空间薄膜褶皱及其动态特性研究
摘要
褶皱作为薄膜的局部屈曲现象,在空间薄膜结构中广泛存在。对于高精度的薄膜结构来说,褶皱是影响其表面精度的主要因素。同时,褶皱产生以后将影响到结构的稳定性,并对结构的动态特性产生一定的影响。目前随着航天领域中高精度薄膜结构应用研究的发展,薄膜褶皱研究已成为热点。
张力场理论是较早提出的薄膜褶皱分析理论,通过引入参数对薄膜褶皱区域的本构关系进行修正,以避免薄膜中压应力的出现。基于张力场理论很好的解决了张拉膜结构的褶皱问题。由于基于张力场理论的薄膜褶皱分析不能得到褶皱的面外变形信息,因此不符合高精度空间薄膜结构的褶皱分析要求。
为了准确描述薄膜褶皱的面外变形,本文提出了褶皱构形的概念,采用波长,幅度及褶皱方向等参数来描述褶皱构形。根据非线性大挠度方程建立了薄膜褶皱构形参数研究的一般性方法—应力极值法,建立了褶皱半波长与褶皱方向拉应力的关系模型,确定了褶皱构形参数之间的关系。采用应力极值法进行褶皱分析时,避开了褶皱具体变形形式的假定,具有很好的通用性。根据应力极值法,研究了剪切薄膜褶皱和对角张拉矩形薄膜褶皱,得到了褶皱构形参数。
将薄膜产生褶皱的过程分为初始屈曲过程和后屈曲过程两个阶段,对两个不同阶段褶皱形成和扩展的机理进行了理论分析。建立了初始屈曲过程剪切薄膜的临界载荷公式,并分析了初始屈曲过程褶皱的形成和扩展规律。对于后屈曲过程的分析,将初始缺陷引入到薄膜褶皱的分析之中,建立了具有初始缺陷的薄膜褶皱的分析模型,分析了褶皱区域的应力分布规律。根据褶皱区域应力分布规律,分析了后屈曲过程褶皱的扩展机理。结合理论分析,讨论了后屈曲过程中可能出现的二次屈曲现象。
基于稳定性理论,建立了薄膜褶皱的数值分析方法—直接扰动法,解决了采用常规的非线性屈曲分析引入的初始缺陷无法去除的问题。采用直接扰动法,分析了薄膜初始屈曲过程的临界载荷和褶皱的形成及扩展规律。得到了后屈曲过程薄膜褶皱的构形参数。分析了薄膜屈曲的平衡路径。通过数值方法研究了初始屈曲过程及后屈曲过程中的二次屈曲现象。并将数值分析结果与理论分析结果进行了对比分析,结果符合较好。
采用数字摄影测量法进行了剪切薄膜褶皱的实验研究。通过数字摄影测量系统实现了薄膜微小面外变形的非接触式的测量。设计了适合高精度测量要求的剪切薄膜的实验装置,该装置可以实现精确的加载过程控制,便于对薄膜屈曲全过程的分析。采用高精度的数字摄影测量系统获得了褶皱的构形及构形参数,在实验中观测到了二次屈曲现象。通过与数值分析结果进行的对比分析,验证了数值分析方法的合理性。
对薄膜屈曲后的动态特性进行了分析。建立了具有褶皱面外变形的薄膜振动的特征值方程,并基于直接扰动法建立了动态分析的数值方法。基于该方法分析剪切褶皱薄膜和对角张拉矩形褶皱薄膜的振动特性。分析了褶皱形成以后薄膜振动的固有频率和主振型的变化规律,及褶皱幅度对于动态特性的影响,研究了褶皱薄膜的振动模态与薄膜褶皱构形的对应关系。
本文对薄膜褶皱的形成过程及形成机理进行了研究,研究了薄膜褶皱的变形特性及薄膜屈曲后的动态性能。为空间薄膜结构的形面精度控制、稳定性控制及振动控制的深入研究提供了理论依据。
Winkles exist extensively in space membrane structures as a local buckling phenomenon. For high precision membrane structure, wrinkles are the main factors related close to the surface accuracy. At the same time, wrinkles may have significant influences on the stability of the structure and dynamic characteristics of the structure. Nowadays, with the development of high precision membrane structure’s application research, the studies on the wrinkling problem have become a hot topic.
Tension field theory is the earlier membrane wrinkle theory. This method introduced parameters to modify the constitutive relation on the membrane wrinkle’s region so as to avoid the compressive stress on the membrane. Winkle problem of tension membrane can be solved by tension field theory very well. Due to that wrinkle analysis based on tension field theory can not achieve the out-of-plane deformation of wrinkles; it is not suit for wrinkle analysis requirement of high-precision space membrane structure.
In order to describe the out-of-plane deformation accurately, the concept of wrinkle configuration is proposed in this paper. Parameters such as wavelength, amplitude and direction of the wrinkle are used to describe the wrinkle configuration. According to nonlinear large deflection equation, a general approach Stress Extreme Method(SEM) is established to describe the wrinkle configuration parameters. The relationship between half-wavelength and tensile stress of wrinkle’s direction is established. The relationships between wrinkle configuration parameters are then determined. Shear membrane wrinkle and rectangular membrane under corner load are studied by using stress extreme method, and the wrinkle’s configuration parameters are obtained in the end.
The wrinkling process of membrane is divided into two stages: the initial buckling and the post-buckling. The mechanism of wrinkle’s formation and expansion are analyzed in theoretical corresponding to these two different stages. The critical load formula of shear membrane at the initial buckling stage is established and the principle of wrinkle’s formation and expansion are then studied at this stage. For the analysis of post-buckling process, initial imperfections will be introduced into the analysis of the membrane wrinkle. The analytical model of membrane wrinkle within initial imperfections is then established, and the law of stress distribution in wrinkle region is analyzed finally. According to the obtained law, expansion process of wrinkling mechanism in the post-buckling is then researched. Combined with theoretical analysis, the probably second buckling phenomenon is also discussed in the post-buckling.
Based on the stability theory, a numerical analysis method Direct Disturbances Method is established to analyze the membrane wrinkle, and this method deals with the problem of unremoved imperfections in the conventional nonlinear buckling analysis. Using the direct disturbance method, the critical load in the initial buckling process and the law of wrinkle’s formation and expansion are analyzed. The configuration parameters of membrane wrinkle at post-buckling process are obtained. The balance path of the membrane buckling is also studied. By using numerical method, the secondary buckling phenomenon is researched both in initial buckling process and post-buckling process. The comparison between numerical analysis and theoretical analysis is done in the end.
The experimental study of shear membrane wrinkle is performed by using digital photogrammetry system. Through digital photogrammetry system, non-contact measurement of small out of plane deformation can be obtained. The experimental device of shear membrane is designed for high precision measurement requirements. This device can achieve accurate control of the loading process, which is convenient to analyze the entire membrane buckling process. By using high precision digital photogrammetry system, the configuration and configuration parameters of wrinkles are obtained, and in the experiment the second buckling phenomenon can be observed. The validity of the numerical analysis is verified by the results compared with numerical analysis.
Dynamic characteristics of membrane buckling are analyzed. Eigenvalue equation of membrane vibration with out-of-plane deformation is established. Numerical method of dynamic analysis is set up based on direct perturbation method. According to this method, vibration characteristics of shear wrinkle membrane and rectangle wrinkle membrane on corner load are studied. Variation rules of nature frequency and fundamental mode are analyzed after wrinkles appear, and so as to influence of wrinkle amplitude on vibration characteristics. The corresponding relationship between vibration mode of wrinkle membrane and wrinkle membrane configuration is reached.
In this paper, the formation process and the formation mechanism of membrane wrinkle are studied. The deformation characteristics of membrane wrinkle and dynamic capability of membrane after buckling are also researched. These results provide a theoretical basis for in-depth study of space membrane structure in surface accuracy control, stability control and vibration control.
张力场理论是较早提出的薄膜褶皱分析理论,通过引入参数对薄膜褶皱区域的本构关系进行修正,以避免薄膜中压应力的出现。基于张力场理论很好的解决了张拉膜结构的褶皱问题。由于基于张力场理论的薄膜褶皱分析不能得到褶皱的面外变形信息,因此不符合高精度空间薄膜结构的褶皱分析要求。
为了准确描述薄膜褶皱的面外变形,本文提出了褶皱构形的概念,采用波长,幅度及褶皱方向等参数来描述褶皱构形。根据非线性大挠度方程建立了薄膜褶皱构形参数研究的一般性方法—应力极值法,建立了褶皱半波长与褶皱方向拉应力的关系模型,确定了褶皱构形参数之间的关系。采用应力极值法进行褶皱分析时,避开了褶皱具体变形形式的假定,具有很好的通用性。根据应力极值法,研究了剪切薄膜褶皱和对角张拉矩形薄膜褶皱,得到了褶皱构形参数。
将薄膜产生褶皱的过程分为初始屈曲过程和后屈曲过程两个阶段,对两个不同阶段褶皱形成和扩展的机理进行了理论分析。建立了初始屈曲过程剪切薄膜的临界载荷公式,并分析了初始屈曲过程褶皱的形成和扩展规律。对于后屈曲过程的分析,将初始缺陷引入到薄膜褶皱的分析之中,建立了具有初始缺陷的薄膜褶皱的分析模型,分析了褶皱区域的应力分布规律。根据褶皱区域应力分布规律,分析了后屈曲过程褶皱的扩展机理。结合理论分析,讨论了后屈曲过程中可能出现的二次屈曲现象。
基于稳定性理论,建立了薄膜褶皱的数值分析方法—直接扰动法,解决了采用常规的非线性屈曲分析引入的初始缺陷无法去除的问题。采用直接扰动法,分析了薄膜初始屈曲过程的临界载荷和褶皱的形成及扩展规律。得到了后屈曲过程薄膜褶皱的构形参数。分析了薄膜屈曲的平衡路径。通过数值方法研究了初始屈曲过程及后屈曲过程中的二次屈曲现象。并将数值分析结果与理论分析结果进行了对比分析,结果符合较好。
采用数字摄影测量法进行了剪切薄膜褶皱的实验研究。通过数字摄影测量系统实现了薄膜微小面外变形的非接触式的测量。设计了适合高精度测量要求的剪切薄膜的实验装置,该装置可以实现精确的加载过程控制,便于对薄膜屈曲全过程的分析。采用高精度的数字摄影测量系统获得了褶皱的构形及构形参数,在实验中观测到了二次屈曲现象。通过与数值分析结果进行的对比分析,验证了数值分析方法的合理性。
对薄膜屈曲后的动态特性进行了分析。建立了具有褶皱面外变形的薄膜振动的特征值方程,并基于直接扰动法建立了动态分析的数值方法。基于该方法分析剪切褶皱薄膜和对角张拉矩形褶皱薄膜的振动特性。分析了褶皱形成以后薄膜振动的固有频率和主振型的变化规律,及褶皱幅度对于动态特性的影响,研究了褶皱薄膜的振动模态与薄膜褶皱构形的对应关系。
本文对薄膜褶皱的形成过程及形成机理进行了研究,研究了薄膜褶皱的变形特性及薄膜屈曲后的动态性能。为空间薄膜结构的形面精度控制、稳定性控制及振动控制的深入研究提供了理论依据。
Winkles exist extensively in space membrane structures as a local buckling phenomenon. For high precision membrane structure, wrinkles are the main factors related close to the surface accuracy. At the same time, wrinkles may have significant influences on the stability of the structure and dynamic characteristics of the structure. Nowadays, with the development of high precision membrane structure’s application research, the studies on the wrinkling problem have become a hot topic.
Tension field theory is the earlier membrane wrinkle theory. This method introduced parameters to modify the constitutive relation on the membrane wrinkle’s region so as to avoid the compressive stress on the membrane. Winkle problem of tension membrane can be solved by tension field theory very well. Due to that wrinkle analysis based on tension field theory can not achieve the out-of-plane deformation of wrinkles; it is not suit for wrinkle analysis requirement of high-precision space membrane structure.
In order to describe the out-of-plane deformation accurately, the concept of wrinkle configuration is proposed in this paper. Parameters such as wavelength, amplitude and direction of the wrinkle are used to describe the wrinkle configuration. According to nonlinear large deflection equation, a general approach Stress Extreme Method(SEM) is established to describe the wrinkle configuration parameters. The relationship between half-wavelength and tensile stress of wrinkle’s direction is established. The relationships between wrinkle configuration parameters are then determined. Shear membrane wrinkle and rectangular membrane under corner load are studied by using stress extreme method, and the wrinkle’s configuration parameters are obtained in the end.
The wrinkling process of membrane is divided into two stages: the initial buckling and the post-buckling. The mechanism of wrinkle’s formation and expansion are analyzed in theoretical corresponding to these two different stages. The critical load formula of shear membrane at the initial buckling stage is established and the principle of wrinkle’s formation and expansion are then studied at this stage. For the analysis of post-buckling process, initial imperfections will be introduced into the analysis of the membrane wrinkle. The analytical model of membrane wrinkle within initial imperfections is then established, and the law of stress distribution in wrinkle region is analyzed finally. According to the obtained law, expansion process of wrinkling mechanism in the post-buckling is then researched. Combined with theoretical analysis, the probably second buckling phenomenon is also discussed in the post-buckling.
Based on the stability theory, a numerical analysis method Direct Disturbances Method is established to analyze the membrane wrinkle, and this method deals with the problem of unremoved imperfections in the conventional nonlinear buckling analysis. Using the direct disturbance method, the critical load in the initial buckling process and the law of wrinkle’s formation and expansion are analyzed. The configuration parameters of membrane wrinkle at post-buckling process are obtained. The balance path of the membrane buckling is also studied. By using numerical method, the secondary buckling phenomenon is researched both in initial buckling process and post-buckling process. The comparison between numerical analysis and theoretical analysis is done in the end.
The experimental study of shear membrane wrinkle is performed by using digital photogrammetry system. Through digital photogrammetry system, non-contact measurement of small out of plane deformation can be obtained. The experimental device of shear membrane is designed for high precision measurement requirements. This device can achieve accurate control of the loading process, which is convenient to analyze the entire membrane buckling process. By using high precision digital photogrammetry system, the configuration and configuration parameters of wrinkles are obtained, and in the experiment the second buckling phenomenon can be observed. The validity of the numerical analysis is verified by the results compared with numerical analysis.
Dynamic characteristics of membrane buckling are analyzed. Eigenvalue equation of membrane vibration with out-of-plane deformation is established. Numerical method of dynamic analysis is set up based on direct perturbation method. According to this method, vibration characteristics of shear wrinkle membrane and rectangle wrinkle membrane on corner load are studied. Variation rules of nature frequency and fundamental mode are analyzed after wrinkles appear, and so as to influence of wrinkle amplitude on vibration characteristics. The corresponding relationship between vibration mode of wrinkle membrane and wrinkle membrane configuration is reached.
In this paper, the formation process and the formation mechanism of membrane wrinkle are studied. The deformation characteristics of membrane wrinkle and dynamic capability of membrane after buckling are also researched. These results provide a theoretical basis for in-depth study of space membrane structure in surface accuracy control, stability control and vibration control.
引文
1 Arthur L P, Yuli huang. Design tool for inflatable space structures. AIAA-97-1378: 2922~2930
2 Freeland R E, Bilyeu G D, Veal G R. Inflatable deployable space structures technology summary. IAF-98-I.5.01: 1~16
3 Mitchell Thomas, Gordon Veal. Scaling characteristics of inflatable paraboloid concentrator.In: Solar Engineering. 1991, No. H00630
4 Freeland R E, Bilyeu G D, Veal G R. Validation of a unique concept for a low cost, lightweight space-deployable antenna structure. IAF-93-1.1.204: 1~10
5 Freeland R E, Bilyeu G D, Veal G R. Large inflatable deployable antenna flight experiment results. ACTA Astronautica. 1997, 41 (4-10): 267~277
6 Freeland R E, Bilyeu G D, Veal G R. Development of flight hardware for a large, inflatable-deployable antenna experiment. ACTA Astronautica. 1996, 38 (4-8): 251~260
7 Freeland R E, Bilyeu G D, Veal G R. Validation of unique concept for a low-cost, lightweight space-deployable antenna structure. ACTA Astronautica. 1995, 35 (9-11): 565~572
8 Murphy D, Murphey T, Gierow P. Scalable solar-sail subsystem design concept. AIAA Journal of Spacecraft and Rockets. 2003, 40(4): 539~547
9 Grossman G, Williams G. Inflatable concentrators for solar propulsion and dynamic space power. Journal of Solar Energy Engineering. 1990: 229~236
10 Akahoshi Y, Nakamura R, Tanaka M. Development of bumper shield using low density materials. International Journal of Impact Engineering. 2001, 26 (1-10): 13~19
11 VanBlaricum L, Reilley J P, Gilbert M A. Quick Feasibility Demonstration for an Inflatable Antenna System in Space. Proceedings of the Ninth Annual DARPA Symposium on Photonic Systems for Antenna Applications Naval Postgraduate School, Monterey, CA 17, 18, 19 February 1999
12 Edward J S, James H. M, Thomas W G. Thin-film technology development for the PowerSphere. Materials Science and Engineering B. 2005,116 :265~272
13 Kondyurin A, Lauke B, Vogel R. Photopolymerisation of composite material in simulated free space environment at low Earth orbital flight. European Polymer Journal. 2006, 42 :2703~2714
14 Delozier D M, Watson K A, Smith J G, Connell J W. Preparation and characterization of space durable polymer nanocomposite films. Composites Science and Technology. 2005,65: 749~755
15 Lichodzidjewski D, Cravey R, Hopkins G.Inflatable Deployed Membrane Waveguide Array Antenna for Space. AIAA 2003-1649
16 Leipold M. Solar sail technology ground and in-orbit deployment testing. In Royal Astronomical Society Discussion Meeting, 10 May 2002
17 Mark S. Lake. A Rationale for Defining Structural Requirements for Large Space Telescopes. AIAA-2001-1685
18 Thomas W, Murphey, David M, Murphy. A Method to Quantify the Thrust Degradation Effects of Structural Wrinkles in Solar Sails. AIAA 2002-1560
19 Kukathasan S, Pellegrino S. Nonlinear vibration of wrinkled membranes. In: 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 7-10 April 2003, Norfolk, VA AIAA-2003-1747
20 Gough A, Hossain N.M. A, Jenkins C.H. Experimental and Numerical Study of Creased Membranes. AIAA 2005-1976
21 Robert R. Measurement of residual wrinkles in polymer membranes.AIAA-2001-1346
22 Thomas, Murphey W. The constitutive modeling of thin films with random material wrinkles. AIAA-2001-1347
23 Wagner H. Flat sheet metal girders with very thin metal webs. Parts I II III, NACA Tech Memoranda. 1929,20:200-314
24 Wagner H, Ballerstedt W.Tension Fields In Originally Curved ThinSheets During Shearing Stresses. NACA Tech. Memoranda. No.774, 1935
25 Khun P, Peterson J P, Levin L R. A Summary of Diagonal Tension.Part I and II, NASA Tech. Note, 1952, Nos.2662 and 2633
26 Croll J G. A Tension Field Solution for Non-Linear Circular Plates. InAspects of The Analysis of Plate Structures: A volume in honor of W. H.Wittrick, D. J. Dawe, et al. Editors, Oxford University Press, Oxford, 1985:309~323
27 Yu T X, Stronge W J. Wrinkling of a circular elastic plate stamped by a spherical punch. International Journal of Solid and Structures. 1985,21:995~1003
28 Yu T X, Johnson W. The buckling of annular plates in relation to the deep drawing process. International Journal of Mechanical Sciences. 1982,24:175~88
29 Stronge WJ, Sutclie MPF, Yu T X. Wrinkling of elastoplastic circular plates during stamping. Experimental Mechanics. 1986,26:345~53
30 Yu T X, Johnson W, Stronge W J. Stamping rectangular plates into doubly-curved dies. Proceedings. Institution of Mechanical Engineers, Part C 1984,198:109~25
31 Tomoshi Miyamura. Wrinkling on stretched circular membrane under in-plane torsion: Bifurcation analyses and experiments. Engineering Structures. 2000,23:1407~1425
32 Cerda E, Mahadevan L. Geometry and Physics of Wrinkling. Physical Review Letters.2003.90.074302
33 Y. Wesley Wong and Sergio Pellegrino. Wrinkled membranes part II: analytical models. Journal of Mechanics of Materials and Structures. 2006, 1 (1): 27~61
34 Y. Wesley Wong and Sergio Pellegrino. Wrinkled membranes part I: experiments. Journal of Mechanics of Materials and Structures. 2006, 1(1): 3~24
35 Y. Wesley Wong and Sergio Pellegrino. Wrinkled membranes part III: numerical simulations. Journal of Mechanics of Materials and Structures. 2006,1(1):63~95
36 Adama Diaby, Anh Le van, Christian Wielgosz. Buckling and wrinkling of prestressed membranes. Finite Elements in Analysis and Design. 2006,42:992~1001
37 C. Wang, X. Du and Z. Wan. Numerical Simulation of Wrinkles in Space Inflatable Structures. AIAA-Journal of Spacecraft and Rockets. 2006,43(5):1146~1149
38杜星文,王长国,万志敏.空间薄膜结构的褶皱研究进展.力学进展,2006,36(2):187~199
39 Wang Changguo, Du Xingwen and Wan Zhimin. Wrinkling Analysis of Circular Annulus-Shaped Space Gossamer Structures under In-Plane Torsion. M2D'2006 the 5th International Conference on Mechanics and Materials in Design. Chapter III: Product Engineering & Development in Design. Editors: J.F. Silva Gomes and Shaker A. Meguid. Porto, Portugal. 24-26 July, 2006
40 Pagitz, M. Computational methods for membrane structures, M.Phil.Dissertation, Department of Engineering, University of Cambridge,2004.
41 Jenkins C H, Haugen F, Spicher W H. Experimental Measurement of Wrinkling in Membranes Undergoing Planar Deformation. Experimental Mechanics. 1998,38(2):147~152
42 Jenkins C H, Fitzgerald D M, Liu X. Wrinkling of An Inflatable Membrane with Thermo-Elastic Boundary Conditions. The
41stAIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Atlanta, GA, April, AIAA 2000-1727
43 Blandino J R, Johnston J D, Miles J J. Thin-Film Membrane Wrinkling Due to Thermal and Mechanical Loads. The 42ndAIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Seattle, WA, April, AIAA 2001-1345
44 Giersch L R, Pathfinder R. Photogrammetry Research for Ultra-Lightweight and Inflatable Space Structures, NASA CR-2001-211244,November, 2001
45 Jones T W, Pappa R S. Dot Projection Photogrammetric Technique for Shape Measurements of Aerospace Test Articles. Proceedings of the 40th AIAA Aerospace Sciences Conference, January. AIAA 2002-0532
46 Jones T W, Dorrington A A, Shortis M R. Validation of Laser-Induced Fluorescent Photogrammetric Targets on Membrane Structures. AIAA 2004-1663
47 Black J T, Pappa R S. Photogrammetry and Videogrammetry Methods for Solar Sails and Other Gossamer Structures. AIAA 2004-1662
48 Karara H M. Handbook of Non-Topographic Photogrammetry, The 2nd edition, American Society of Photogrammetry, Falls Church, VA, 1989
49 Mikhail E M, Bethel J S, Mcglone J C. Introduction to Modern Photogrammetry, John Wiley & Sons, New York, NY, 2001
50 Pappa, R S, Giersch L R, Quagliaroli J M. Photogrammetry of a 5-m Inflatable Space Antenna With Consumer Digital Cameras. Experimental Techniques, July/Aug. 2001, pp. 21-29.
51 Pappa R S, Jones T W, Black J T, et al. Photogrammetry Methodology Development for Gossamer Space Structures. The 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, April 22-25, Denver, Colorado. AIAA 2002-1375
52 Pappa R S, Black J T, Blandino J R, et al. Dot Projection Photogrammetry and Videogrammetry of Gossamer Space Structures. Journal of Spacecraft and Rockets, NASA/TM-2003-212146, February 2003
53 Pappa R S, Black J T, Blandino J R. Photogrammetric Measurement of Gossamer Spacecraft Membrane Wrinkling, NASA 2003-SEM-RSP
54 Stein M. Loads and deformation of buckled rectangular plates. NASA Technical Report R-40, National Aeronautics and Space Administration. 1959
55 Keller H B, Reiss E L. Nonlinear bending and buckling of circular plate, Proc. 3d, U.S. Nat. Cong. Appl. Mech., Am.Soc. Mech. Eng. 1958:375~385.
56 Stoll F, Olson S E. Finite element investigation of the snap phenomenon in buckled plates. In: Proceedings of the 1997 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, (4): 2703~2712.
57 Falzon B G, Steven G P. Buckling mode transition in hat-stifiened composite panels loaded in uniaxial compression. Composite Structures.1997,37:253~267
58 Chai H. On the post-buckling behavior of bilaterally constrained plates. International Journal of Solids and Structures.2002,39:2911~2926
59 Herzl Chai. Contact buckling and postbuckling of thin rectangular plates.Journal of the Mechanics and Physics of Solids. 2001,49:209~230
60 Marcinowski J. Postbuckling behaviour of rectangular plates in axial compression. Archives of Civil Engineering. 1999,45: 275~288
61 Tiwari N, Hyer M W. Secondary buckling of compression-loaded composite plates. AIAA Journal.2002, 40:2120~2126.
62 Riks E, Rankin C C, Brogan FA. On the solution of mode jumping phenomena in thin-walled shell structures. Computer Methods in AppliedMechanics and Engineering. 1996,136:59~92
63 Riks, E., Rankin, C.C., 2002. Sandwich modeling with an application to the residual strength analysis of a damaged compression panel. International Journal of Non-Linear Mechanics 37, 897–908.
64 Muheim D M, Johnson E R. Mode jumping of an isogrid panel under quasi-static compression. In: Proceedings of 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, AIAA-2003-1790, vol. 5, Norfolk, VA,April 2003, 3591~3601
65 Chien C S, Gong S Y, Mei Z. Mode jumping in the von Karman equations. SIAM Journal of Scienti.c Computing.2000, 22:1354~1385
66沈惠申,张建武.单向压缩简支矩形板后屈曲摄动分析.应用数学和力学,1998,9(8):741~752
67沈惠申.矩形板屈曲和后屈曲弹塑性分析.应用数学和力学,1990,11(10):871~879
68沈惠申,张建武.双向压缩简支矩形板的后屈曲性态.应用数学和力学,1989,6(2):61~67
69沈惠申,矩形板在横向压力和面内压缩共同作用下的后屈曲.应用数学和力学,1989,10(1):51~58
70张建武,范祖尧.压缩简支矩形板二次屈曲和二次分支点分析.应用力学学报,1986,3(3):1~23
71程昌钧.二次分支与模态跃迁.力学与实践,1992,14(3):9~19
72何录武,程昌钧.矩形薄板的屈曲状态.应用数学和力学,1992,13(5):401~406
73何录武,程昌钧.确定薄板在二重特征值处屈曲状态的一种方法.应用数学和力学,1992,13(4):307~311
74吴柏生.弹性基础上的杆在轴压下的二次屈曲.力学学报,1993,
25(4):443~451
75吴柏生.非线性弹性地基上杆的屈曲缺陷敏感度.上海力学,1991,12(3):19~27
76吴柏生.细长杆在轴压下的二次分叉.力学学报, 1991 , 23(3) :347~354
77剧锦三,蒋秀根,郭彦林等.拱结构的弹塑性二次分岔屈曲性能.工程力学,2006,23(9):12~17
78剧锦三,郭彦林.拱结构的弹性二次分岔屈曲性能初探.中国农业大学学报,2001,6(2):105~108
79剧锦三,郭彦林,刘玉擎.拱结构的弹性二次屈曲性能.工程力学,2002,19(4):109~112
80 Buchanan G R, Peddieson JR J. Vibration of Circular, Annular Membranes with Variable Density. Journal of Sound and Vibration. 1999, 226: 379~382
81 Filipich C P, Rosales M B. Vibration of non-homogeneous rectangular membranes with arbitrary interfaces. Journal of Sound and Vibration. 2007,305: 582-595
82 Changho Shina, Jintai Chungb, Hong Hee Yoo.Dynamic responses of the in-plane and out-of-plane vibrations for an axially moving membrane. Journal of Sound and Vibration. 2006,297: 794~809
83 Buchanan G R. Vibration of circular membranes with linearly varying density along a diameter. Journal of Sound and Vibration. 2005, 280: 407~414
84 Meyers C A, Hyer M W. Thermal buckling and postbuckling of symmetrically laminated composite plates. Journal of Thermal Stresses. 1991,14:519~540
85 Librescu L, Souza M A. Post-buckling of geometrically imperfect shear-deformable flat panels under combined thermal and compressive edge loading. Journal of Applied Mechanics. 1993,60:526~533
86 Librescu L, Lin W, Nemeth M P. Thermomechanical postbuckling of geometrically imperfect flat and curved panels taking into account tangential constraints. Journal of Thermal Stresses. 1995,18:465~482.
87 Librescu L, Nemeth M P, Starnes J H. Nonlinear response of flat and curved panels subjected to thermomechanical loads. Journal of Thermal Stresses. 2000,23:549~582
88 Shen H S.Thermomechanical post-buckling analyses of imperfect laminated plates using a higher order sheardeformation theory.Computers and Structures. 1998,66: 395~409
89 Chen L W, Chen L Y. Thermal postbuckling behaviors of laminated composite plates with temperature dependent properties. Composite Structures.1991,19:267~283
90 Singh G, Rao G V, Iyenger N G R. Thermal postbuckling behavior of laminated composite plates. AIAA Journal. 1994,32:1336~1338
91 Singha M K, Ramachandra L S, Bandyopadhyay J N. Thermal postbuckling analysis of laminated composite plates. Composite Structures. 2001,54:453~458
92 Bisplinghoff R L, Pian T H H. On the vibration of thermally buckled bars and plates, Proceedings of the 9th International Congress for Applied Mechanics1957, 7:307~318
93 Yang T Y, Han A D. Buckled plate vibrations and large amplitude vibrations using high-order triangular elements. AIAA Journal. 1983,21:758~766
94 Hui D, Leissa A W. Effects of geometric imperfections on vibrations of biaxially compressed rectangular flat plates. Journal of Applied Mechanics. 1983,50:750~756
95 Illanko S.Vibration and post-buckling of in-plane loaded rectangular plates using a multiterm Galerkin’s method. Journal of Applied Mechanics. 2002,69: 589~592
96 Lee D M, Lee I. Vibration behaviors of thermally postbuckled anisotropic plates using first-order shear deformable plate theory. Computers and Structures. 1997,63:371~378
97 Librescu L, Lin W, Nemeth M P. Vibration of geometrically imperfect panels subjected to thermal and mechanical loads. Journal of Spacecraft and Rockets. 1996,33:285~291
98 Librescu L, Lin W, Nemeth M P. Frequency– load interaction of geometrically imperfect curved panels subjected to heating,.AIAA Journal. 1996,34:166~177
99 Librescu L, Lin W. Vibration of thermomechanically loaded flat and curved panels taking into account geometric imperfections and tangential edge constraints. International Journal of Solids Structures. 1997,34:2161~2181
100 Oh I K, Han J H, Lee I. Postbuckling and vibration characteristics of piezolaminated composite plate subject to thermo-piezoelectric loads. Journal of Sound and Vibration. 2000,233:19~40
101 Oh I K, Lee I. Thermal snapping and vibration characteristics of cylindrical composite panels using layerwise theory. Composite Structures.2001,51:49~61
102 Girish J, Ramachandra LS. Thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections. Journal of Sound and Vibration. 2005,282: 1137~1153
103 Pradeep V, Ganesan N. Thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates. Journal of Sound and Vibration 2008,310:169~183
104 Chen H, Virgin L N. Dynamic analysis of modal shiftingand mode jumping in thermally buckled plates. Journal of Sound and Vibration. 2004,278:233~256
105 Hui Chen, Wenbin Yu. Postbuckling and mode jumping analysis of composite laminates using an asymptotically correct, geometrically non-linear theory. International Journal of Non-Linear Mechanics. 2006,41:1143 ~1160
106 Hui Chen, Lawrence N. Virgin. Finite element analysis of post-buckling dynamics in plates—Part I: An asymptotic approach. International Journal of Solids and Structures. 2006,43:3983~4007
107 Hui Chen, Lawrence N. Virgin. Finite element analysis of post-buckling dynamics in plates. Part II: A non-stationary analysis. International Journal of Solids and Structures. 2006,43:4008~4027
108 Hossain N M A. Jenkins C H. Wrinkles and gravity effects on transverse vibration of membranes. In: 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 18-21 April 2005, Austin, Texas, AIAA-2005-1978
109 Hossain N M A. Jenkins C H. Jenkins. Transverse Vibration Analysis for Partly Wrinkled Membranes. Journal of Spacecraft and Rockets.2006, 43(3):626~637
110饶正清,杨庆山.薄膜结构褶皱处理方法.工程力学(增刊),2003:308~311
111李作为,杨庆山,刘瑞霞.薄膜结构褶皱研究评述.中国安全科学学报,2004,14(7):16~20
112谭锋,杨庆山,李作为.薄膜结构分析中的褶皱判别准则及其分析方法.北京交通大学学报,2006,30(1):35~39
113谭锋.张拉薄膜结构的褶皱和动力分析.北京交通大学博士学位论文.2007:39~92
114 Faraday M. Acoustic streaming over vibrating plates. Philosophical Transactions of the Royal Society,1831, 299–318. In: Lindsay R B, Acoustics: Historical and Philosophical Development, New York: Wiley, 1973, 211
115 Lord Rayleigh. Theory of Sound (two volumes). New York: Dover Publications, 1945
116 Bourget M. Memoire surle movement vibratoire des membranes circulaires. Annales De l’ecole normale v. III 1866. In: Lord Rayleigh, Theory of Sound, Vol. 1, New York: Dover Publications, 1877, re-issued 1945, 329
117 Chobotov V A, Binder R C. Nonlinear response of a circular membrane to sinusoidal acoustic excitation. Journal of Acoustical Society of America. 1964,36:59~73
118 Sewall J, Miserentino R, Pappa R S. Vibration studies of a lightweight three-sided membrane suitable for space application. NASA Technical Paper 2095, January 1983
119 Jenkins C H, Tampi M. Local membrane vibrations and inflatable space structures. In: Johnson S W, Chua K M, Galloway R G, Richler P I (Eds.), Space 2000, Albuquerque, NM, 2000
120 Richard S P, Thomas W J, Jonathan T B. Photogrammetry methodology development for gossamer spacecraft structures. AIAA-2002-1375
121 James L, Gaspar, Richard S P. Membrane vibration tests using surface-bonded piezoelectric patch actuation. NASA/TM-2003-2121
122 Leyland G, Young, Suresh R, Jiazhu H P, Frank P. Numerical and experimental dynamic characteristics of thin-film membranes. International Journal of Solids and Structures.2005,42:3001~3025
123 Jarasjarungkiat A, Wu R, chner, K.-U. Bletzinger. A wrinkling model based on material modification for isotropicand orthotropic membranes. Comput. Methods Appl. Mech. Engrg.2008,197:773~788
124 Valdes J G, Onate E, Canet J M. A modified material model to simulate wrinkling of orthotropic membranes at finite deformations. Textile Composites and Inflatable Structures (Structural Membranes 2005), CIMNE, 2005, 113~122
125 Raible T, Tegeler K, Lohnert S. Development of a wrinkling algorithm fororthotropic membrane materials. Comput. Methods Appl. Mech. Engrg. 2005,194:2550~2568
126 Epstein M, Forcinito MA. Anisotropic membrane wrinkling: theory and analysis. Int. J. Solid Struct. 2001,38:5253~5272
127张其林等.只受拉单元的修正平衡迭代方程.钢结构,2001,16(2):63~64
128张其林,张莉.膜结构形状确定的三类问题及其求解.建筑结构学报,2000,21(5):33~40
129 Zhang Q L, et al. Numerical Method for Form Finding and Cutting Pattern of Membrane Structures. Computational Civil and Structural Engineering. 2000:115~120
130张其林.索和膜结构.同济大学出版社,2002:124~134
131 Contri P. and Schrefker B. A. A geometrically nonlinear finite element analysis of wrinkled membrane surface by a no-compression material model. Communication in Applied Numerical Methods. 1988,4:5~15
132 Tabarrok B, Qin Z. Nonlinear analysis of tension structures. Computers and Structures. 1992,45:973~984
133 Lu K, Accorsi M, Leonard J. Finite element analysis of membrane wrinkling. Int. J. Numer. Methods Eng. 2001,50:1017~1038
134 Roddeman D G , Drukker J, Oomens C W, Janssen J D. The Wrinkling of Thin Membranes:Part I– Theory. Journal of Applied Mechanics, 1987,54:884~887
135 Roddeman D G , Drukker J, Oomens C W, Janssen J D. The Wrinkling of Thin Membranes:Part II– Numerical Analysis. Journal of Applied Mechanics, 1987,54: 888~892
136 Epstein M, Forcinito M A. Anisotropic membrane wrinkling: theory and analysis. International Journal of Solids and Structures 2001,38:525~5272.
137 Kang S, Im S. Finite element analysis of wrinkling membranes. Journal of Applied Mechanics 1997,64:263~269
138 Kang S, Im S. Finite element analysis of dynamic response of wrinkling membranes. Computer Methods in Applied Mechanics and Engineering. 1999,173:227~240
139 Stein M, Hedgepeth J M. Analysis of partly wrinkled membranes. NASA,Tech Notes, D-813, 1961
140 Miller R K, Hedgepeth J M. Finite element analysis of partly wrinkled membranes. Comp Struc.1985,l20(1-3):631~639
141 Hongli Ding, Bingen Yang.The modeling and numerical analysis of wrinkled membranes. Int. J. Numer. Meth. Engng. 2003,58:1785~1801
142 Yang B, Ding H, et al. A new approach to wrinkling rediction for space membrane structures. The 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit Seattle, WA 16-19, AIAA-2001-1348
143 Stanuszek M. FE analysis of large deformations of membranes with wrinkling. Finite Elements in Analysis and Design. 2003,39:599~618
144 Von Karman and Tsien H S(钱学森).The buckling of thin cylindrical shells under axial compression.J.Aeronaut.Sci.1941,8:303-312
145 Stein M. The influence of prebuckling deformations and stresses on the buckling of perfect cylinders.NASA TR-190,Feb,1964
146 Stein M. The effect on the buckling of perfect cylinders of prebuckling deformations and stresses induced by edge support. Collected papers on instability of shell structures. NASA TN D-1510,Dec.1962,217
147 Stein M. Some recent advances in the investigation of shell buckling.AIAA.J. 1968,6(12) 2339
148 Koiter W T. On the stability of elastic equilibrium, PH.D.Thesis,Delft,H.J.Paris,Amsterdam,1945;English Translation issued as NASA TTF-10,833,1967
149 Koiter W T. Elastic stability and postbuckling behavior.“Non-linear Problems”,Proc.of symp.conducted by Math.Res. Center,U.S.Army,at the Uni.Of Wisconsin,Apr.1962;edited by R.E.Langer,1963:257~275
150 Y. W. Wong. Analysis of Wrinkle Patterns in Prestressed Membrane Structures. [Master Thesis], University of Cambridge, Department of Engineering, Cambridge, UK, August, 2000
151 Y.W. Wong, S. Pellegrino. Prediction of Wrinkle Amplitudes in Square Solar Sails. AIAA 2003-1982
152 George H. Sapna III, John Folke. Inflatable Boom Controlled Deployment Mechanism for the Inflatable Sunshield In Space (ISIS) FlightExperiment.34th Aerospace Mechanisms Conference, May 11-13 2000, NASA GSFC, Greenbelt, MD.IAC-04-I.4.10
153 Sickinger C, Herbeck L, Strohlein T. Lightweight Deployable Booms: Design, Manufacture,Verification, and Smart Materials Application.IAC-04-I.4.10, 55th International Astronautical Congress, IAF/IAA/IISL, Vancouver, Canada, Oct 04 ~08, 2004
154 David P. Cadogan, Mark S. Grahne.Deployment Control Mechanisms for Inflatable Space Structures.33rd Aerospace Mechanisms Conference– May 1999
155 David Lichodziejewski, Gordon Veal, Billy Derbès.Spiral Wrapped Aluminum Laminate Rigidization Technology.AIAA 2002-1701
2 Freeland R E, Bilyeu G D, Veal G R. Inflatable deployable space structures technology summary. IAF-98-I.5.01: 1~16
3 Mitchell Thomas, Gordon Veal. Scaling characteristics of inflatable paraboloid concentrator.In: Solar Engineering. 1991, No. H00630
4 Freeland R E, Bilyeu G D, Veal G R. Validation of a unique concept for a low cost, lightweight space-deployable antenna structure. IAF-93-1.1.204: 1~10
5 Freeland R E, Bilyeu G D, Veal G R. Large inflatable deployable antenna flight experiment results. ACTA Astronautica. 1997, 41 (4-10): 267~277
6 Freeland R E, Bilyeu G D, Veal G R. Development of flight hardware for a large, inflatable-deployable antenna experiment. ACTA Astronautica. 1996, 38 (4-8): 251~260
7 Freeland R E, Bilyeu G D, Veal G R. Validation of unique concept for a low-cost, lightweight space-deployable antenna structure. ACTA Astronautica. 1995, 35 (9-11): 565~572
8 Murphy D, Murphey T, Gierow P. Scalable solar-sail subsystem design concept. AIAA Journal of Spacecraft and Rockets. 2003, 40(4): 539~547
9 Grossman G, Williams G. Inflatable concentrators for solar propulsion and dynamic space power. Journal of Solar Energy Engineering. 1990: 229~236
10 Akahoshi Y, Nakamura R, Tanaka M. Development of bumper shield using low density materials. International Journal of Impact Engineering. 2001, 26 (1-10): 13~19
11 VanBlaricum L, Reilley J P, Gilbert M A. Quick Feasibility Demonstration for an Inflatable Antenna System in Space. Proceedings of the Ninth Annual DARPA Symposium on Photonic Systems for Antenna Applications Naval Postgraduate School, Monterey, CA 17, 18, 19 February 1999
12 Edward J S, James H. M, Thomas W G. Thin-film technology development for the PowerSphere. Materials Science and Engineering B. 2005,116 :265~272
13 Kondyurin A, Lauke B, Vogel R. Photopolymerisation of composite material in simulated free space environment at low Earth orbital flight. European Polymer Journal. 2006, 42 :2703~2714
14 Delozier D M, Watson K A, Smith J G, Connell J W. Preparation and characterization of space durable polymer nanocomposite films. Composites Science and Technology. 2005,65: 749~755
15 Lichodzidjewski D, Cravey R, Hopkins G.Inflatable Deployed Membrane Waveguide Array Antenna for Space. AIAA 2003-1649
16 Leipold M. Solar sail technology ground and in-orbit deployment testing. In Royal Astronomical Society Discussion Meeting, 10 May 2002
17 Mark S. Lake. A Rationale for Defining Structural Requirements for Large Space Telescopes. AIAA-2001-1685
18 Thomas W, Murphey, David M, Murphy. A Method to Quantify the Thrust Degradation Effects of Structural Wrinkles in Solar Sails. AIAA 2002-1560
19 Kukathasan S, Pellegrino S. Nonlinear vibration of wrinkled membranes. In: 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 7-10 April 2003, Norfolk, VA AIAA-2003-1747
20 Gough A, Hossain N.M. A, Jenkins C.H. Experimental and Numerical Study of Creased Membranes. AIAA 2005-1976
21 Robert R. Measurement of residual wrinkles in polymer membranes.AIAA-2001-1346
22 Thomas, Murphey W. The constitutive modeling of thin films with random material wrinkles. AIAA-2001-1347
23 Wagner H. Flat sheet metal girders with very thin metal webs. Parts I II III, NACA Tech Memoranda. 1929,20:200-314
24 Wagner H, Ballerstedt W.Tension Fields In Originally Curved ThinSheets During Shearing Stresses. NACA Tech. Memoranda. No.774, 1935
25 Khun P, Peterson J P, Levin L R. A Summary of Diagonal Tension.Part I and II, NASA Tech. Note, 1952, Nos.2662 and 2633
26 Croll J G. A Tension Field Solution for Non-Linear Circular Plates. InAspects of The Analysis of Plate Structures: A volume in honor of W. H.Wittrick, D. J. Dawe, et al. Editors, Oxford University Press, Oxford, 1985:309~323
27 Yu T X, Stronge W J. Wrinkling of a circular elastic plate stamped by a spherical punch. International Journal of Solid and Structures. 1985,21:995~1003
28 Yu T X, Johnson W. The buckling of annular plates in relation to the deep drawing process. International Journal of Mechanical Sciences. 1982,24:175~88
29 Stronge WJ, Sutclie MPF, Yu T X. Wrinkling of elastoplastic circular plates during stamping. Experimental Mechanics. 1986,26:345~53
30 Yu T X, Johnson W, Stronge W J. Stamping rectangular plates into doubly-curved dies. Proceedings. Institution of Mechanical Engineers, Part C 1984,198:109~25
31 Tomoshi Miyamura. Wrinkling on stretched circular membrane under in-plane torsion: Bifurcation analyses and experiments. Engineering Structures. 2000,23:1407~1425
32 Cerda E, Mahadevan L. Geometry and Physics of Wrinkling. Physical Review Letters.2003.90.074302
33 Y. Wesley Wong and Sergio Pellegrino. Wrinkled membranes part II: analytical models. Journal of Mechanics of Materials and Structures. 2006, 1 (1): 27~61
34 Y. Wesley Wong and Sergio Pellegrino. Wrinkled membranes part I: experiments. Journal of Mechanics of Materials and Structures. 2006, 1(1): 3~24
35 Y. Wesley Wong and Sergio Pellegrino. Wrinkled membranes part III: numerical simulations. Journal of Mechanics of Materials and Structures. 2006,1(1):63~95
36 Adama Diaby, Anh Le van, Christian Wielgosz. Buckling and wrinkling of prestressed membranes. Finite Elements in Analysis and Design. 2006,42:992~1001
37 C. Wang, X. Du and Z. Wan. Numerical Simulation of Wrinkles in Space Inflatable Structures. AIAA-Journal of Spacecraft and Rockets. 2006,43(5):1146~1149
38杜星文,王长国,万志敏.空间薄膜结构的褶皱研究进展.力学进展,2006,36(2):187~199
39 Wang Changguo, Du Xingwen and Wan Zhimin. Wrinkling Analysis of Circular Annulus-Shaped Space Gossamer Structures under In-Plane Torsion. M2D'2006 the 5th International Conference on Mechanics and Materials in Design. Chapter III: Product Engineering & Development in Design. Editors: J.F. Silva Gomes and Shaker A. Meguid. Porto, Portugal. 24-26 July, 2006
40 Pagitz, M. Computational methods for membrane structures, M.Phil.Dissertation, Department of Engineering, University of Cambridge,2004.
41 Jenkins C H, Haugen F, Spicher W H. Experimental Measurement of Wrinkling in Membranes Undergoing Planar Deformation. Experimental Mechanics. 1998,38(2):147~152
42 Jenkins C H, Fitzgerald D M, Liu X. Wrinkling of An Inflatable Membrane with Thermo-Elastic Boundary Conditions. The
41stAIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Atlanta, GA, April, AIAA 2000-1727
43 Blandino J R, Johnston J D, Miles J J. Thin-Film Membrane Wrinkling Due to Thermal and Mechanical Loads. The 42ndAIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Seattle, WA, April, AIAA 2001-1345
44 Giersch L R, Pathfinder R. Photogrammetry Research for Ultra-Lightweight and Inflatable Space Structures, NASA CR-2001-211244,November, 2001
45 Jones T W, Pappa R S. Dot Projection Photogrammetric Technique for Shape Measurements of Aerospace Test Articles. Proceedings of the 40th AIAA Aerospace Sciences Conference, January. AIAA 2002-0532
46 Jones T W, Dorrington A A, Shortis M R. Validation of Laser-Induced Fluorescent Photogrammetric Targets on Membrane Structures. AIAA 2004-1663
47 Black J T, Pappa R S. Photogrammetry and Videogrammetry Methods for Solar Sails and Other Gossamer Structures. AIAA 2004-1662
48 Karara H M. Handbook of Non-Topographic Photogrammetry, The 2nd edition, American Society of Photogrammetry, Falls Church, VA, 1989
49 Mikhail E M, Bethel J S, Mcglone J C. Introduction to Modern Photogrammetry, John Wiley & Sons, New York, NY, 2001
50 Pappa, R S, Giersch L R, Quagliaroli J M. Photogrammetry of a 5-m Inflatable Space Antenna With Consumer Digital Cameras. Experimental Techniques, July/Aug. 2001, pp. 21-29.
51 Pappa R S, Jones T W, Black J T, et al. Photogrammetry Methodology Development for Gossamer Space Structures. The 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, April 22-25, Denver, Colorado. AIAA 2002-1375
52 Pappa R S, Black J T, Blandino J R, et al. Dot Projection Photogrammetry and Videogrammetry of Gossamer Space Structures. Journal of Spacecraft and Rockets, NASA/TM-2003-212146, February 2003
53 Pappa R S, Black J T, Blandino J R. Photogrammetric Measurement of Gossamer Spacecraft Membrane Wrinkling, NASA 2003-SEM-RSP
54 Stein M. Loads and deformation of buckled rectangular plates. NASA Technical Report R-40, National Aeronautics and Space Administration. 1959
55 Keller H B, Reiss E L. Nonlinear bending and buckling of circular plate, Proc. 3d, U.S. Nat. Cong. Appl. Mech., Am.Soc. Mech. Eng. 1958:375~385.
56 Stoll F, Olson S E. Finite element investigation of the snap phenomenon in buckled plates. In: Proceedings of the 1997 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, (4): 2703~2712.
57 Falzon B G, Steven G P. Buckling mode transition in hat-stifiened composite panels loaded in uniaxial compression. Composite Structures.1997,37:253~267
58 Chai H. On the post-buckling behavior of bilaterally constrained plates. International Journal of Solids and Structures.2002,39:2911~2926
59 Herzl Chai. Contact buckling and postbuckling of thin rectangular plates.Journal of the Mechanics and Physics of Solids. 2001,49:209~230
60 Marcinowski J. Postbuckling behaviour of rectangular plates in axial compression. Archives of Civil Engineering. 1999,45: 275~288
61 Tiwari N, Hyer M W. Secondary buckling of compression-loaded composite plates. AIAA Journal.2002, 40:2120~2126.
62 Riks E, Rankin C C, Brogan FA. On the solution of mode jumping phenomena in thin-walled shell structures. Computer Methods in AppliedMechanics and Engineering. 1996,136:59~92
63 Riks, E., Rankin, C.C., 2002. Sandwich modeling with an application to the residual strength analysis of a damaged compression panel. International Journal of Non-Linear Mechanics 37, 897–908.
64 Muheim D M, Johnson E R. Mode jumping of an isogrid panel under quasi-static compression. In: Proceedings of 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, AIAA-2003-1790, vol. 5, Norfolk, VA,April 2003, 3591~3601
65 Chien C S, Gong S Y, Mei Z. Mode jumping in the von Karman equations. SIAM Journal of Scienti.c Computing.2000, 22:1354~1385
66沈惠申,张建武.单向压缩简支矩形板后屈曲摄动分析.应用数学和力学,1998,9(8):741~752
67沈惠申.矩形板屈曲和后屈曲弹塑性分析.应用数学和力学,1990,11(10):871~879
68沈惠申,张建武.双向压缩简支矩形板的后屈曲性态.应用数学和力学,1989,6(2):61~67
69沈惠申,矩形板在横向压力和面内压缩共同作用下的后屈曲.应用数学和力学,1989,10(1):51~58
70张建武,范祖尧.压缩简支矩形板二次屈曲和二次分支点分析.应用力学学报,1986,3(3):1~23
71程昌钧.二次分支与模态跃迁.力学与实践,1992,14(3):9~19
72何录武,程昌钧.矩形薄板的屈曲状态.应用数学和力学,1992,13(5):401~406
73何录武,程昌钧.确定薄板在二重特征值处屈曲状态的一种方法.应用数学和力学,1992,13(4):307~311
74吴柏生.弹性基础上的杆在轴压下的二次屈曲.力学学报,1993,
25(4):443~451
75吴柏生.非线性弹性地基上杆的屈曲缺陷敏感度.上海力学,1991,12(3):19~27
76吴柏生.细长杆在轴压下的二次分叉.力学学报, 1991 , 23(3) :347~354
77剧锦三,蒋秀根,郭彦林等.拱结构的弹塑性二次分岔屈曲性能.工程力学,2006,23(9):12~17
78剧锦三,郭彦林.拱结构的弹性二次分岔屈曲性能初探.中国农业大学学报,2001,6(2):105~108
79剧锦三,郭彦林,刘玉擎.拱结构的弹性二次屈曲性能.工程力学,2002,19(4):109~112
80 Buchanan G R, Peddieson JR J. Vibration of Circular, Annular Membranes with Variable Density. Journal of Sound and Vibration. 1999, 226: 379~382
81 Filipich C P, Rosales M B. Vibration of non-homogeneous rectangular membranes with arbitrary interfaces. Journal of Sound and Vibration. 2007,305: 582-595
82 Changho Shina, Jintai Chungb, Hong Hee Yoo.Dynamic responses of the in-plane and out-of-plane vibrations for an axially moving membrane. Journal of Sound and Vibration. 2006,297: 794~809
83 Buchanan G R. Vibration of circular membranes with linearly varying density along a diameter. Journal of Sound and Vibration. 2005, 280: 407~414
84 Meyers C A, Hyer M W. Thermal buckling and postbuckling of symmetrically laminated composite plates. Journal of Thermal Stresses. 1991,14:519~540
85 Librescu L, Souza M A. Post-buckling of geometrically imperfect shear-deformable flat panels under combined thermal and compressive edge loading. Journal of Applied Mechanics. 1993,60:526~533
86 Librescu L, Lin W, Nemeth M P. Thermomechanical postbuckling of geometrically imperfect flat and curved panels taking into account tangential constraints. Journal of Thermal Stresses. 1995,18:465~482.
87 Librescu L, Nemeth M P, Starnes J H. Nonlinear response of flat and curved panels subjected to thermomechanical loads. Journal of Thermal Stresses. 2000,23:549~582
88 Shen H S.Thermomechanical post-buckling analyses of imperfect laminated plates using a higher order sheardeformation theory.Computers and Structures. 1998,66: 395~409
89 Chen L W, Chen L Y. Thermal postbuckling behaviors of laminated composite plates with temperature dependent properties. Composite Structures.1991,19:267~283
90 Singh G, Rao G V, Iyenger N G R. Thermal postbuckling behavior of laminated composite plates. AIAA Journal. 1994,32:1336~1338
91 Singha M K, Ramachandra L S, Bandyopadhyay J N. Thermal postbuckling analysis of laminated composite plates. Composite Structures. 2001,54:453~458
92 Bisplinghoff R L, Pian T H H. On the vibration of thermally buckled bars and plates, Proceedings of the 9th International Congress for Applied Mechanics1957, 7:307~318
93 Yang T Y, Han A D. Buckled plate vibrations and large amplitude vibrations using high-order triangular elements. AIAA Journal. 1983,21:758~766
94 Hui D, Leissa A W. Effects of geometric imperfections on vibrations of biaxially compressed rectangular flat plates. Journal of Applied Mechanics. 1983,50:750~756
95 Illanko S.Vibration and post-buckling of in-plane loaded rectangular plates using a multiterm Galerkin’s method. Journal of Applied Mechanics. 2002,69: 589~592
96 Lee D M, Lee I. Vibration behaviors of thermally postbuckled anisotropic plates using first-order shear deformable plate theory. Computers and Structures. 1997,63:371~378
97 Librescu L, Lin W, Nemeth M P. Vibration of geometrically imperfect panels subjected to thermal and mechanical loads. Journal of Spacecraft and Rockets. 1996,33:285~291
98 Librescu L, Lin W, Nemeth M P. Frequency– load interaction of geometrically imperfect curved panels subjected to heating,.AIAA Journal. 1996,34:166~177
99 Librescu L, Lin W. Vibration of thermomechanically loaded flat and curved panels taking into account geometric imperfections and tangential edge constraints. International Journal of Solids Structures. 1997,34:2161~2181
100 Oh I K, Han J H, Lee I. Postbuckling and vibration characteristics of piezolaminated composite plate subject to thermo-piezoelectric loads. Journal of Sound and Vibration. 2000,233:19~40
101 Oh I K, Lee I. Thermal snapping and vibration characteristics of cylindrical composite panels using layerwise theory. Composite Structures.2001,51:49~61
102 Girish J, Ramachandra LS. Thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections. Journal of Sound and Vibration. 2005,282: 1137~1153
103 Pradeep V, Ganesan N. Thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates. Journal of Sound and Vibration 2008,310:169~183
104 Chen H, Virgin L N. Dynamic analysis of modal shiftingand mode jumping in thermally buckled plates. Journal of Sound and Vibration. 2004,278:233~256
105 Hui Chen, Wenbin Yu. Postbuckling and mode jumping analysis of composite laminates using an asymptotically correct, geometrically non-linear theory. International Journal of Non-Linear Mechanics. 2006,41:1143 ~1160
106 Hui Chen, Lawrence N. Virgin. Finite element analysis of post-buckling dynamics in plates—Part I: An asymptotic approach. International Journal of Solids and Structures. 2006,43:3983~4007
107 Hui Chen, Lawrence N. Virgin. Finite element analysis of post-buckling dynamics in plates. Part II: A non-stationary analysis. International Journal of Solids and Structures. 2006,43:4008~4027
108 Hossain N M A. Jenkins C H. Wrinkles and gravity effects on transverse vibration of membranes. In: 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 18-21 April 2005, Austin, Texas, AIAA-2005-1978
109 Hossain N M A. Jenkins C H. Jenkins. Transverse Vibration Analysis for Partly Wrinkled Membranes. Journal of Spacecraft and Rockets.2006, 43(3):626~637
110饶正清,杨庆山.薄膜结构褶皱处理方法.工程力学(增刊),2003:308~311
111李作为,杨庆山,刘瑞霞.薄膜结构褶皱研究评述.中国安全科学学报,2004,14(7):16~20
112谭锋,杨庆山,李作为.薄膜结构分析中的褶皱判别准则及其分析方法.北京交通大学学报,2006,30(1):35~39
113谭锋.张拉薄膜结构的褶皱和动力分析.北京交通大学博士学位论文.2007:39~92
114 Faraday M. Acoustic streaming over vibrating plates. Philosophical Transactions of the Royal Society,1831, 299–318. In: Lindsay R B, Acoustics: Historical and Philosophical Development, New York: Wiley, 1973, 211
115 Lord Rayleigh. Theory of Sound (two volumes). New York: Dover Publications, 1945
116 Bourget M. Memoire surle movement vibratoire des membranes circulaires. Annales De l’ecole normale v. III 1866. In: Lord Rayleigh, Theory of Sound, Vol. 1, New York: Dover Publications, 1877, re-issued 1945, 329
117 Chobotov V A, Binder R C. Nonlinear response of a circular membrane to sinusoidal acoustic excitation. Journal of Acoustical Society of America. 1964,36:59~73
118 Sewall J, Miserentino R, Pappa R S. Vibration studies of a lightweight three-sided membrane suitable for space application. NASA Technical Paper 2095, January 1983
119 Jenkins C H, Tampi M. Local membrane vibrations and inflatable space structures. In: Johnson S W, Chua K M, Galloway R G, Richler P I (Eds.), Space 2000, Albuquerque, NM, 2000
120 Richard S P, Thomas W J, Jonathan T B. Photogrammetry methodology development for gossamer spacecraft structures. AIAA-2002-1375
121 James L, Gaspar, Richard S P. Membrane vibration tests using surface-bonded piezoelectric patch actuation. NASA/TM-2003-2121
122 Leyland G, Young, Suresh R, Jiazhu H P, Frank P. Numerical and experimental dynamic characteristics of thin-film membranes. International Journal of Solids and Structures.2005,42:3001~3025
123 Jarasjarungkiat A, Wu R, chner, K.-U. Bletzinger. A wrinkling model based on material modification for isotropicand orthotropic membranes. Comput. Methods Appl. Mech. Engrg.2008,197:773~788
124 Valdes J G, Onate E, Canet J M. A modified material model to simulate wrinkling of orthotropic membranes at finite deformations. Textile Composites and Inflatable Structures (Structural Membranes 2005), CIMNE, 2005, 113~122
125 Raible T, Tegeler K, Lohnert S. Development of a wrinkling algorithm fororthotropic membrane materials. Comput. Methods Appl. Mech. Engrg. 2005,194:2550~2568
126 Epstein M, Forcinito MA. Anisotropic membrane wrinkling: theory and analysis. Int. J. Solid Struct. 2001,38:5253~5272
127张其林等.只受拉单元的修正平衡迭代方程.钢结构,2001,16(2):63~64
128张其林,张莉.膜结构形状确定的三类问题及其求解.建筑结构学报,2000,21(5):33~40
129 Zhang Q L, et al. Numerical Method for Form Finding and Cutting Pattern of Membrane Structures. Computational Civil and Structural Engineering. 2000:115~120
130张其林.索和膜结构.同济大学出版社,2002:124~134
131 Contri P. and Schrefker B. A. A geometrically nonlinear finite element analysis of wrinkled membrane surface by a no-compression material model. Communication in Applied Numerical Methods. 1988,4:5~15
132 Tabarrok B, Qin Z. Nonlinear analysis of tension structures. Computers and Structures. 1992,45:973~984
133 Lu K, Accorsi M, Leonard J. Finite element analysis of membrane wrinkling. Int. J. Numer. Methods Eng. 2001,50:1017~1038
134 Roddeman D G , Drukker J, Oomens C W, Janssen J D. The Wrinkling of Thin Membranes:Part I– Theory. Journal of Applied Mechanics, 1987,54:884~887
135 Roddeman D G , Drukker J, Oomens C W, Janssen J D. The Wrinkling of Thin Membranes:Part II– Numerical Analysis. Journal of Applied Mechanics, 1987,54: 888~892
136 Epstein M, Forcinito M A. Anisotropic membrane wrinkling: theory and analysis. International Journal of Solids and Structures 2001,38:525~5272.
137 Kang S, Im S. Finite element analysis of wrinkling membranes. Journal of Applied Mechanics 1997,64:263~269
138 Kang S, Im S. Finite element analysis of dynamic response of wrinkling membranes. Computer Methods in Applied Mechanics and Engineering. 1999,173:227~240
139 Stein M, Hedgepeth J M. Analysis of partly wrinkled membranes. NASA,Tech Notes, D-813, 1961
140 Miller R K, Hedgepeth J M. Finite element analysis of partly wrinkled membranes. Comp Struc.1985,l20(1-3):631~639
141 Hongli Ding, Bingen Yang.The modeling and numerical analysis of wrinkled membranes. Int. J. Numer. Meth. Engng. 2003,58:1785~1801
142 Yang B, Ding H, et al. A new approach to wrinkling rediction for space membrane structures. The 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit Seattle, WA 16-19, AIAA-2001-1348
143 Stanuszek M. FE analysis of large deformations of membranes with wrinkling. Finite Elements in Analysis and Design. 2003,39:599~618
144 Von Karman and Tsien H S(钱学森).The buckling of thin cylindrical shells under axial compression.J.Aeronaut.Sci.1941,8:303-312
145 Stein M. The influence of prebuckling deformations and stresses on the buckling of perfect cylinders.NASA TR-190,Feb,1964
146 Stein M. The effect on the buckling of perfect cylinders of prebuckling deformations and stresses induced by edge support. Collected papers on instability of shell structures. NASA TN D-1510,Dec.1962,217
147 Stein M. Some recent advances in the investigation of shell buckling.AIAA.J. 1968,6(12) 2339
148 Koiter W T. On the stability of elastic equilibrium, PH.D.Thesis,Delft,H.J.Paris,Amsterdam,1945;English Translation issued as NASA TTF-10,833,1967
149 Koiter W T. Elastic stability and postbuckling behavior.“Non-linear Problems”,Proc.of symp.conducted by Math.Res. Center,U.S.Army,at the Uni.Of Wisconsin,Apr.1962;edited by R.E.Langer,1963:257~275
150 Y. W. Wong. Analysis of Wrinkle Patterns in Prestressed Membrane Structures. [Master Thesis], University of Cambridge, Department of Engineering, Cambridge, UK, August, 2000
151 Y.W. Wong, S. Pellegrino. Prediction of Wrinkle Amplitudes in Square Solar Sails. AIAA 2003-1982
152 George H. Sapna III, John Folke. Inflatable Boom Controlled Deployment Mechanism for the Inflatable Sunshield In Space (ISIS) FlightExperiment.34th Aerospace Mechanisms Conference, May 11-13 2000, NASA GSFC, Greenbelt, MD.IAC-04-I.4.10
153 Sickinger C, Herbeck L, Strohlein T. Lightweight Deployable Booms: Design, Manufacture,Verification, and Smart Materials Application.IAC-04-I.4.10, 55th International Astronautical Congress, IAF/IAA/IISL, Vancouver, Canada, Oct 04 ~08, 2004
154 David P. Cadogan, Mark S. Grahne.Deployment Control Mechanisms for Inflatable Space Structures.33rd Aerospace Mechanisms Conference– May 1999
155 David Lichodziejewski, Gordon Veal, Billy Derbès.Spiral Wrapped Aluminum Laminate Rigidization Technology.AIAA 2002-1701
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