轴压载荷下复合材料层合圆柱壳的设计与试验研究
|
摘要
飞行器舱段在在飞行过程中除了受到轴向压缩载荷外，还要承受由自身重量引起的惯性载荷。轴向压缩破坏是其主要的破坏形式，当飞行器舱段复合材料圆柱壳体结构所受的压缩载荷达到某一临界值时壳体结构的平衡将会发生改变,导致结构失稳或屈曲,无法保证正常飞行。
本项研究针以飞行器舱段结构为例，采用试验研究与数值分析相结合的方法，对四种不同初始缺陷类型的圆柱壳体在轴向压缩载荷作用下的强度和屈曲特性进行了试验研究，采用经典理论对正交铺层的圆柱壳体临界屈曲载荷进行了计算，在此基础上对各类不同铺层的圆柱壳体及经过口盖修复的圆柱壳体的屈曲特性进行了有限元分析，给出了飞行器舱段轴向压缩稳定性的优化设计，为复合材料圆柱壳舱段设计提供了理论依据。研究成果可用于舱段复合材料结构设计，保障了飞行器舱段结构在使用过程中不发生失稳和破坏，具有重要的工程应用价值。
主要研究内容包括：
一、飞行器舱段为例，研制了全尺寸的四种含有不同初始缺陷的复合材料圆柱壳体试验件，并分别对其进行了轴向压缩破坏试验。采用多通道数据采集器进行试验数据采集和可视化实时监测壳体各部位的应变变化状态。通过试验研究得出了飞行器舱段的压缩失稳破坏载荷及各个测量点的有效试验数据；
二、通过对试验结果数据进行数值分析，得出了四种含有不同初始缺陷的复合材料圆柱壳体试验件在轴向压缩载荷作用下的破坏形式，均为压缩屈曲破坏。根据测得的四种复合材料圆柱壳体结构轴向压缩破坏试验结果数据和载荷输入—应变输出关系曲线、时间—应变关系曲线和位移—应变关系曲线，得出以下结论：
1、完整复合材料圆柱壳结构的破坏形式为屈曲破坏，破坏时中段的变形比较明显。结构破坏时复合材料层间破坏的情况比较严重。
2、含椭圆开孔的圆柱壳体结构在结构受载过程发生了非线性屈曲变形。在136kN时发生局部破坏，但是仍然具有承载能力，当载荷达到144kN时结构完全破坏，失去承载能力。结构破坏主要集中在椭圆形开孔右侧，结构产生断裂，裂痕沿周向延伸至后方，应力集中部位与有限元分析结果相一致。
3、含开缝的圆柱壳体结构在受到轴向压缩载荷的状态下出现了较为复杂的屈曲变形，当载荷达到315kN时出现了局部破坏，在320kN和330kN时陆续出现局部破坏，当载荷达到338kN时，结构完全破坏。最终裂痕出现的开缝的中间位置的左侧，破坏形式为内凹。而开缝右侧变形较为复杂，中段偏上部位和偏下部位在结构出现破坏时呈外凸，而中段部位则是内凹破坏，反映了柱壳结构失稳时的复杂变形。
4、含低速冲击损伤复合材料圆柱壳体结构破坏载荷为360kN，结构在受轴向压缩载荷过程中并未出现大幅度的非线性屈曲变形，结构破坏形式为压缩断裂破坏。
5、在压缩过程中所有圆柱壳体试验件屈曲变形均主要集中在圆柱壳体中部，试验件两端仍然为线弹性变形。其中完整圆柱壳体和含冲击损伤的圆柱壳体两种相对完好的试验件，在轴向受压缩载荷时屈曲变形较小，而开缝和开椭圆形孔的圆柱壳体在轴向受压时的非线性屈曲变形较大，试验结果表明在轴向载荷作用下复合材料圆柱壳体的损伤越大其稳定性越差。
三、通过ANSYS有限元软件建立了四种复合材料圆柱壳体的有限元模型，分析其在受到轴向压缩载荷作用下的屈曲特性，从而得到各个复合材料圆柱壳体的1到10阶特征屈曲载荷。与试验结果对比，发现含有不同初始缺陷的复合材料圆柱壳体试验件在轴向压缩载荷作用下，其破坏屈曲载荷数值在第4阶与第5阶特征屈曲载荷之间，进而得出了该复合材料圆柱壳体在轴向压缩载荷作用下的破坏屈曲载荷判断区间。
四、基于ANSYS有限元分别计算各圆柱壳体特征屈曲载荷，并计算复合材料圆柱壳体铺层角度的变化对轴向压缩载荷的影响。得出了在四种不同初始损伤的复合材料圆柱壳体屈曲特性；铺层角度与特征屈曲载荷之间的关系曲线。给出了四种复合材料圆柱壳体的最优铺层角度，从而提升了在轴向压缩载荷下的屈曲强度。
五、为了对矩形开口的复合材料圆柱壳体进行补强，在壳体上加装复合材料口盖，设计复合材料口盖的铺层角度和铺层厚度，提出了一种在受轴向压缩载荷时，稳定性高而且又经济的口盖设计方案。综合考虑复合材料加强口盖的优化铺层方式、铺层厚度和不含口盖的复合材料圆柱壳结构的优化铺层方式，提出了一种含矩形口盖的复合材料圆柱壳体结构优化设计方法。经过优化设计后的舱段结构的屈曲强度与完整的柱壳结构基本相当，反映出经优化设计后的飞行器舱段得到了有效的修补和增强，满足了等强度设计和维修使用要求。
本项研究已经用于飞行器结构设备舱段设计，具有重要的工程意义和实用价值。
Aircraft in flight process was under bothr axial compression load and inertial load caused byits own weight. axial compression failure was the main form of damage, when the projectilecomposite cylindrical shell structure by compression load reached a certain critical value balanceleading to structural instability or buckling and unable to ensure the normal flight.
Taking projectile bodies structure as an example, the paper adopted the combination ofexperimental study and numerical analysis method. Same-size ratio test objects were studiedusing damage destructive tests and numeric analysis method. Four cylindrical shells’ strength andbuckling characteristics under axial compression load were researched with different types ofinitial defects. Critical buckling load was computed by classical theory about orthogonality ply ofcomposite cylindrical shell. On the basis of research above, finite element analysis was performedabout buckling characteristics of different ply and strengthened covering cap. Optimal designabout the reliability of aircraft body under axis compression load was brought forward, which wasable to ensure the reliability and security of cylindrical shells. The result has great importantengineering application value.
The main research included are as following：
Four same-size ratio cylindrical shells with different type of initial defects were developedaccording to the prototype of certain type aircraft and axis compression destructive tests werecarried out. The experimental data was acquainted and strain changes were visually monitored bymulti-channel data acquisition experiment.
Through numerical analysis of test data, it was indicated that four cylindrical shells withdifferent type of initial defects under axis compression destructive tests were destroyed in thesame way-compression buckling damage. According to the test data, load-strain curve,time-strain curve and displacement-strain curve, it had come to conclusion as following:
1. For complete composite cylindrical shell structure, its’ destructive form was bucklingdamage and the middle part deformed obviously. When structure damaging, interlamination wasdestroyed seriously.
2. Nonlinearity buckling deformation appeared during destructive test of compositecylindrical shell with oval-shaped open. When axis load equal to136kN，it had local failure butstill with certain carrying capacity. When axis load equal to144kN, it had been destroyed completely. Structure damage mostly appeared at the right of oval-shaped open, crack extended tothe rear at circumference directions. Stress concentration position was consistent with finiteelement analysis results.
3. Complexity buckling deformation occurred for composite cylindrical shell with initialcrack under axis compression load When axis load equal to315kN, it was destroyed locally.When axis compression load between320kN and330kN，local damage was in succession andwhen axis load reached338kN，it was damaged completely. Final damage crack appeared at theleft to initial crack and indent damage appeared. Deformation at the right to initial crack wasrelatively complex, it was convex at the upper and lower position in the middle part of cylindricalshell, while indent damaged appeared in the middle part.
4. Composite cylindrical shell was damaged under360kN axis low-velocity impact load. Inthe process of axis compression, there was no nonlinear buckling deformation drasticallyappeared and it had been damaged in broken compression.
5. In destructive tests, all test objects’ buckling deformation appeared in the middle positionmostly, both ends of test objects’ appeared with linear elasticity. The complete and the impacteddefects cylindrical shells had less buckling deformation, meanwhile nonlinear deformation waslarger for cylindrical shell with initial crack and oval-shaped hole. The result indicated cylindricalshell with more damage under axis compression load had poor reliability.
Finite element models were developed for four composite cylindrical shells with ANSYSsoftware. Buckling characteristics of each were analyzed under axis compression load with theresult of1to10order eigenvalue buckling loads. After compared with test results, it came toconclusion that damaged buckling load was between4and5order eigenvalue buckling loads forcomposite cylindrical shells under axis compression load.
Characteristic buckling load was computed by ANSYS for different cylindrical shellsindependently, and changes of ply angle’ influence on buckling characteristics considered.Buckling characteristic of four cylindrical shells with different initial defects were achieved andply angle-characteristic buckling load curve were captured too. Optimized ply angles were givento improve buckling strength for different cylindrical shells.
Aimed to enhance composite cylindrical shell with rectangle open, ply angle and thick ofcomposite covering cap was designed. An optimized design plan was put forward under axiscompression load, which had higher reliability and economic. Optimized design method forcomposite cylindrical shells with rectangle covering cap was found considering many factors, including best ply way, thickness of cylindrical shell with enhanced covering cap and withoutcovering cap. Aircraft body structure’s strength was equal to the whole cylindrical shells afteroptimized design, which meet the needs of equal-strength design and maintenance.
The research results had been applied to a certain type of aircraft equipment cabin structuredesign successfully, and will have important engineering significance and practical value infuture.
本项研究针以飞行器舱段结构为例，采用试验研究与数值分析相结合的方法，对四种不同初始缺陷类型的圆柱壳体在轴向压缩载荷作用下的强度和屈曲特性进行了试验研究，采用经典理论对正交铺层的圆柱壳体临界屈曲载荷进行了计算，在此基础上对各类不同铺层的圆柱壳体及经过口盖修复的圆柱壳体的屈曲特性进行了有限元分析，给出了飞行器舱段轴向压缩稳定性的优化设计，为复合材料圆柱壳舱段设计提供了理论依据。研究成果可用于舱段复合材料结构设计，保障了飞行器舱段结构在使用过程中不发生失稳和破坏，具有重要的工程应用价值。
主要研究内容包括：
一、飞行器舱段为例，研制了全尺寸的四种含有不同初始缺陷的复合材料圆柱壳体试验件，并分别对其进行了轴向压缩破坏试验。采用多通道数据采集器进行试验数据采集和可视化实时监测壳体各部位的应变变化状态。通过试验研究得出了飞行器舱段的压缩失稳破坏载荷及各个测量点的有效试验数据；
二、通过对试验结果数据进行数值分析，得出了四种含有不同初始缺陷的复合材料圆柱壳体试验件在轴向压缩载荷作用下的破坏形式，均为压缩屈曲破坏。根据测得的四种复合材料圆柱壳体结构轴向压缩破坏试验结果数据和载荷输入—应变输出关系曲线、时间—应变关系曲线和位移—应变关系曲线，得出以下结论：
1、完整复合材料圆柱壳结构的破坏形式为屈曲破坏，破坏时中段的变形比较明显。结构破坏时复合材料层间破坏的情况比较严重。
2、含椭圆开孔的圆柱壳体结构在结构受载过程发生了非线性屈曲变形。在136kN时发生局部破坏，但是仍然具有承载能力，当载荷达到144kN时结构完全破坏，失去承载能力。结构破坏主要集中在椭圆形开孔右侧，结构产生断裂，裂痕沿周向延伸至后方，应力集中部位与有限元分析结果相一致。
3、含开缝的圆柱壳体结构在受到轴向压缩载荷的状态下出现了较为复杂的屈曲变形，当载荷达到315kN时出现了局部破坏，在320kN和330kN时陆续出现局部破坏，当载荷达到338kN时，结构完全破坏。最终裂痕出现的开缝的中间位置的左侧，破坏形式为内凹。而开缝右侧变形较为复杂，中段偏上部位和偏下部位在结构出现破坏时呈外凸，而中段部位则是内凹破坏，反映了柱壳结构失稳时的复杂变形。
4、含低速冲击损伤复合材料圆柱壳体结构破坏载荷为360kN，结构在受轴向压缩载荷过程中并未出现大幅度的非线性屈曲变形，结构破坏形式为压缩断裂破坏。
5、在压缩过程中所有圆柱壳体试验件屈曲变形均主要集中在圆柱壳体中部，试验件两端仍然为线弹性变形。其中完整圆柱壳体和含冲击损伤的圆柱壳体两种相对完好的试验件，在轴向受压缩载荷时屈曲变形较小，而开缝和开椭圆形孔的圆柱壳体在轴向受压时的非线性屈曲变形较大，试验结果表明在轴向载荷作用下复合材料圆柱壳体的损伤越大其稳定性越差。
三、通过ANSYS有限元软件建立了四种复合材料圆柱壳体的有限元模型，分析其在受到轴向压缩载荷作用下的屈曲特性，从而得到各个复合材料圆柱壳体的1到10阶特征屈曲载荷。与试验结果对比，发现含有不同初始缺陷的复合材料圆柱壳体试验件在轴向压缩载荷作用下，其破坏屈曲载荷数值在第4阶与第5阶特征屈曲载荷之间，进而得出了该复合材料圆柱壳体在轴向压缩载荷作用下的破坏屈曲载荷判断区间。
四、基于ANSYS有限元分别计算各圆柱壳体特征屈曲载荷，并计算复合材料圆柱壳体铺层角度的变化对轴向压缩载荷的影响。得出了在四种不同初始损伤的复合材料圆柱壳体屈曲特性；铺层角度与特征屈曲载荷之间的关系曲线。给出了四种复合材料圆柱壳体的最优铺层角度，从而提升了在轴向压缩载荷下的屈曲强度。
五、为了对矩形开口的复合材料圆柱壳体进行补强，在壳体上加装复合材料口盖，设计复合材料口盖的铺层角度和铺层厚度，提出了一种在受轴向压缩载荷时，稳定性高而且又经济的口盖设计方案。综合考虑复合材料加强口盖的优化铺层方式、铺层厚度和不含口盖的复合材料圆柱壳结构的优化铺层方式，提出了一种含矩形口盖的复合材料圆柱壳体结构优化设计方法。经过优化设计后的舱段结构的屈曲强度与完整的柱壳结构基本相当，反映出经优化设计后的飞行器舱段得到了有效的修补和增强，满足了等强度设计和维修使用要求。
本项研究已经用于飞行器结构设备舱段设计，具有重要的工程意义和实用价值。
Aircraft in flight process was under bothr axial compression load and inertial load caused byits own weight. axial compression failure was the main form of damage, when the projectilecomposite cylindrical shell structure by compression load reached a certain critical value balanceleading to structural instability or buckling and unable to ensure the normal flight.
Taking projectile bodies structure as an example, the paper adopted the combination ofexperimental study and numerical analysis method. Same-size ratio test objects were studiedusing damage destructive tests and numeric analysis method. Four cylindrical shells’ strength andbuckling characteristics under axial compression load were researched with different types ofinitial defects. Critical buckling load was computed by classical theory about orthogonality ply ofcomposite cylindrical shell. On the basis of research above, finite element analysis was performedabout buckling characteristics of different ply and strengthened covering cap. Optimal designabout the reliability of aircraft body under axis compression load was brought forward, which wasable to ensure the reliability and security of cylindrical shells. The result has great importantengineering application value.
The main research included are as following：
Four same-size ratio cylindrical shells with different type of initial defects were developedaccording to the prototype of certain type aircraft and axis compression destructive tests werecarried out. The experimental data was acquainted and strain changes were visually monitored bymulti-channel data acquisition experiment.
Through numerical analysis of test data, it was indicated that four cylindrical shells withdifferent type of initial defects under axis compression destructive tests were destroyed in thesame way-compression buckling damage. According to the test data, load-strain curve,time-strain curve and displacement-strain curve, it had come to conclusion as following:
1. For complete composite cylindrical shell structure, its’ destructive form was bucklingdamage and the middle part deformed obviously. When structure damaging, interlamination wasdestroyed seriously.
2. Nonlinearity buckling deformation appeared during destructive test of compositecylindrical shell with oval-shaped open. When axis load equal to136kN，it had local failure butstill with certain carrying capacity. When axis load equal to144kN, it had been destroyed completely. Structure damage mostly appeared at the right of oval-shaped open, crack extended tothe rear at circumference directions. Stress concentration position was consistent with finiteelement analysis results.
3. Complexity buckling deformation occurred for composite cylindrical shell with initialcrack under axis compression load When axis load equal to315kN, it was destroyed locally.When axis compression load between320kN and330kN，local damage was in succession andwhen axis load reached338kN，it was damaged completely. Final damage crack appeared at theleft to initial crack and indent damage appeared. Deformation at the right to initial crack wasrelatively complex, it was convex at the upper and lower position in the middle part of cylindricalshell, while indent damaged appeared in the middle part.
4. Composite cylindrical shell was damaged under360kN axis low-velocity impact load. Inthe process of axis compression, there was no nonlinear buckling deformation drasticallyappeared and it had been damaged in broken compression.
5. In destructive tests, all test objects’ buckling deformation appeared in the middle positionmostly, both ends of test objects’ appeared with linear elasticity. The complete and the impacteddefects cylindrical shells had less buckling deformation, meanwhile nonlinear deformation waslarger for cylindrical shell with initial crack and oval-shaped hole. The result indicated cylindricalshell with more damage under axis compression load had poor reliability.
Finite element models were developed for four composite cylindrical shells with ANSYSsoftware. Buckling characteristics of each were analyzed under axis compression load with theresult of1to10order eigenvalue buckling loads. After compared with test results, it came toconclusion that damaged buckling load was between4and5order eigenvalue buckling loads forcomposite cylindrical shells under axis compression load.
Characteristic buckling load was computed by ANSYS for different cylindrical shellsindependently, and changes of ply angle’ influence on buckling characteristics considered.Buckling characteristic of four cylindrical shells with different initial defects were achieved andply angle-characteristic buckling load curve were captured too. Optimized ply angles were givento improve buckling strength for different cylindrical shells.
Aimed to enhance composite cylindrical shell with rectangle open, ply angle and thick ofcomposite covering cap was designed. An optimized design plan was put forward under axiscompression load, which had higher reliability and economic. Optimized design method forcomposite cylindrical shells with rectangle covering cap was found considering many factors, including best ply way, thickness of cylindrical shell with enhanced covering cap and withoutcovering cap. Aircraft body structure’s strength was equal to the whole cylindrical shells afteroptimized design, which meet the needs of equal-strength design and maintenance.
The research results had been applied to a certain type of aircraft equipment cabin structuredesign successfully, and will have important engineering significance and practical value infuture.
引文
[1]曾竟成,罗青,唐羽章.复合材料理化性能［M］.合肥:国防科技大学出版社,1998.
[2] Peter Morgan.Carbon Fibers and their Composites.New York: Taylor&Franicis Group,2005.
[3] D.Perreux， P.Robinet and D.Chapelle， Composites Part A: Applied Science andManufacturing，2006，37(4):630-635.
[4]何东晓.先进复合材料在航空航天的应用综述［J］.高科技纤维与应用,2006.
[5]廖灵洪,隆小庆.先进客机与复合材料［J］.中国民用航空,2006
[6]管德，郦正能.飞机结构强度.[M].北京，北京航空航天大学出版社，2005.
[7]赵景丽.蜂窝夹层结构复合材料的性能研究［D］.西北工业大学，2002
[8] Weiming Chen， Yunhua Yu， Peng Li，Chengzhong Wang， Tongyue Zhou, XiaopingYang.Effect of new epoxy matrix for T800carbon fiber/epoxy filament wound composites［J］.Composites Science and Technology，2007，67(9):2261-2270.
[9] P.Mertiny，F.Ellyin.Influence of the filament winding tension on physical and mechanicalproperties of reinforced composites［J］.Composites Part A: Applied Science andManufacturing，2002，33(12):16151622.
[10] Zbigniew Kolakowski, Tomasz Kubiak.Interactive dynamic buckling of orthotropicthinwalled channels subjected toinplane pulse loading［J］.Composite Structures,2007，（81）：222-232.
[11] R.M.Jones and H. S. Morgan.Analysis of Nonlinear StressStrain Behavior ofFiberR einforced Composite Materials［J］.AIAAJournal，1977.
[12] R.S.Sandhu.Nonlinear Behavior of unidirectional and Angle ply Laminate［J］.JournalAircraft,1976.
[13] R.M.Jones and A. R Dudley.Material Models for Nonlinear Deformation of Graphite［J］AIAAJournal，1976.
[14]黄根来,孙志杰,王明超.玄武岩纤维及其复合材料基本力学性能实验研究［J］.玻璃钢/复合材料,2006，(1):24-27.
[15]王瑁成，邵敏．有限单元法基本原理和数值方法［M］．北京：清华大学出版社，1996。
[16]陈平，蹇锡高，陈辉，高巨龙，朱兴松，韩冰.碳纤维复合材料发动机壳体用韧性环氧树脂基体的研究［J］.复合材料学报，2002，19(2)：24-27.
[17] J.N.Craddock, A. R. Zak and J. N. Majerus, Nonlinear Response of Composite MaterialStructures［J］.Journal of Composite Materials，1977，（11)：204-221.
[18]刘锡礼，王秉权．复合材料力学基础［M］．北京：中国建筑工业出版社,1984.
[19]沈观林,胡更开.复合材料力学［M］.北京：清华大学出版社,2006.
[20] S.Y. Lee, S.C..Wooh Finite element vibration analysis of composite box structuresusing the high order plate theory［J］.Journal of Sound and Vibration，2004，（277）：801-814.
[21]复合材料力学R.M.琼斯［美］著，朱颐龄译校［M］.上海:上海科学技术出版社，1981：42-44.
[22] R.M.Jones.Modeling Nonlinear Deformation of CarbonCarbon Composite Materials［J］.AIAAJournal，1980，18（8)：995-1001.
[23]王晓洁，张炜，刘炳禹等.高性能碳纤维复合材料耐压容器研究进展［J］.宇航材料工艺，2003，33(4)：20-23.
[24]张学富等.考虑剪滞剪切效应的复合材料薄壁箱型梁梁单元［J］.工程力学,2003.
[25]曹志远,杨升田.厚板动力学理论及其应用［M］.北京：科学出版社，1983.
[26]王震鸣.复合材料力学和复合材料结构力学[M].北京，机械工业出版社，1991
[27]杨乃宾，章怡宁.复合材料飞机结构设计[M].北京，航空工业出版社，2002
[28]萨林斯等著，薛克兴，扬汉祥译.夹层板和壳结构稳定性分析手册[M].北京：国防工业出版社，1976
[29] Liviu Librescu，Terry Hause.Recent developments in the modeling and behavior ofadvanced sandwich constructions：a survey[J].Composite Structure，2000,48:1-17.
[30] Guedra-Degeorges D.Recent advances to assess mono-and multi-delaminations behavior ofaerospace composites[J].Composites Science and Technology，2006,66:796-806.
[31] Kim Jang-Kyo.Yu Tong-Xi.Forming and failure behavior of coated，laminated andsandwich sheet metals：a review[J].Journal of Material Processing Technology，1997,63:33-42.
[32]范家让著.强厚度叠层板壳的精确理论[M].北京：科学出版社1996.
[33] Fan jiarang，Ye Jianqiao. An exact solution for the static and dynamics of Laminated thickplates with orthotropic layers[J].Int.J.Solids Structures，1990,26（5/6），655-662.
[34] Fan jiarang，Ye Jianqiao. Exact solution of buckling for simply support thick laminates[J].Composite Structures，199324:23-28
[35]陈绍杰，复合材料设计手册[M].北京：航空工业出版社，1990
[36]范家让，盛宏玉.任意厚度叠层板的变分解[J]安徽建筑工业学院学报（自然科学版）1997,5（3）：6-12.
[37]邹贵平，唐立民.层合双曲率厚度的状态方程及其半解析解[J].航空学报1994,15（12）：1424-1432
[38] Holt P.J.，Webber J.P.H. Exact solutions to some honeycomb sandwich beam，plate andshell problems[J].Journal of strain analysis.1982,17:1-18.
[39]刘人怀.夹层圆板的非线性弯曲[J].应用数学和力学，1981,2（2）：173-190.
[40]徐家初，王乘，刘人怀.变厚度夹层环形板的非线性弯曲[J].工程力学.2001,18（4）：28-37.
[41]刘人怀，成振强.简支夹层矩形板的非线性弯曲[J].应用数学与力学.1993,14（3）：203-218.
[42]刘人怀.在边缘力矩作用下夹层圆板的非线性轴对称弯曲问题[J].中国科学技术大学学报，1980,10（2）：56-57.
[43]徐家初，王乘，刘人怀.一般夹层旋转壳在轴对称变形下的大扰度方程[J].力学季刊.2000,21（1）：21-26.
[44]徐家初，王乘，刘人怀.具有不同表层夹层扁锥壳的非线性稳定性问题[J].华中理工大学学报.1999,1（27）：1-3.
[45]徐家初，王乘，刘人怀.变厚度夹层截顶扁锥壳的非线性稳定性分析[J].应用数学和力学，2000,21（9）：881-889.
[46]叶开沅，刘人怀.圆底扁球壳在均匀线布载荷作用下的非线性稳定性分析[J].科学通报，1965，（2）：142-145.
[47]王志伟，刘人怀.复合材料面层夹层扁壳非线性精化理论及应用[J].应用力学学报，2000,17（4）：86-93.
[48]王璠，刘人怀.复合材料层合开顶扁球壳的非线性动态屈曲[J].固体力学学报.2001,22（3）：309-314.
[49]陈浩然，白瑞祥.含损伤复合材料夹层板剩余压缩强度数值分析[J].大连理工大学学报，2001,41（4）：405-411.
[50] Kassapoglous C.，Jones P.L.，Abbott R..Compressive strength of composite sandwich panelafter impact damage：an experimental and analytical study[J].J composites Tech Res，1988,10:65-73
[51] Kassapoglous C.，Abbott R. A correlation parameter for predicting the compressivestrength of composite sandwich panels after low speed impact[J].AIAA-88-2294,1988
[52]寇长河，程小全，郦正能.复合材料蜂窝夹芯板低速冲击后压缩强度估算[J].北京航空航天大学学报，1998,24（5）：555-558.
[53] Lin C.C.，Cheng S.H.，Wang J.T.S..Local buckling of delaminated of composite sandwichplates[J]. J ofAIAA，1996,34（10）：2176-2183.
[54] Cheng S.H.，Lin C.C.，Wang J.T.S.. Local buckling of delaminated sandwich beams usingcontinues analysis[J].International Journal of Solids and Structures，1997,34（2）：275-288.
[55]白瑞祥，陈浩然，高鹏.含损伤复合材料夹层板非线性热屈曲分析[J].复合材料的现状与发展：第十一届全国复合材料会议论文集，2000:724-728.
[56]白瑞祥，陈浩然.含界面开裂损伤的复合材料夹层板线性和非线性热-机械力屈曲性态研究[J].工程力学（增刊），2000:383-388.
[57]白瑞祥，陈浩然，含界面脱粘及表板基体开裂损伤的复合材料夹层板非线性稳定性的研究[J].复合材料学报，2002,18（2）：80-84
[58]陈浩然，白瑞祥.含损伤复合材料夹层板剩余压缩强度数值分析[J].大连理工大学学报，2001,41（4）：405-411.
[59] Chai H.，Babcock C.D.，Knayss W.G. One dimensional modeling of failure laminated platesby delamination buckling[J].Solids and Structure，1981,17（11）：1069-1083.
[60] Vizzini A.J.,Lagace P.A..The buckling of a delaminating sublaminate on an elasticfoundation[J].Composite Materials，1987,21（12）：1106-1117.
[61]徐永峰，张志民，王俊奎.复合材料夹层板面芯二维分层研究[J].复合材料学报.1997,14（4）：101-107
[62]王星，董石麟.板锥网壳结构的拟三层壳分析法［J］.建筑结构学报，2001，22(6)：4348.
[63]王勖成，邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社，1997:1
[64] Bellman R.，Casti J..Differential quardarature and long term integration[J].Journal ofMathematical AnalysisApplications，1971,34:235-238.
[65] Bellman R.E., Kashef B.G.，Casti J..Differential quadrature：a technique for the rapidsolution of nonlinear partial differential equations[J].Journal of computational Physics，1972,10:40-52.
[66] Civan F., Sliepcevich C.M..Application of differential quadrature to transport process[J].JMathAnal，1983,93:206-210.
[67] Bert C.W.,Jang S.K.,Striz A.G..Two new approximate methods for analyzing free vibrationof structural components[J].American Institute of Aeronautics and Astronauts Journal，1988,26:612-618.
[68] Bert C.W.,Malik M..Differential quadrature method in computational mechanics：areview[J].Appl Mech Rev,1996,49:1-27.
[69] Shu C..differential quadrature and its application in engineering[M].Springer, Berlin，2000
[70] Jang S.K.,Bert C.W.,Striz A.G..Application of differential quadrature method to deflectionand buckling of structure components[J].International Journal for Numerical Methods inEngineering，1989,28:561-577.
[71] Karami G.,Malekzadeh P..A New differential quadrature methodology for beam analysisand the associated differential quadrature element method[J].Comput. MethodAppl.Mech.Engrg.,2002,191:3509-3526
[72] Zong Z..A variable order approach to improve differential quadrature accuracy in dynamicanalysis[J].Journal of sound and vibration，2003,266:307-323.
[73] Zhang L.,Xiang Y.,Wei G W..Local adaptive differential quadrature for free vibrationanalysis of cylindrical shells with various boundary conditions[J].International Journal ofMechanical Science，2006,48:1126-1138.
[74] Wang Y., Zhao Y.B., Wei G.W.. A Note on the numerical solution of high-order dimerentialequations [J]. Journal of Computational andApplied Mathematics，2003,159:387-398.
[75] Sherbourne A.N., Pandey M.D..Differential method in the buckling analysis of beams andcomposite plates[J].Comp. and Struck，1991,40（4）：903-913.
[76] Wang X.，Striz A. G, Bert C. W. Buckling and vibration analysis of skew plates by the DQmethod[J]. AIAAJ.1994,32(4)：866-889.
[77] Bert C.W., Wang X., Striz A.G. New development in differential quadrature analysis ofelements[J].the29th Annual Technical Society of Engineering Science，La Jolla，CA，USA，1992:14-16.
[78] Shu C., Du H..Implementation of clamped and simply support boundary conditions in theGDQ free vibration analysis of beams and plates[J].Int.J. Solids Struct.1997,34（7）：819-835.
[79] T.C.Fung Stability and accuracy of differential quadrature method in solving dynamicproblems[J].Comput. Methods Appl. Mech Engrg.,2002,191:1311-1331.
[80] Omer Civalek. Harmonic differential quadrature-finite difference coupled approaches forgeometrically nonlinear static and dynamic analysis of rectangular plates on elasticfoundation [J].Journal of Sound and Vibration，2006,294:966-980.
[81] Omer Civalek，Dokuz Eylul，Application of differential quadrature（DQ）and harmonicdifferential quadrature（HDQ）for buckling analysis of thin isotonic plates and elasticcolumns[J].Engineering Structures，2004,26:171-186.
[82] Jinquan Cheng., Biao Wang., ShanYi Du. A theoretical analysis of piezoelectric/compositelaminate with larger-amplitude deflection effect，Part II：Hermite differential quadraturemethod and application[J].International Journal of Solids and Structures，2005,42:6181-6201.
[83] Liew K.M.,Huang Y.Q.,Reddy J.N..Moving least Squares Differential quadrature methodand its application to the analysis of shear deformable plates [J]. Int J Num Meth Eng，2003,56:2331-51.
[84] Liew K.M.,Huang Y.Q.,Reddy J.N..A hybrid moving least squares and differentialquadrature meshfree method[J]. Int J Comput Eng Sci,2002,3:1-12.
[85] Liew K.M.,Huang Y.Q.,Reddy J.N..Analysis of general shaped thin plates by the movingleast-squares differential quadrature method [J].Finite Elements in Analysis and Design，2004,40:1453-1474.
[86] Liew K.M.,Huang Y.Q.，Bending and buckling of thick symmetric rectangular laminatesusing the moving least-squares differential quadrature method[J].International Journal ofMechanical Science，2003,45:95-114.
[87] AD779927, R. S. Sandhu.Ultimate StrengthAnalysis of Symmetric Laminates,1974.
[88] Caprino，G. On the Prediction of Residual Strength for Notched Laminates. Journal ofMaterials Science，1983,18:2269.
[89] Caprino，G. Residual Strength Prediction of Impacted CFRP Laminates. Journal ofComposite Materials1984,18:508-518.
[90]郑海燕，刘元镛，郭伟国.编织型复合材料的冲击及冲击后压缩强度的实验研究.航空材料学报，2002,22（3）：33-37.
[91] Jang-Kyo， K.M. Impact and Delamination Failure of Woven-fabric Composites.Composites Science and Technology，2000,60(5):745-761.
[92] De Moura MFSF and Goncalves JPM，Marques AT，Castro PMST. Modeling compressionfailure after low velocity impact on laminated composites using interface elements. Journalof composite Materials，1997,31:1462-1479.
[93] De Moura MFSF and Goncalves JPM. Modeling the interaction between matrix crackingand Delamination in carbon-epoxy laminates under low velocity impact. CompositesScience and Technology，2004,64:1021-1027.
[94] Milan,M.,Hahn,H.T.,Greg,P.C.，et al. Effect of loading parameters on the fatigue behaviorof impact damaged composite laminates. Composites Science and Technology，1999,59（14）：2059-2078.
[95] Choi，H.Y.Chang，F.K. A model for predicting damage in graphite/epoxy laminatedcomposites resulting from low-velocity point impact.Journal of Composite Materials，1992,26:2134-2169.
[96] Melin，L.G.，et al Buckling behavior and delamination growth in impacted compositespecimens under fatigue load：an experimental study.Composites Science and Technology，2001,61（13）：1841-1852.
[97]孙慧玉,吴长春,卞恩荣.三维编织复合材料面内刚度和强度性能研究[J].复合材料学报.1998,15(4):102~106.
[98]杨振宇,卢子兴等.三维四向编织复合材料力学性能的有限元分析[J].复合材料学报，2005.22(5).155~161.
[99]孙先念，陈浩然，苏长健，刘相斌.含分层损伤复合材料层合板分层扩展研究.力学学报，2000,32（2）：223-232
[100]吴金松，薛量束，永平，张建武.复合材料剪切圆柱壳在轴压下的屈曲与后屈曲[J].华东船舶工业学院学报.1999,3:125-135
[101]沈惠申.湿热环境中复合材料层合圆柱薄壳的屈曲和后屈曲[J].应用数学和力学.2001,5:38-43
[102]彭伟斌，朱森元.大挠度高阶剪切理论下复合材料圆柱壳的屈曲[J].导弹与航天运载技术.2001,5:76-80
[103] The behavior of damage tolerance hat-stiffened composite panels loaded in uniaxialcompression[J].Composite：Part A32(2001)1255-1262
[104]李道奎，周建平.含环向贯穿脱层的轴压圆柱层壳屈曲分析Ⅱ─本方程与定解条件复合材料学报[J].复合材料学报.2002,14(2):88-93
[105]王毅，罗永峰，沈惠申.各向异性复合材料圆柱薄壳轴压下的屈曲性能[J].同济大学学报.2002,11(4):99-104
[106] P.M. Weaver, J.R. Driesen, P. Roberts. Anisotropic effects in the compression bucklingoflaminated composite cylindrical shells[J].Composites Science and Technology62(2002):91–105
[107]何煌，唐国金，蒋志刚，王可晟.编织复合材料圆柱壳的蠕变屈曲分析[J].重庆交通学院学报.2003,3:82-87
[108]王珂晟，刘国强，朱晓莹.含初始缺陷的加强复合材料圆柱壳的非线性屈曲分析[J]《.机械设计与制造》.2003,6：90-94
[109] S. Büsing. Stress analysis and strength prediction of mechanically fastened joints in FRP: areview[J]. Composites: PartA.34(2003):38-45
[110]杨娜,沈世钊.板壳结构屈曲分析的非线性有限元法[J].哈尔滨工业大学学报.2003.
[111] Azam Tafreshi. Buckling and post-buckling analysis of composite cylindrical shell withcutouts subject to internal pressure and axial compression loads[J] Interntional Journal ofPressure Vessel and Piping79（2002）：351-359
[112]赵阳,金锋.轴压作用下矩形开口圆柱壳的稳定性[J].工程设计学报.2004,7:77-83
[113]何录武，冯春本.复合材料层合圆柱壳的有限元分析[J].力学季刊.2004,3:55-62
[114]王珂晟,朱晓莹,曹凤利.含加强肋(环)的非完善复合材料圆柱壳的稳定性分析[J]机械设计.2004,3:102-106
[115]杨金花，傅衣铭.具脱层复合材料层合圆柱壳的屈曲分析[J].湖南大学学报(自然科学版).2005,5:22-29
[116] Ji-Ho Kang, Chun-Gon Kim.Minimum-weight design of compressively loaded compositeplates and stiffened panels for postbuckling strength by genetic algorithm[J]. CompositeStructures69(2005)239–246
[117] Marco Cerini,Brian G. Falzon. Use of Arc-Length method for capturing mode jumping inpostbuckling aerostructures[J].AIAA JOUR NALVol.43, No.3, March (2005)239–246
[118] S.A.M. Ghannadpour, A. Najafi, B. Mohammadi. On the buckling behavior of cross-plylaminated composite plates due to circular/elliptical cutouts[J]. Aerospace EngineeringDepartment, Amirkabir University of Technology, Tehran, Iran Available online16June(2006)156-165
[119]左惟炜、肖来元、廖道训.三维编织复合材料高压储气瓶的屈曲分析与优化设计[J]中国机械工程.2007,16(3)77-83
[120]李志敏.三维编织复合材料圆柱壳轴压下的屈曲分析[J].强度与环境.2007.23(3)83-89
[121]王爱军，王鑫伟，陆浦.圆柱壳板非线性屈曲的分叉解[J].南京航空航天大学学报，2008,4:111-116
[122]张志峰，陈浩然，白瑞祥.先进复合材料格栅加筋圆柱壳体稳定性分析[J].大连理工大学学报，2008,3:88-93
[123] Xinsheng Xu, Jianqing Ma, C.W. Limb, Hongjie Chu. Dynamic local and global bucklingof cylindrical shells under axial impact [J].Engineering Structures31(2009)111140
[124]霍世慧，王富生，岳珠峰.压缩载荷作用下复合材料开孔补强稳定性分析[J].应用力学学报，2009,15(2):56-62
[125]王蔓，白瑞祥，杨继新.碳纤维增强聚合物基复合材料修补空心柱体结构的屈曲分析[J].大连工业大学学报，2010,12(3):44-48
[126]王振，孙秦基.复合材料机翼整体油箱结构分析与设计[J].科学技术与工程，2010,5:69-74
[127]李钟海，程小全，杨琨等.复合材料柱面壳压缩性能分析[J].复合材料学报,2011,28(1):206-210
[128]李钟海，程小全，张纪奎.开口复合材料柱壳屈曲与补救有限元分析[J].应用力学学报,2011
[129]丁皓江.弹性力学和塑性有限元分析法［M］.北京：机械工业出版社，1989
[130]彭超义，曾竟成．缠绕管件轴压下径向形变和破坏模式的有限元分析与验证［J］．玻璃钢/复合材料，2005，（2）：7-8.
[131]陈浩然.非线性多模量复合材料的增量应力和增量应变关系［C］.中国力学学会“复合材料力学专题讨论会”，1984.
[132]陈烈民，杨宝宁.复合材料的力学分析［M］.北京：中国科学技术出版社，2006：1-3.
[133] NASA CR2313.Nonl inear Behavior of Fiber［J］.Composite Laminates,1974.
[134] SADAO AMIJIMA AND TSONDYOKI ADACH.Nonlinear StressSt min Response ofLaminate Composites［J］.Journal of Composite Materials，1979,(13):206-218.
[135]陈烈民，杨宝宁，复合材料的力学性能分析[M].北京，中国科学技术出版社，2006
[2] Peter Morgan.Carbon Fibers and their Composites.New York: Taylor&Franicis Group,2005.
[3] D.Perreux， P.Robinet and D.Chapelle， Composites Part A: Applied Science andManufacturing，2006，37(4):630-635.
[4]何东晓.先进复合材料在航空航天的应用综述［J］.高科技纤维与应用,2006.
[5]廖灵洪,隆小庆.先进客机与复合材料［J］.中国民用航空,2006
[6]管德，郦正能.飞机结构强度.[M].北京，北京航空航天大学出版社，2005.
[7]赵景丽.蜂窝夹层结构复合材料的性能研究［D］.西北工业大学，2002
[8] Weiming Chen， Yunhua Yu， Peng Li，Chengzhong Wang， Tongyue Zhou, XiaopingYang.Effect of new epoxy matrix for T800carbon fiber/epoxy filament wound composites［J］.Composites Science and Technology，2007，67(9):2261-2270.
[9] P.Mertiny，F.Ellyin.Influence of the filament winding tension on physical and mechanicalproperties of reinforced composites［J］.Composites Part A: Applied Science andManufacturing，2002，33(12):16151622.
[10] Zbigniew Kolakowski, Tomasz Kubiak.Interactive dynamic buckling of orthotropicthinwalled channels subjected toinplane pulse loading［J］.Composite Structures,2007，（81）：222-232.
[11] R.M.Jones and H. S. Morgan.Analysis of Nonlinear StressStrain Behavior ofFiberR einforced Composite Materials［J］.AIAAJournal，1977.
[12] R.S.Sandhu.Nonlinear Behavior of unidirectional and Angle ply Laminate［J］.JournalAircraft,1976.
[13] R.M.Jones and A. R Dudley.Material Models for Nonlinear Deformation of Graphite［J］AIAAJournal，1976.
[14]黄根来,孙志杰,王明超.玄武岩纤维及其复合材料基本力学性能实验研究［J］.玻璃钢/复合材料,2006，(1):24-27.
[15]王瑁成，邵敏．有限单元法基本原理和数值方法［M］．北京：清华大学出版社，1996。
[16]陈平，蹇锡高，陈辉，高巨龙，朱兴松，韩冰.碳纤维复合材料发动机壳体用韧性环氧树脂基体的研究［J］.复合材料学报，2002，19(2)：24-27.
[17] J.N.Craddock, A. R. Zak and J. N. Majerus, Nonlinear Response of Composite MaterialStructures［J］.Journal of Composite Materials，1977，（11)：204-221.
[18]刘锡礼，王秉权．复合材料力学基础［M］．北京：中国建筑工业出版社,1984.
[19]沈观林,胡更开.复合材料力学［M］.北京：清华大学出版社,2006.
[20] S.Y. Lee, S.C..Wooh Finite element vibration analysis of composite box structuresusing the high order plate theory［J］.Journal of Sound and Vibration，2004，（277）：801-814.
[21]复合材料力学R.M.琼斯［美］著，朱颐龄译校［M］.上海:上海科学技术出版社，1981：42-44.
[22] R.M.Jones.Modeling Nonlinear Deformation of CarbonCarbon Composite Materials［J］.AIAAJournal，1980，18（8)：995-1001.
[23]王晓洁，张炜，刘炳禹等.高性能碳纤维复合材料耐压容器研究进展［J］.宇航材料工艺，2003，33(4)：20-23.
[24]张学富等.考虑剪滞剪切效应的复合材料薄壁箱型梁梁单元［J］.工程力学,2003.
[25]曹志远,杨升田.厚板动力学理论及其应用［M］.北京：科学出版社，1983.
[26]王震鸣.复合材料力学和复合材料结构力学[M].北京，机械工业出版社，1991
[27]杨乃宾，章怡宁.复合材料飞机结构设计[M].北京，航空工业出版社，2002
[28]萨林斯等著，薛克兴，扬汉祥译.夹层板和壳结构稳定性分析手册[M].北京：国防工业出版社，1976
[29] Liviu Librescu，Terry Hause.Recent developments in the modeling and behavior ofadvanced sandwich constructions：a survey[J].Composite Structure，2000,48:1-17.
[30] Guedra-Degeorges D.Recent advances to assess mono-and multi-delaminations behavior ofaerospace composites[J].Composites Science and Technology，2006,66:796-806.
[31] Kim Jang-Kyo.Yu Tong-Xi.Forming and failure behavior of coated，laminated andsandwich sheet metals：a review[J].Journal of Material Processing Technology，1997,63:33-42.
[32]范家让著.强厚度叠层板壳的精确理论[M].北京：科学出版社1996.
[33] Fan jiarang，Ye Jianqiao. An exact solution for the static and dynamics of Laminated thickplates with orthotropic layers[J].Int.J.Solids Structures，1990,26（5/6），655-662.
[34] Fan jiarang，Ye Jianqiao. Exact solution of buckling for simply support thick laminates[J].Composite Structures，199324:23-28
[35]陈绍杰，复合材料设计手册[M].北京：航空工业出版社，1990
[36]范家让，盛宏玉.任意厚度叠层板的变分解[J]安徽建筑工业学院学报（自然科学版）1997,5（3）：6-12.
[37]邹贵平，唐立民.层合双曲率厚度的状态方程及其半解析解[J].航空学报1994,15（12）：1424-1432
[38] Holt P.J.，Webber J.P.H. Exact solutions to some honeycomb sandwich beam，plate andshell problems[J].Journal of strain analysis.1982,17:1-18.
[39]刘人怀.夹层圆板的非线性弯曲[J].应用数学和力学，1981,2（2）：173-190.
[40]徐家初，王乘，刘人怀.变厚度夹层环形板的非线性弯曲[J].工程力学.2001,18（4）：28-37.
[41]刘人怀，成振强.简支夹层矩形板的非线性弯曲[J].应用数学与力学.1993,14（3）：203-218.
[42]刘人怀.在边缘力矩作用下夹层圆板的非线性轴对称弯曲问题[J].中国科学技术大学学报，1980,10（2）：56-57.
[43]徐家初，王乘，刘人怀.一般夹层旋转壳在轴对称变形下的大扰度方程[J].力学季刊.2000,21（1）：21-26.
[44]徐家初，王乘，刘人怀.具有不同表层夹层扁锥壳的非线性稳定性问题[J].华中理工大学学报.1999,1（27）：1-3.
[45]徐家初，王乘，刘人怀.变厚度夹层截顶扁锥壳的非线性稳定性分析[J].应用数学和力学，2000,21（9）：881-889.
[46]叶开沅，刘人怀.圆底扁球壳在均匀线布载荷作用下的非线性稳定性分析[J].科学通报，1965，（2）：142-145.
[47]王志伟，刘人怀.复合材料面层夹层扁壳非线性精化理论及应用[J].应用力学学报，2000,17（4）：86-93.
[48]王璠，刘人怀.复合材料层合开顶扁球壳的非线性动态屈曲[J].固体力学学报.2001,22（3）：309-314.
[49]陈浩然，白瑞祥.含损伤复合材料夹层板剩余压缩强度数值分析[J].大连理工大学学报，2001,41（4）：405-411.
[50] Kassapoglous C.，Jones P.L.，Abbott R..Compressive strength of composite sandwich panelafter impact damage：an experimental and analytical study[J].J composites Tech Res，1988,10:65-73
[51] Kassapoglous C.，Abbott R. A correlation parameter for predicting the compressivestrength of composite sandwich panels after low speed impact[J].AIAA-88-2294,1988
[52]寇长河，程小全，郦正能.复合材料蜂窝夹芯板低速冲击后压缩强度估算[J].北京航空航天大学学报，1998,24（5）：555-558.
[53] Lin C.C.，Cheng S.H.，Wang J.T.S..Local buckling of delaminated of composite sandwichplates[J]. J ofAIAA，1996,34（10）：2176-2183.
[54] Cheng S.H.，Lin C.C.，Wang J.T.S.. Local buckling of delaminated sandwich beams usingcontinues analysis[J].International Journal of Solids and Structures，1997,34（2）：275-288.
[55]白瑞祥，陈浩然，高鹏.含损伤复合材料夹层板非线性热屈曲分析[J].复合材料的现状与发展：第十一届全国复合材料会议论文集，2000:724-728.
[56]白瑞祥，陈浩然.含界面开裂损伤的复合材料夹层板线性和非线性热-机械力屈曲性态研究[J].工程力学（增刊），2000:383-388.
[57]白瑞祥，陈浩然，含界面脱粘及表板基体开裂损伤的复合材料夹层板非线性稳定性的研究[J].复合材料学报，2002,18（2）：80-84
[58]陈浩然，白瑞祥.含损伤复合材料夹层板剩余压缩强度数值分析[J].大连理工大学学报，2001,41（4）：405-411.
[59] Chai H.，Babcock C.D.，Knayss W.G. One dimensional modeling of failure laminated platesby delamination buckling[J].Solids and Structure，1981,17（11）：1069-1083.
[60] Vizzini A.J.,Lagace P.A..The buckling of a delaminating sublaminate on an elasticfoundation[J].Composite Materials，1987,21（12）：1106-1117.
[61]徐永峰，张志民，王俊奎.复合材料夹层板面芯二维分层研究[J].复合材料学报.1997,14（4）：101-107
[62]王星，董石麟.板锥网壳结构的拟三层壳分析法［J］.建筑结构学报，2001，22(6)：4348.
[63]王勖成，邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社，1997:1
[64] Bellman R.，Casti J..Differential quardarature and long term integration[J].Journal ofMathematical AnalysisApplications，1971,34:235-238.
[65] Bellman R.E., Kashef B.G.，Casti J..Differential quadrature：a technique for the rapidsolution of nonlinear partial differential equations[J].Journal of computational Physics，1972,10:40-52.
[66] Civan F., Sliepcevich C.M..Application of differential quadrature to transport process[J].JMathAnal，1983,93:206-210.
[67] Bert C.W.,Jang S.K.,Striz A.G..Two new approximate methods for analyzing free vibrationof structural components[J].American Institute of Aeronautics and Astronauts Journal，1988,26:612-618.
[68] Bert C.W.,Malik M..Differential quadrature method in computational mechanics：areview[J].Appl Mech Rev,1996,49:1-27.
[69] Shu C..differential quadrature and its application in engineering[M].Springer, Berlin，2000
[70] Jang S.K.,Bert C.W.,Striz A.G..Application of differential quadrature method to deflectionand buckling of structure components[J].International Journal for Numerical Methods inEngineering，1989,28:561-577.
[71] Karami G.,Malekzadeh P..A New differential quadrature methodology for beam analysisand the associated differential quadrature element method[J].Comput. MethodAppl.Mech.Engrg.,2002,191:3509-3526
[72] Zong Z..A variable order approach to improve differential quadrature accuracy in dynamicanalysis[J].Journal of sound and vibration，2003,266:307-323.
[73] Zhang L.,Xiang Y.,Wei G W..Local adaptive differential quadrature for free vibrationanalysis of cylindrical shells with various boundary conditions[J].International Journal ofMechanical Science，2006,48:1126-1138.
[74] Wang Y., Zhao Y.B., Wei G.W.. A Note on the numerical solution of high-order dimerentialequations [J]. Journal of Computational andApplied Mathematics，2003,159:387-398.
[75] Sherbourne A.N., Pandey M.D..Differential method in the buckling analysis of beams andcomposite plates[J].Comp. and Struck，1991,40（4）：903-913.
[76] Wang X.，Striz A. G, Bert C. W. Buckling and vibration analysis of skew plates by the DQmethod[J]. AIAAJ.1994,32(4)：866-889.
[77] Bert C.W., Wang X., Striz A.G. New development in differential quadrature analysis ofelements[J].the29th Annual Technical Society of Engineering Science，La Jolla，CA，USA，1992:14-16.
[78] Shu C., Du H..Implementation of clamped and simply support boundary conditions in theGDQ free vibration analysis of beams and plates[J].Int.J. Solids Struct.1997,34（7）：819-835.
[79] T.C.Fung Stability and accuracy of differential quadrature method in solving dynamicproblems[J].Comput. Methods Appl. Mech Engrg.,2002,191:1311-1331.
[80] Omer Civalek. Harmonic differential quadrature-finite difference coupled approaches forgeometrically nonlinear static and dynamic analysis of rectangular plates on elasticfoundation [J].Journal of Sound and Vibration，2006,294:966-980.
[81] Omer Civalek，Dokuz Eylul，Application of differential quadrature（DQ）and harmonicdifferential quadrature（HDQ）for buckling analysis of thin isotonic plates and elasticcolumns[J].Engineering Structures，2004,26:171-186.
[82] Jinquan Cheng., Biao Wang., ShanYi Du. A theoretical analysis of piezoelectric/compositelaminate with larger-amplitude deflection effect，Part II：Hermite differential quadraturemethod and application[J].International Journal of Solids and Structures，2005,42:6181-6201.
[83] Liew K.M.,Huang Y.Q.,Reddy J.N..Moving least Squares Differential quadrature methodand its application to the analysis of shear deformable plates [J]. Int J Num Meth Eng，2003,56:2331-51.
[84] Liew K.M.,Huang Y.Q.,Reddy J.N..A hybrid moving least squares and differentialquadrature meshfree method[J]. Int J Comput Eng Sci,2002,3:1-12.
[85] Liew K.M.,Huang Y.Q.,Reddy J.N..Analysis of general shaped thin plates by the movingleast-squares differential quadrature method [J].Finite Elements in Analysis and Design，2004,40:1453-1474.
[86] Liew K.M.,Huang Y.Q.，Bending and buckling of thick symmetric rectangular laminatesusing the moving least-squares differential quadrature method[J].International Journal ofMechanical Science，2003,45:95-114.
[87] AD779927, R. S. Sandhu.Ultimate StrengthAnalysis of Symmetric Laminates,1974.
[88] Caprino，G. On the Prediction of Residual Strength for Notched Laminates. Journal ofMaterials Science，1983,18:2269.
[89] Caprino，G. Residual Strength Prediction of Impacted CFRP Laminates. Journal ofComposite Materials1984,18:508-518.
[90]郑海燕，刘元镛，郭伟国.编织型复合材料的冲击及冲击后压缩强度的实验研究.航空材料学报，2002,22（3）：33-37.
[91] Jang-Kyo， K.M. Impact and Delamination Failure of Woven-fabric Composites.Composites Science and Technology，2000,60(5):745-761.
[92] De Moura MFSF and Goncalves JPM，Marques AT，Castro PMST. Modeling compressionfailure after low velocity impact on laminated composites using interface elements. Journalof composite Materials，1997,31:1462-1479.
[93] De Moura MFSF and Goncalves JPM. Modeling the interaction between matrix crackingand Delamination in carbon-epoxy laminates under low velocity impact. CompositesScience and Technology，2004,64:1021-1027.
[94] Milan,M.,Hahn,H.T.,Greg,P.C.，et al. Effect of loading parameters on the fatigue behaviorof impact damaged composite laminates. Composites Science and Technology，1999,59（14）：2059-2078.
[95] Choi，H.Y.Chang，F.K. A model for predicting damage in graphite/epoxy laminatedcomposites resulting from low-velocity point impact.Journal of Composite Materials，1992,26:2134-2169.
[96] Melin，L.G.，et al Buckling behavior and delamination growth in impacted compositespecimens under fatigue load：an experimental study.Composites Science and Technology，2001,61（13）：1841-1852.
[97]孙慧玉,吴长春,卞恩荣.三维编织复合材料面内刚度和强度性能研究[J].复合材料学报.1998,15(4):102~106.
[98]杨振宇,卢子兴等.三维四向编织复合材料力学性能的有限元分析[J].复合材料学报，2005.22(5).155~161.
[99]孙先念，陈浩然，苏长健，刘相斌.含分层损伤复合材料层合板分层扩展研究.力学学报，2000,32（2）：223-232
[100]吴金松，薛量束，永平，张建武.复合材料剪切圆柱壳在轴压下的屈曲与后屈曲[J].华东船舶工业学院学报.1999,3:125-135
[101]沈惠申.湿热环境中复合材料层合圆柱薄壳的屈曲和后屈曲[J].应用数学和力学.2001,5:38-43
[102]彭伟斌，朱森元.大挠度高阶剪切理论下复合材料圆柱壳的屈曲[J].导弹与航天运载技术.2001,5:76-80
[103] The behavior of damage tolerance hat-stiffened composite panels loaded in uniaxialcompression[J].Composite：Part A32(2001)1255-1262
[104]李道奎，周建平.含环向贯穿脱层的轴压圆柱层壳屈曲分析Ⅱ─本方程与定解条件复合材料学报[J].复合材料学报.2002,14(2):88-93
[105]王毅，罗永峰，沈惠申.各向异性复合材料圆柱薄壳轴压下的屈曲性能[J].同济大学学报.2002,11(4):99-104
[106] P.M. Weaver, J.R. Driesen, P. Roberts. Anisotropic effects in the compression bucklingoflaminated composite cylindrical shells[J].Composites Science and Technology62(2002):91–105
[107]何煌，唐国金，蒋志刚，王可晟.编织复合材料圆柱壳的蠕变屈曲分析[J].重庆交通学院学报.2003,3:82-87
[108]王珂晟，刘国强，朱晓莹.含初始缺陷的加强复合材料圆柱壳的非线性屈曲分析[J]《.机械设计与制造》.2003,6：90-94
[109] S. Büsing. Stress analysis and strength prediction of mechanically fastened joints in FRP: areview[J]. Composites: PartA.34(2003):38-45
[110]杨娜,沈世钊.板壳结构屈曲分析的非线性有限元法[J].哈尔滨工业大学学报.2003.
[111] Azam Tafreshi. Buckling and post-buckling analysis of composite cylindrical shell withcutouts subject to internal pressure and axial compression loads[J] Interntional Journal ofPressure Vessel and Piping79（2002）：351-359
[112]赵阳,金锋.轴压作用下矩形开口圆柱壳的稳定性[J].工程设计学报.2004,7:77-83
[113]何录武，冯春本.复合材料层合圆柱壳的有限元分析[J].力学季刊.2004,3:55-62
[114]王珂晟,朱晓莹,曹凤利.含加强肋(环)的非完善复合材料圆柱壳的稳定性分析[J]机械设计.2004,3:102-106
[115]杨金花，傅衣铭.具脱层复合材料层合圆柱壳的屈曲分析[J].湖南大学学报(自然科学版).2005,5:22-29
[116] Ji-Ho Kang, Chun-Gon Kim.Minimum-weight design of compressively loaded compositeplates and stiffened panels for postbuckling strength by genetic algorithm[J]. CompositeStructures69(2005)239–246
[117] Marco Cerini,Brian G. Falzon. Use of Arc-Length method for capturing mode jumping inpostbuckling aerostructures[J].AIAA JOUR NALVol.43, No.3, March (2005)239–246
[118] S.A.M. Ghannadpour, A. Najafi, B. Mohammadi. On the buckling behavior of cross-plylaminated composite plates due to circular/elliptical cutouts[J]. Aerospace EngineeringDepartment, Amirkabir University of Technology, Tehran, Iran Available online16June(2006)156-165
[119]左惟炜、肖来元、廖道训.三维编织复合材料高压储气瓶的屈曲分析与优化设计[J]中国机械工程.2007,16(3)77-83
[120]李志敏.三维编织复合材料圆柱壳轴压下的屈曲分析[J].强度与环境.2007.23(3)83-89
[121]王爱军，王鑫伟，陆浦.圆柱壳板非线性屈曲的分叉解[J].南京航空航天大学学报，2008,4:111-116
[122]张志峰，陈浩然，白瑞祥.先进复合材料格栅加筋圆柱壳体稳定性分析[J].大连理工大学学报，2008,3:88-93
[123] Xinsheng Xu, Jianqing Ma, C.W. Limb, Hongjie Chu. Dynamic local and global bucklingof cylindrical shells under axial impact [J].Engineering Structures31(2009)111140
[124]霍世慧，王富生，岳珠峰.压缩载荷作用下复合材料开孔补强稳定性分析[J].应用力学学报，2009,15(2):56-62
[125]王蔓，白瑞祥，杨继新.碳纤维增强聚合物基复合材料修补空心柱体结构的屈曲分析[J].大连工业大学学报，2010,12(3):44-48
[126]王振，孙秦基.复合材料机翼整体油箱结构分析与设计[J].科学技术与工程，2010,5:69-74
[127]李钟海，程小全，杨琨等.复合材料柱面壳压缩性能分析[J].复合材料学报,2011,28(1):206-210
[128]李钟海，程小全，张纪奎.开口复合材料柱壳屈曲与补救有限元分析[J].应用力学学报,2011
[129]丁皓江.弹性力学和塑性有限元分析法［M］.北京：机械工业出版社，1989
[130]彭超义，曾竟成．缠绕管件轴压下径向形变和破坏模式的有限元分析与验证［J］．玻璃钢/复合材料，2005，（2）：7-8.
[131]陈浩然.非线性多模量复合材料的增量应力和增量应变关系［C］.中国力学学会“复合材料力学专题讨论会”，1984.
[132]陈烈民，杨宝宁.复合材料的力学分析［M］.北京：中国科学技术出版社，2006：1-3.
[133] NASA CR2313.Nonl inear Behavior of Fiber［J］.Composite Laminates,1974.
[134] SADAO AMIJIMA AND TSONDYOKI ADACH.Nonlinear StressSt min Response ofLaminate Composites［J］.Journal of Composite Materials，1979,(13):206-218.
[135]陈烈民，杨宝宁，复合材料的力学性能分析[M].北京，中国科学技术出版社，2006