 2103-2123
[110] G. Lu, Renjie Mao, A study of the plastic buckling of axially compressed cylindrical shells with a thick-shell theory, International Journal of Mechanical Sciences, 43(2001), pp. 2319-2330
[111] J. M. Alexander, An approximate analysis of the collapse of thin cylindrical shells under axial loading, Quarterly Journal of Mechanics and Applied Mathematics, 13(1960), pp. 10-15
[112] T. Wierzbicki, S. U. Bhat, A Moving Hinge Solution for Axisymmetric Crushing of Tubes, International Journal of Mechanical Sciences, 28(1986), pp. 135-151
[113] A. G. Mamalis, D. E. Manolakos, S. Saigal, G. Viegelahn, W. Johnson, Extensible Plastic Collapse of Thin-wall Frusta as Energy Absorbers, International Journal of Mechanical Sciences, 28(1986), pp. 219-229
[114] A. G. Mamalis, D. E. Manolakos, G. Viegelahn, W. Johnson, The Modelling of the Progressive Extensible Plastic Collapse of Thin-wall Shells, International Journal of Mechanical Sciences, 30(1988), pp. 249-261
[115] T. Wierzbicki, S.U. Bhat, W. Abramowicz, D. Brodkin, Alexander Revisited—A Two Folding Elements Model of Progressive Crushing of Tubes, International Journal of Solids and Structures, 29(1992), pp. 3269-3288
[116] A. A. Singace, H. Elsobky, T. Y. Reddy, On the Eccentricity Factor in the Progressive Crushing of Tubes, International Journal of Solids and Structures, 32(1995), pp. 3589-3602
[117] R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, London, 1950
[118] F. Proksa, Plastischen Biegen von Blechen, Stahlbau, 28(2)1959, pp. 29-36
[119] R. Crafoord, Plastic sheet bending, Gteborg, 1970
[120] 余同希，章亮炽，宽板弹塑性纯弯曲的一个精化理论，北京大学学报(自然科学版)，1988，24，65-72
[121] 余同希，章亮炽著，塑性弯曲理论及其应用，科学出版社，1992年5月
[122] 粱炳文，胡世光编著，弹塑性稳定理论，国防工业出版社，1983年11月
[123] 黄克智，夏之熙，薛明德，任文敏编著，板壳理论，清华大选出版社，1987年6月
[124] Z. P. Bazant, Structural Stability, International Journal of Solids and Structures, 37(2000), pp. 55-67
[125] 吴洪飞，苑世剑，王仲仁，轴压柱壳弹塑性稳定性分析的通用方程推导，哈尔滨工业大学学报，2002，34(1)，35-39 261-268
[126] F. R. Shanley, The Column Paradox, Journal of Aeronautical Science, 13(1946), p. 648
[127] F. R. Shanley, Inelastic Column Theory, Journal of Aeronautical Science, 14(1947), pp. 261-268
[128] 周承倜编，薄壳弹塑性稳定性理论，国防工业出版社，1979年12月
[129] 蒋咏秋，穆霞英编，塑性力学基础，机械工业出版社，1984年11月
[130] L. H. Donnell C. C. Wan, Effect of imperfections on buckling of thin cylinders and columns under axial compression, Journal of Applied Mechanics, 17(1950), p. 73
[131] L. H. Donnell, Effect of imperfections on buckling of thin cylinders under external pressure, Journal of Applied Mechanics, 23(1956), p. 569
[132] 扬耀乾著，薄壳理论，中国铁道出版社，1984年1月
[133] 夏永旭，孙忠弟，任艺宏编著，板壳力学中的加权残值法，西北工业大学出版社，1994年11月
[134] 张志涌，刘瑞桢，杨祖樱编著，掌握和精通MATLAB，北京航空航天大学出版社，1999年1月
[135] 楼顺天，于卫，闫华梁编著，MATLAB程序设计语言，西安电子科技大学出版社，1998年12月
[2] G. Morphy, Hydroforming High Strength Steel Tube for Automotive Structural Application Using Expansion, SAE Technical PaperNo. 970373, 1997
[3] Ch. Bruggenmann, S. Shah, Hydroforming Product and Process—Requirements and Implementation, TPA 2nd Annual Automotive Tube Conference, 1997, pp.89-103
[4] M. Koc, T. Altan, An overall review of the tube hydroforming (THF) technology, Journal of Materials Processing Technology, 108 (2001), pp.384-393
[5] F.-U. Leitloff, Hydroforimg Gives the Right Shape to Hollow Components, IMPRESSION, Edition 8, 1997, SMG Sddeutsche Maschinenbau GmbH & Co, p.4
[6] Anon., Hydroforming Technology, Advanced Materials & Processes, 5/97, pp.50-53
[7] M. Ahmetoglu, K. Sutter, X. J. Li, T. Altan, Tube hydroforming: current research, applications and need for training, Journal of Materials Processing Technology, 98(2000), pp.224-231
[8] F. Klaas, Innovation in high-pressure hydroforming, Proceedings of the 2th International Conference on Innovations in Hydroforming Technology, Columbus, Ohio State University, 1997, pp. 15-19
[9] H. Cherek, Part cost reduction in the hydroforming processes, Proceedings of the 2th International Conference on Innovations in Hydroforming Technology, Columbus, Ohio State University, 1997, pp.22-26
[10] G. Morphy, Tube Hydroforming: Dimensional Capability Analysis of a High Volume Automotive Structural Component Production Process, SAE Technical Paper No. 980450, 1998
[11] Th. A. Hannibal, J. R. Dieffenbach, Hydroformed Structural Elements: An Economic Evaluation of the Technology, SAE Technical Paper No. 980451, 1998
[12] E. Doege, R. Ksters, M.-I. Rotarescu, C. Ropers, Neue Mglichkeiten der Berechnung von Prozessparametern fr die Innenhochdruckumformung von rohrfrmigen Bauteilen, Umformen Trennen Fgen, 1/2001, Seiten 4-7
[13] H.-U. Lcke, Ch. Hartl, T. Abbey, Hydroforming, Journal of Materials Processing Technology, 115 (2001), pp.87-91
[14] G. Holzinger, Mit IHU zu hochprzisen Leichtbauteilen, STAHL, 1/2000, Seiten 58-59
[15] M. Ahmetoglu, T. Altan, Tube hydroforming: state-of-the-art and future trends, Journal of Materials Processing Technology, 98 (2000), pp.25-33
[16] J. Neubert, Innenhochdruckumformung im ULSAB-Projekt, Blech Rohre Profile, 43 (1996) 1/2, Seite 62
[17] U. Herberg, Umformen von Platinen mit Innendruck, Blech Rohre Profile, 43 (1996) 1/2, Seite 57
[18] M. Geiger, P. Hein, Neue Ideen zum Innenhochdmckumformen, Blech Rohre Profile, 43 (1996) 1/2, Seiten 63-64
[19] M. Geiger, P. Hein, S. Bobbert, FE-Analysis and Process Design for the Hydroforming of Sheet Metal Pairs, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept. 1999, Besancon, France, pp.9-14
[20] M. Geiger, F. Vollertsen, P. Hein, Hydroforming of sheet metal pairs, Proceedings of SheMet'98, 1998, pp.37-51
[21] M. Kleiner, R. Kolleck, J. Rauer, Die-less forming of sheet metal parts, Proceedings of SheMet'98, 1998, pp.63-70
[22] S. Novotny, P. Hein, Hydroforming of sheet metal pairs from aluminum alloys, Proceedings ofSheMet'99, 1999, pp.591-606
[23] P. Hein, F. Vollertsen, Hydroforming of sheet metal pairs, Journal of Materials Processing Technology, 87(1999), pp.154-164
[24] O. Kreis, P. Hein, Manufacturing system for the integrated hydroforming, trimming and welding of sheet metal pairs, Journal of Materials Processing Technology, 115(2001), pp.49-54
[25] S. Novotny, P. Hein, Hydroforming of sheet metal pairs from aluminium alloys, Journal of Materials Processing Technology, 115(2001), pp.65-69
[26] A. Eichhorn, S. Motsch, Hydroforming of Tailored Tubes, Proceedings of the 21st Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor,Michigan, USA, pp.23-31
[27] K. Siegert, M. Hussermann, B. Lsch, R. Rieger, Recent developments in hydroforming technology, Journal of Materials Processing Technology, 98 (2000), pp.251-258
[28] MERCER Management Consult, IHU-Anwendungen in der Automobilindustrie, Mnchen, Mai 2000
[29] S. Lichtenberg, H.-G. Hoff, Stand der Innenhochdruckumformung in Deutschland, Blech Rohre Profile, 43 (1996) 1/2, Seiten 40-46
[30] H. Grabowski, Preface, Proceedings of the Workshop Universal Design Theory, Aachen Shaker Verlag, 1998
[31] 王同海编著，管材塑性加工技术，机械工业出版社，1998年7月
[32] 苑世剑，王仲仁，轻量化结构内高压成形技术，材料科学与工艺，1999，7(增刊)，PP．139-142
[33] 王仲仁，球形容器整体成形新工艺，压力容器，1988，5(1)，pp．78-81
[34] Z. R. Wang, T. Wang, D. C. Kang, S. H. Zhang, Y. Fang, The technology of the hydrobulging of whole spherical vessels and experimental analysis, Journal of Mechanical Working Technology, 1989, 18 (1), pp.85-94
[35] S. H. Zhang, Z. R. Wang, The stress distribution and plastic hastening-sphere effect in the integral hydrobulge forming of spherical vessels, International Journal of Materials and Product Technology, 1990, 5, pp.293-300
[36] S. H. Zhang, Z. R. Wang, Experimental research and FEM analysis of the hydroforming technology of double-layer spherical vessels, Advanced Technology of Plasticity, Proceedings of the 4th ICTP, 1993, 1, pp.49-53
[37] 王仲仁，曾元松，苑世剑，张士宏，椭球壳体液压成形的塑性变形规律的研究，固体力学学报，1998，19(3)，pp．259-264
[38] 王仲仁，苑世剑，曾元松，张士宏，董建令，王凤志，无模胀球的原理与研究进展，机械工程学报，1999，35(4)，pp．64-66
[39] J. L. Dong, Z.R. Wang, C.D. Liu, Single-curvature polyhedron hydrobuilding technology for manufacturing spherical vessels, Proceedings of the 7th International Conference on Pressure Vessel Technology, 1999, pp.128-134
[40] 苑世剑，郎利辉，王仲仁，内高压成形技术研究与应用进展，哈尔滨工业大学学报，2000，32(5)，pp．60-63
[41] 张士宏，许沂，王忠堂，郎利辉，刘钢，板材零件成对液压成形新技术，哈尔滨工业大学学报，2000，32(4)，pp．7-9
[42] 赵长财，张涛，刘国晖，刘助柏，有限长薄壁管胀形研究，塑性工程学报，1997，4(1)，pp．36-41
[43] 赵长财，薄壁管在内压，轴力作用下的初始屈服，塑性工程学报，2000，8(3)，pp．29-31
[44] 李新军，周贤宾，K．Sutter，T．Altan，薄壁管轴压胀形的加载与控制，第七届全国锻压学术年会论文集，中国机械工程学会锻压学会编，航空工业出版社，1999年10月，pp．256-260
[45] 李新军，周贤宾，李敏，W．Thomas，T．Altan，计算机仿真技术在钣料冲压成形中的应用，航空制造工程，1998，3，pp．24-26
[46] H. Tautenhahn, Anisotropie und Textur von Rohren, Blech Rohre Profile, 43(1996)5, Seiten 234-239
[47] S. D. Liu, D. Meuleman, K. Thompson, Analytical and Experimental Examination of Tubular Hydroforming Limits, SAE Technical Paper No. 980449, 1998
[48] R. Kergen, J. C. Lescart, P. Duroux, Analysis of the Tube Formability in Perspective of Tube Hydroforming, Proceedings of the 21st Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor, Michigan, USA, pp.33-41
[49] T. Yoshida, Y. Kuriyama, Effects of Material Properties and Process Parameters on Deformation Behavior of Tube in Hydroforming, Proceedings of the 21th Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor, Michigan, USA, pp.43-52
[50] B. Carleer, G. van der Kevie, L. de Winter, B. van Veldhuizen, Analysis of the effect of material properties on the hydroforming process of tubes, Journal of Materials Processing Technology, 104 (2000), pp.158-166
[51] 王仁，熊祝华，黄文彬，塑性力学基础，科学出版社，1998年3月
[52] T. Sokolowski, K. Gerke, M. Ahmetoglu, T. Altan, Evaluation of Material Characteristics in Tube Hydroforming: Hydraulic Bulge Testing of Tubes, Advanced Technology of Plasticity, Vol. Ⅱ, Proceedings of the 6th ICTP, Sept. 19-24, 1999, pp. 1217-1222
[53] T. Sokolowski, K. Gerke, M. Ahmetoglu, T. Altan, Evaluation of Tube Formability and Material Characteristics: Hydraulic Bulge Testing of Tubes, Journal of Materials Processing Technology, 98 (2000), pp.34-40
[54] Abschluβbericht: Werkstckfestigkeitsmessung dutch freies Aufweitstauchen, LUF, Universitt Paderborn, 2000.9
[55] E. Doege, D. Drmann, C. Frank, Tiefziehen mit pulsierendem Niederhalter, Blech, 5/1996, Seiten 68-74
[56] C. M. Ziegler, Schwingende Niederhalterkraft und Regelkreise beim Tiefziehen, Dissertation: Beitrtge zur Umformtechnik, IFU, Universitt Stuttgart, Band 19, 1999
[57] E. Doege, C. Frank, G. Kurz, Schwingende Niederhalterkraft verbessert die Tiefziehergebnisse, Maschinenmarkt, 37/2000, Seiten28-34
[58] DASYLab Anwenderhandbuch Version 3.5, DATALOG GmbH, 1996
[59] J. Woitschig, Diplomarbeit: Prozefioptimierung durch die Schwingungs-berlagerung beim Innenhochdruckumformen, LUF, Universitt Paderbom, 2001.4
[60] Abschluβbericht: Untersuchung der Prozeβbeeinflussung beim Innenhochdruekumformen dutch eine pulsierende Anregung, LUF, Universitt Paderborn, 2001.8
[61] 肖景容，李尚健主编，塑性成形模拟理论，华中理工大学出版社，1994年12月
[62] 马泽恩主编，计算机辅助塑性成形，西北工业大学出版社，1995年5月
[63] 李顺平，杨合，神经网络在塑性加工中的应用，航空制造工程，1998，3，pp．27-28
[64] 吴林志，’99全国固体力学学术会议简介，力学进展，2000，30(1)，pp．156-158
[65] 戴昆，何祝斌，王仲仁，管材内压液力成形的稳定性分析，塑性工程学报，2000，7(4)，pp．49-52
[66] 吴洪飞，苑世剑，王仲仁，内高压成形塑性屈曲分析，锻压技术，2001，5，pp．29-31
[67] 方开泰，均匀设计与均匀设计表，科学出版社，1994年6月
[68] 程相君，王春宁，陈生潭，神经网络原理及其应用，国防工业出版社，1995．1
[69] 楼顺天，施阳，基于MATLAB的系统分析与设计——神经网络，西安电子科技大学出版社，1998
[70] S. Haykin, Neural networks: a comprehensive foundation (second edition), Prentice-Hall Inc., 1999
[71] H. Demuth, M. Beale, User's Guide for Neural Network Toolbox Version 3.0, MathWorks Inc., 1998
[72] G. F. Page, J. B. Gomm, D. Williams, Application of Neural Networks to Modelling and Control, Chapman and Hall, 1993
[73] 张际先，宓霞，神经网络及其在工程中的应用，机械工业出版社，1998．5
[74] J. A. Freeman, D. M. Skapura, Neural networks: algorithms, applications, and programming techniques, Addison-Wesley Publishing Company, 1992
[75] J. G. Taylor, The Promise of Neural Networks, Springer-Verlag London Limited, 1993
[76] B. Widrow and S. D. Sterns, Adaptive Signal Processing, New York: Prentice-Hall Inc., 1985
[77] M.T. Hagan, H.B. Demuth, M.H. Beale, Neural Network Design, PWS Publishing Company, Boston, MA 1996
[78] D.E Rumelhart, G.E. Hinton, R.J. Williams, Learning internal representations by error propagation, Parallel Data Processing (edited by D. Rumeihart and J. McClelland), Vol.1, Chapter 8, the M.I.T.Press, Cambridge, MA 1986, pp. 318-362
[79] D. Nguyen, B. Widrow, Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights, Proceedings of the International Joint Conference on Neural Networks, vol3, pp. 21-26, 1990
[80] D. Schmoeckel, C. Hessler, B. Engel, Pressure Control in Hydraulic Tube Forming, Annals of the CIRP, 1992, 41(1), pp. 311-314
[81] S. Thiruvarudchelvan, G. L. Seet, H. E. Ang, Computer-monitored hydraulic bulging of tubes, Journal of Materials Processing Technology, 57(1996), pp. 182-188
[82] T. Altan, M. Koc, I. Aue-u-lan, K. Tibari, Umformbarkeits-und Konstruktionsgesichtspunkte bei der Innenhochdruck-Umformung, Vortragstexte des Symposiums "Internationale Konferenz Hydroumformung" in Fellbach bei Stuttgart, am 12. und 13. Oktober 1999, Hydroumformung von Rohren, Strangpreβprofilen und Blechen, MAT-INFO Werkstoff-Informationsgesellschaft mbH, 1999, Seiten 135-151
[83] Z. C. Xia, S. C. Tang, On Path Dependence of Tubular Hydroforming, Proceedings of the 21st Biennial Congress of the International Deep Drawing Research Group, June 5-7, 2000, Ann Arbor, Michigan, USA, pp. 53-59
[84] J. B. Yang, B. H. Jeon, S. I. Oh, Design sensitivity analysis and optimization of the hydroforming process, Journal of Materials Processing Technology, 113 (2001), pp. 666-672
[85] L. P. Lei, D. H. Kim, S. J. Kang, S. M. Hwang, B. S. Kang, Analysis and design of hydroforming processes by the rigid-plastic finite element method, Journal of Materials Processing Technology, 114 (2001), pp. 201-206
[86] K. Manabe, H. Nishimura, Einfluβ des Werkstoffes bei der Formgebung von Rohren, BNDER BLECHE ROHRE, 1983, 4, Seiten 92-95
[87] J. Tirosh, A. Neuberger, A. Shirizly, On Tube Expansion by Internal Fluid Pressure with Additional Compressive Stress, International Journal of Mechanical Sciences, 38(1996), pp. 839-851
[88] S. Fuchizawa, M. Narazaki, A. Shirayori, Bulge Forming of Aluminum Alloy Tubes by Internal Pressure and Axial Compression, Advanced Technology of Plasticity 1996, Vol. Ⅰ, proceedings of the 5th ICTP, Oct. 7-10, 1996, pp.497-500
[89] J. Tirosh, A. Neuberger, A. Shirizly, Tube Expansion with 'unlimited' strain, Advanced Technology of Plasticity 1996, Vol. Ⅰ , proceedings of the 5th ICTP, Oct. 7-10, 1996, pp.527-530
[90] F. Dohmann, Ch. Hartl, Entwicklungen und Anwendungen des Innenhochdruckumformens, Blech Rohre Profile, 43(1996) 1/2, Seiten 30-35
[91] F. Dohmann, Ch. Hartl, Hydroforming—a method to manufacture light-weight parts, Journal of Materials Processing Technology, 60(1996), pp.669-676
[92] F. Dohmann, Ch. Hartl, Tube hydroforming—research and practical application, Journal of Materials Processing Technology, 71(1997), pp.174-186
[93] S. Toyoda, K. Uwai, K. Suzuki, T. Saito, A. Yoshitake, T. Mori, Hydroforming Formability of Electric Resistance Welded Tubes for Automobiles, SAE Technical Paper No. 1999-01-0027, 1999
[94] D. Thuvesen, I. Rask, Simulation of a Product Engineering Process—Tube Hydroforming, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept. 1999, Besancon, France, pp.485-489
[95] S. C. Rama, J. M. Zhang, A Numerical Approach to Analyze Tubular Hydroforming, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept.1999, Besancon, France, pp.497-502
[96] L. FUice, L. Fratini, E Micari, A Simple Experiment to Characterize Material Formability in Tube Hydroforming, Annals of the CIRP, Vol. 50, 1/2001, pp. 181-184
[97] H. L. Xing, A. Makinouchi, Virtual Design for Hydroforming of Tubes, Proceedings of the 4th International Conference and Workshop NUMISHEET'99, 13-17 Sept. 1999, Besancon, France, pp.479-484
[98] H. L. Xing, A. Makinouchi, Numerical analysis and design for tubular hydroforming, International Journal of Mechanical Sciences, 43(2001), pp. 1009-1026
[99] 郞利辉，苑世剑，王仲仁，王小松，付庄，内高压液力成形陷产生及其失效分析，塑性工程学报，2001，8 (4)，30-35
[100] E. Ore, D. Durban, Elastoplastic Buckling of Axially Compressed Circular Cylindrical Shells, International Journal of Mechanical Sciences, 34(1992), pp. 727-742
[101] S. Li, S. R. Reid, The Plastic Buckling of Axially Compressed Square Tubes, ASME Journal of Applied Mechanics, 59(1992), pp.276-282
[102] S. R. Reid, Plastic Deformation Mechanisms in Axially Compressed Metal Tubes Used as Impact Energy Absorbers, International Journal of Mechanical Sciences, 35(1993), pp. 1035-1052
[103] Seishi Yamada, J. G. A. Croll, Buckling and Post-buckling Characteristics of Pressure-Loaded Cylinders, ASME Journal of Applied Mechanics, 60(1993), pp.290-299
[104] G. A. Kardomateas, Stability Loss in Thick Transversely Isotropic Cylindrical Shells Under Axial Compression, ASME Journal of Applied Mechanics, 60(1993), pp.506-513
[105] Lars P. Mikkelsen, Elastic-viscoplastic buckling of circular cylindrical shells under axial compression, European Journal of Mechanics, A/Solids, 14(1995), pp.901-920
[106] G. A. Kardomateas, Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression, ASME Journal of Applied Mechanics, 62(1995), pp.43-52
[107] A. A. Singace, Axial crushing analysis of tubes deforming in the multi-lobe mode, International Journal of Mechanical Sciences, 41(1999), pp. 865-890
[108] Seishi Yamada, J. G. A. Croll, Contributions to Understanding the Behavior of Axially Compressed Cylinders, ASME Journal of Applied Mechanics, 66(1999), pp.299-309
[109] S. R. Guillow, G. Lu, R. H. Grzebieta, Quasi-static axial compression of thin-walled circular aluminium tubes, International Journal of Mechanical Sciences, 43(2001), pp. 2103-2123
[110] G. Lu, Renjie Mao, A study of the plastic buckling of axially compressed cylindrical shells with a thick-shell theory, International Journal of Mechanical Sciences, 43(2001), pp. 2319-2330
[111] J. M. Alexander, An approximate analysis of the collapse of thin cylindrical shells under axial loading, Quarterly Journal of Mechanics and Applied Mathematics, 13(1960), pp. 10-15
[112] T. Wierzbicki, S. U. Bhat, A Moving Hinge Solution for Axisymmetric Crushing of Tubes, International Journal of Mechanical Sciences, 28(1986), pp. 135-151
[113] A. G. Mamalis, D. E. Manolakos, S. Saigal, G. Viegelahn, W. Johnson, Extensible Plastic Collapse of Thin-wall Frusta as Energy Absorbers, International Journal of Mechanical Sciences, 28(1986), pp. 219-229
[114] A. G. Mamalis, D. E. Manolakos, G. Viegelahn, W. Johnson, The Modelling of the Progressive Extensible Plastic Collapse of Thin-wall Shells, International Journal of Mechanical Sciences, 30(1988), pp. 249-261
[115] T. Wierzbicki, S.U. Bhat, W. Abramowicz, D. Brodkin, Alexander Revisited—A Two Folding Elements Model of Progressive Crushing of Tubes, International Journal of Solids and Structures, 29(1992), pp. 3269-3288
[116] A. A. Singace, H. Elsobky, T. Y. Reddy, On the Eccentricity Factor in the Progressive Crushing of Tubes, International Journal of Solids and Structures, 32(1995), pp. 3589-3602
[117] R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, London, 1950
[118] F. Proksa, Plastischen Biegen von Blechen, Stahlbau, 28(2)1959, pp. 29-36
[119] R. Crafoord, Plastic sheet bending, Gteborg, 1970
[120] 余同希，章亮炽，宽板弹塑性纯弯曲的一个精化理论，北京大学学报(自然科学版)，1988，24，65-72
[121] 余同希，章亮炽著，塑性弯曲理论及其应用，科学出版社，1992年5月
[122] 粱炳文，胡世光编著，弹塑性稳定理论，国防工业出版社，1983年11月
[123] 黄克智，夏之熙，薛明德，任文敏编著，板壳理论，清华大选出版社，1987年6月
[124] Z. P. Bazant, Structural Stability, International Journal of Solids and Structures, 37(2000), pp. 55-67
[125] 吴洪飞，苑世剑，王仲仁，轴压柱壳弹塑性稳定性分析的通用方程推导，哈尔滨工业大学学报，2002，34(1)，35-39 261-268
[126] F. R. Shanley, The Column Paradox, Journal of Aeronautical Science, 13(1946), p. 648
[127] F. R. Shanley, Inelastic Column Theory, Journal of Aeronautical Science, 14(1947), pp. 261-268
[128] 周承倜编，薄壳弹塑性稳定性理论，国防工业出版社，1979年12月
[129] 蒋咏秋，穆霞英编，塑性力学基础，机械工业出版社，1984年11月
[130] L. H. Donnell C. C. Wan, Effect of imperfections on buckling of thin cylinders and columns under axial compression, Journal of Applied Mechanics, 17(1950), p. 73
[131] L. H. Donnell, Effect of imperfections on buckling of thin cylinders under external pressure, Journal of Applied Mechanics, 23(1956), p. 569
[132] 扬耀乾著，薄壳理论，中国铁道出版社，1984年1月
[133] 夏永旭，孙忠弟，任艺宏编著，板壳力学中的加权残值法，西北工业大学出版社，1994年11月
[134] 张志涌，刘瑞桢，杨祖樱编著，掌握和精通MATLAB，北京航空航天大学出版社，1999年1月
[135] 楼顺天，于卫，闫华梁编著，MATLAB程序设计语言，西安电子科技大学出版社，1998年12月