船舶与海洋工程中复合材料圆柱壳结构屈曲和后屈曲行为研究
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摘要
纤维增强和编织复合材料是由基体和高性能的纤维材料根据实际需要组合而成的两种复合材料,具有比强度高、比刚度大、易成型、易修补、材料性能可以设计等一系列优点,适宜制造结构复杂的船型,可缩短建造周期,复合材料船艇的维护费用也低于钢船和木船。圆柱壳结构是复合材料实际应用中最为常见的结构形式之一,比如海洋平台的立管、输水输油管道、贮液罐、潜器、高速舰艇的推进器及鱼雷的外壳等等。近几年,无论在复合材料及其结构的设计、制造和应用领域,还是在复合材料及其结构力学问题的理论研究方面,国内外发展迅速,取得很大进展。随着制造工艺的改进,复合材料的各项性能指标不断提高,许多工程结构中的主要受力构件已由复合材料制造,这些结构在使用过程中,有可能受到外部机械载荷的作用发生屈曲而出现承载能力下降甚至破坏的情况,因此复合材料结构的屈曲问题一直受到国内外学者的关注。为了更加深入了解圆柱壳结构的屈曲和后屈曲特性,更好地发挥其在船舶和海洋工程结构中的作用,我们有必要应用边界层理论对中等厚度的纤维增强和编织复合材料剪切圆柱壳的屈曲和后屈曲特性进行研究。
本文的研究工作主要包括:将壳体屈曲的边界层理论推广运用到纤维增强各向异性层合剪切圆柱壳。分析中同时考虑前屈曲非线性变形,后屈曲大挠度和初始几何缺陷的影响以及横向剪切变形和耦合刚度的影响,采用奇异摄动方法给出完全各向异性层合圆柱剪切壳在轴压、外压和扭矩作用下的既满足控制方程又在渐近意义上严格满足边界条件的后屈曲大挠度渐近解。通过对屈曲与后屈曲等一系列问题的求解和分析揭示中等厚度各向异性层合圆柱壳结构在轴压、外压和扭矩作用下的后屈曲行为的规律,为复合材料结构的设计提供科学依据;
根据四步法1×1圆型编织工艺过程中编织纱线的运动轨迹特征和纱线的结构特点,将预成型件分为三个不同的区域,分别定义不同的控制体积单元,识别预成型件的局部单胞模型,分析预成型件的纱线构造,并推导出了编织结构参数之间的关系。编织结构主要的参数包括试件的外形尺寸、主体纱径向层数和周向列数、三个区域各自所占的体积百分比、纱线填充因子(缺省取为常数)、纤维体积含量、编织角以及编织花节长度。在预成型件分析的基础上,导出三维编织复合材料的局部单胞模型,分析复合材料的纱线构造,研究复合材料的编织结构参数之间的关系。从而,建立三维编织预成型件单胞弹性性能关系。采用三维应力-应变分析,在单胞的长度方向积分和平均,在给定的应变边界条件下,采用刚度体积平均的方法计算了单胞的有效弹性性能,预测三维编织结构复合材料的有效弹性模量。在此基础上提出一种三维四向编织复合材料圆柱壳的宏-细观力学模型。
在壳体屈曲的边界层理论框架下,给出了三维编织复合材料圆柱壳在热环境下和在轴压、外压、扭矩及轴压和外压复合加载作用下的大挠度渐近解。分析中同时考虑前屈曲非线性变形,后屈曲大挠度和初始几何缺陷的影响,横向剪切变形的影响,以及材料物性参数对温度变化的依赖性。
基于本文理论分析,用Fortran语言编制了相应的数值分析程序包,在上述研究领域内给出了大量的计算分析结果。
本文得到国家自然科学基金:“混合智能结构非线性行为和动力特性建模与分析”(50375091)的部分支持。
本文研究成果有助于推动纤维增强和三维编织复合材料结构的非线性稳定性的研究,对此两类复合材料结构在船舶和海洋工程中的应用具有积极意义。
Currently there is a wide range of naval structures being developed using fibre-reinforced polymer composites, due to considerable strength-to-weight ratio. There has been considerable attention in the structural instability of relatively thick shells. Many current potential applications involve the moderately thick shell type configuration. For example, large patrol boats, hovercraft, minecountermeasure vessels and corvettes that are built completely of composite material, to mention a few. Other new or potential uses for composites are in the superstructures, advanced mast systems, bulkheads, decks, propellers, propulsion shafts and rudders for large surface combatants such as frigates and destroyers. In submarines, the future applications of composites may include control surfaces and mast systems. Navies are also exploring the feasibility of using composites for internal equipment and fittings, such as machinery, heat exchangers, equipment foundations, values, pumps, pipes and ducts. A new class of composite material known as braided composites have been received considerable attention. Textile composites are manufactured by fabrication methods derived from the textile industry. Unlike laminated composites, in which cracking and debonding may occur at high temperature due to the material property mismatch at the interface of two discrete materials, the textile composites are able to eliminate the delamination due to the inter-lacing of the tows in the through-thickness direction. Braided composites are now developed for general use as structural components in naval ship and submarine, offshore structures due to their light weight and easy handling secure their place in the industry.
As a primary load carrying structure, the buckling and postbuckling behavior of laminated or braided cylindrical shell subjected to mechanical load is a vital safety consideration, and improvement of its prediction accuracy behavior is thus essential for reliable design.
This paper consists of two parts: A boundary layer theory of shell buckling is extended to the case of general shear deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression, external pressure, torsion, respectively. The material properties of each layer of the shell are assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence.
Then, established a micro-macro-mechanical model, a 3D braided composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. A postbuckling analysis is presented for a 3D braided composite cylindrical shell of finite length subjected to axial compression, external pressure, torsion, combined loading of external pressure and axial compression in thermal environments, respectively. The governing equations are based on Reddy's higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling loads and postbuckling paths when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling load and postbuckling behavior of braided composite cylindrical shells.
Finally, based on the present perturbation technique combined with perturbation method, the computer program packages are made by using FORTRAN computer language, this paper provides comprehensive first-ever-known results which are helpful in better understanding the postbuckling behavior of the 3D braided and fiber-reinforced shells.
本文的研究工作主要包括:将壳体屈曲的边界层理论推广运用到纤维增强各向异性层合剪切圆柱壳。分析中同时考虑前屈曲非线性变形,后屈曲大挠度和初始几何缺陷的影响以及横向剪切变形和耦合刚度的影响,采用奇异摄动方法给出完全各向异性层合圆柱剪切壳在轴压、外压和扭矩作用下的既满足控制方程又在渐近意义上严格满足边界条件的后屈曲大挠度渐近解。通过对屈曲与后屈曲等一系列问题的求解和分析揭示中等厚度各向异性层合圆柱壳结构在轴压、外压和扭矩作用下的后屈曲行为的规律,为复合材料结构的设计提供科学依据;
根据四步法1×1圆型编织工艺过程中编织纱线的运动轨迹特征和纱线的结构特点,将预成型件分为三个不同的区域,分别定义不同的控制体积单元,识别预成型件的局部单胞模型,分析预成型件的纱线构造,并推导出了编织结构参数之间的关系。编织结构主要的参数包括试件的外形尺寸、主体纱径向层数和周向列数、三个区域各自所占的体积百分比、纱线填充因子(缺省取为常数)、纤维体积含量、编织角以及编织花节长度。在预成型件分析的基础上,导出三维编织复合材料的局部单胞模型,分析复合材料的纱线构造,研究复合材料的编织结构参数之间的关系。从而,建立三维编织预成型件单胞弹性性能关系。采用三维应力-应变分析,在单胞的长度方向积分和平均,在给定的应变边界条件下,采用刚度体积平均的方法计算了单胞的有效弹性性能,预测三维编织结构复合材料的有效弹性模量。在此基础上提出一种三维四向编织复合材料圆柱壳的宏-细观力学模型。
在壳体屈曲的边界层理论框架下,给出了三维编织复合材料圆柱壳在热环境下和在轴压、外压、扭矩及轴压和外压复合加载作用下的大挠度渐近解。分析中同时考虑前屈曲非线性变形,后屈曲大挠度和初始几何缺陷的影响,横向剪切变形的影响,以及材料物性参数对温度变化的依赖性。
基于本文理论分析,用Fortran语言编制了相应的数值分析程序包,在上述研究领域内给出了大量的计算分析结果。
本文得到国家自然科学基金:“混合智能结构非线性行为和动力特性建模与分析”(50375091)的部分支持。
本文研究成果有助于推动纤维增强和三维编织复合材料结构的非线性稳定性的研究,对此两类复合材料结构在船舶和海洋工程中的应用具有积极意义。
Currently there is a wide range of naval structures being developed using fibre-reinforced polymer composites, due to considerable strength-to-weight ratio. There has been considerable attention in the structural instability of relatively thick shells. Many current potential applications involve the moderately thick shell type configuration. For example, large patrol boats, hovercraft, minecountermeasure vessels and corvettes that are built completely of composite material, to mention a few. Other new or potential uses for composites are in the superstructures, advanced mast systems, bulkheads, decks, propellers, propulsion shafts and rudders for large surface combatants such as frigates and destroyers. In submarines, the future applications of composites may include control surfaces and mast systems. Navies are also exploring the feasibility of using composites for internal equipment and fittings, such as machinery, heat exchangers, equipment foundations, values, pumps, pipes and ducts. A new class of composite material known as braided composites have been received considerable attention. Textile composites are manufactured by fabrication methods derived from the textile industry. Unlike laminated composites, in which cracking and debonding may occur at high temperature due to the material property mismatch at the interface of two discrete materials, the textile composites are able to eliminate the delamination due to the inter-lacing of the tows in the through-thickness direction. Braided composites are now developed for general use as structural components in naval ship and submarine, offshore structures due to their light weight and easy handling secure their place in the industry.
As a primary load carrying structure, the buckling and postbuckling behavior of laminated or braided cylindrical shell subjected to mechanical load is a vital safety consideration, and improvement of its prediction accuracy behavior is thus essential for reliable design.
This paper consists of two parts: A boundary layer theory of shell buckling is extended to the case of general shear deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression, external pressure, torsion, respectively. The material properties of each layer of the shell are assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence.
Then, established a micro-macro-mechanical model, a 3D braided composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. A postbuckling analysis is presented for a 3D braided composite cylindrical shell of finite length subjected to axial compression, external pressure, torsion, combined loading of external pressure and axial compression in thermal environments, respectively. The governing equations are based on Reddy's higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling loads and postbuckling paths when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling load and postbuckling behavior of braided composite cylindrical shells.
Finally, based on the present perturbation technique combined with perturbation method, the computer program packages are made by using FORTRAN computer language, this paper provides comprehensive first-ever-known results which are helpful in better understanding the postbuckling behavior of the 3D braided and fiber-reinforced shells.
引文
[1] Mouritz, A.P., Gellert, E., Burchill, P., Challis, K. Review of advanced composite structures for naval ships and submarines. Composites Structures, 2001, 53: 21-41.
[2] Sharpe, R. Jane’s fighting ships 1999-2000. Coulsdon, UK: Jane’s Information Group Limited, 1999.
[3]蔡斌.复合材料在船艇工业中的应用.功能高分子材料, 2003, 16(1): 113-119.
[4] Chucheepsakul, S., Monprapussorny, T. Nonlinear buckling of marine elastica pipes transporting fluid. International Journal of Structural Stability and Dynamics, 2001, 1: 333-365.
[5]曾锐,昂海松.“天使鸟”号地效翼艇的设计与试航.兵工学报, 2006, 27: 380-384.
[6] Macander, A. An X-D braided composite marine propeller. In: Proceedings of the 10th DOD/NASA/FAA Conference on Fibrous Composites in Structural Design. pp.19-53, 1994.
[7] Macander A. Multidimensionally braided composite marine propeller. Proceedings of 3-D Composite Materials. NASA Conference Publication 2420. pp. 171-183, 1986.
[8] Pegg, R.L., Reyes, H. Composites promise navy weight, tactical advantages. Sea Technology.1986, 27: 31-35.
[9]朱孝信.舰船用高技术新材料的发展.材料开发与应用, 1999, 14(1): 24-30.
[10]邱建新.玻璃钢材料在船舶结构设计中应注意的问题.中国水运, 2007, 5(1): 8-9.
[11] Carvelli, V., Panzeri, N., Poggi, C. Buckling strength of GFRP under-water vehicles. Composite Part: B, 2001, 32: 89-101.
[12] Yousefpour, A., Ghasemi Nejhad, M.N. Design, analysis, manufacture, and test of APC-2/AS4 thermoplastic composite pressure vessels for deep water marine applications. Journal of Composite Materials, 2004, 38: 1701-1732.
[13]中科院力学所.加筋圆柱曲板与圆柱壳.北京:科学出版社, 1983.
[14] Bernitsas, M. M. Riser top tension and riser buckling loads. Computer Methods for Offshore Structures, ASME, New York, pp.101-109, 1980.
[15] Bernitsas, M.M., Kokkinis, T. Buckling of columns with nonmovable boundaries, Journal of Engineering Structures, ASCE, 1983, 105: 2113-2128.
[16] Bernitsas, M.M., Kokkinis, T. Buckling of columns with movable boundaries. Journal of Structural Engineering, ASCE, 1983, 11: 351-370.
[17] Bernitsas, M.M., Kokkinis, T. Asymptotic behavior of heavy column and riser stability boundaries. Journal of Applied Mechanics, ASME, 1984, 51: 560-565.
[18] Vaz, M. A., Patel, M. H. Analysis of drill strings in vertical and deviated holes using the Galerkin technique. Engineering Structures, 1995, 17: 437-442.
[19] Donnell, L.H. A new theory for the buckling of thin cylinders under axial compression and bending. Transaction ASME, 1934, 56: 775-806.
[20] Karman, T.V., Tsien, H.S. The buckling of spherical shell by external pressure. Journal of Aeronaut Science, 1937, 7: 43-50.
[21] Karman, T.V., Tsien, H.S. The buckling of thin cylindrical shell under axial compression. Journal of Aeronaut Science, 1941, 8: 303-312.
[22] Karman, T.V., Tsien, H.S. A theory for the buckling of thin shells. Journal of Aeronaut Science, 1942, 9: 373-384.
[23] Stein, M. The effect on the buckling of perfect cylinders of prebuckling deformations and stresses induced by edge support. NASA TN D-1510, 1962.
[24] Stein, M. The influence of pre-buckling deformations and stresses on the buckling of perfect cylinders. NASA TR-190, 1964.
[25] Koiter, W.T. On the stability of elastic equilibrium (in Dutch). PhD Thesis, Delft, H. J. Paris, Amsterdam; also NASA TTF-10, 833, 1967.
[26] Koiter, W.T. Elastic stability and postbuckling behavior. In Nonlinear Problems (ed. by Langer, R.E.) University of Wisconsin Press, 1963.
[27] Budiansky, B., Hutchinson, J.W. A survey of some buckling problems. AIAA Journal, 1966, 4: 1505-1510.
[28] Babcock, C.D. Shell stability. Journal of Applied Mechanics, 1983, 50: 935-940.
[29] Simitses, G.J. Buckling and postbuckling of imperfect cylindrical shells: a review. ASME, Applied Mechanics Reviews, 1986, 39: 1517-1524.
[30] Simitses, G.J., Anastasiadis, J.S. Shear deformable theories for cylindrical laminates- equilibrium and buckling with applications. AIAA Journal, 1992, 30: 826-834.
[31] Simitses, G.J., Tabiei, A., Anastasiadis, J.S. Buckling of moderately thick laminated cylindrical shells under lateral pressure. Composites Engineering, 1993, 3: 409-417.
[32] Teng, J.G. Buckling of thin shells: recent advances and trends. Applied Mechanics Reviews, 1996, 49: 263-274.
[33]王俊奎,王虎.复合材料薄壁壳体的稳定性.航空学报, 1991, 12(12): 598-605.
[34]杜启端.现代薄壳非线性稳定性理论的发展和应用.强度与环境, 2002, 29(1): 41-58.
[35]白雪飞,郭日修.近代弹性稳定性理论的几个重要分支.海军工程大学学报, 2004, 16(3):40-46.
[36]周利,黄义.薄壳非线性稳定理论的最新发展.建筑钢结构进展, 2006, 8(4): 23-32.
[37]陈铁云,沈惠申.结构的屈曲.上海:上海科学技术文献出版社, 1993.
[38]沈惠申.板壳后屈曲行为.上海:上海科学技术出版社, 2002.
[39] Tielemann, W.F., Esslinger, M.E. On the postbuckling behavior of thin-walled, axially compressed circular cylinders of finite length. Proceedings of Symposium of the Theory of Shells (ed. by Muster, D.), 1967, pp. 433-479, University of Houston.
[40] Yamaki, N., Otomo, K., Matsuda, K. Experiments on the postbuckling behavior of circular cylindrical shells under compression. Experimental Mechanics, 1975, 15: 23-28.
[41] Yamaki, N. Elastic stability of circular cylindrical shells. Elsevier Science Publishers, B.V., 1984.
[42] Tennyson, R.C., Muggeridge, D.B. Buckling of laminated anisotropic imperfect circular cylinders under axial compression. Journal of Spacecraft, 1973, 10: 143-148.
[43] Katz, L. Compression tests on integrally stiffened cylinders. NASA TM X-55315.
[44] Seleim, S.S., Roorda, J. Theoretical and experimental results on the post-buckling of ring-stiffened cylinders. Mechanics of Structures and Machines, 1987, 15: 69-87.
[45] Tennyson, R.C. Buckling of laminated composite cylinders: a review. Composites, 1975, 6: 17-24.
[46] Yamaki, N. Postbuckling and imperfection sensitivity of circular cylindrical shells under compression. In Theoretical and Applied Mechanics (ed. by Koiter, W.T.), pp. 461-476, North-Holland Publishing Co, 1976.
[47]沈惠申.近海平台管状构件弹性稳定性[博士学位论文].上海:上海交通大学, 1986.
[48]沈惠申,陈铁云.圆柱薄壳在外压作用下屈曲的边界层理论.应用数学和力学, 1988, 9: 515-527.
[49] Shen, H.-S., Chen, T.-Y. A Boundary layer theory for the buckling of thin cylindrical shells under axial compression. In Advances in Applied Mathematics and Mechanics in China (eds. Chien, W.Z. and Fu, Z.Z.), 1990, Vol. 2, pp 155-172, International Academic Publishers.
[50] Shen, H.-S., Chen, T.-Y. Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression. Thin-Walled Structures, 1991, 12: 321-334.
[51] Stum, R.G. A study of the collapsing pressure of thin-walled cylinders. Engineering Experimental Statistics, Bull. No. 329, University Illinois, 1941.
[52] Weigarten, V.I., Seide, P. Elastic stability of thin-walled cylindrical and concial shells under combined external pressure and axial compression. AIAA Journal, 1965, 3: 913-920.
[53] Winderburg, D.F., Trilling, C. Collapse by instability of thin cylindrical shells under externalpressure. Transaction ASME, 1934, 56: 819-825.
[54] Yamaki, N., Otomo, K.. Experiments on the postbuckling behavior of circular cylindrical shells under hydrostatic pressure. Experimental Mechanics, 1973, 13: 299-304.
[55]沈惠申,周频,陈铁云.加肋圆柱壳在轴压作用下的屈曲和后屈曲.应用数学和力学, 1991, 12: 1127-1139.
[56] Shen, H.-S. Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and axial compression. Computers and Structures, 1997, 63: 335-348.
[57] Shen, H.-S. Postbuckling analysis of stiffened laminated cylindrical shells under combined external liquid pressure and axial compression. Engineering Structures, 1998, 20: 738-751.
[58] Shen, H.-S. Thermal postbuckling analysis of imperfect stiffened laminated cylindrical shells. International Journal of Non-linear Mechanics, 1997, 32: 259-275.
[59] Shen, H.-S. Thermomechanical postbuckling of stiffened laminated cylindrical shell. Journal of Engineering Mechanics, 1997, 123: 433-443.
[60] Shen, H.-S. Thermomechanical postbuckling of composite laminated cylindrical shells with local geometric imperfections. International Journal of Solids and Structures, 1999, 36: 597-617.
[61] Shen, H.-S. Hygrothermal effects on the post-buckling of composite laminated cylindrical shells. Composites Science and Technology, 2000, 60: 1227-1240.
[62]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.应用数学和力学, 2001, 22: 228-238.
[63] Shen, H.-S. Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators. European Journal of Mechanics A-Solids, 2001, 20: 1007-1022.
[64] Shen, H.-S. Thermal postbuckling analysis of laminated cylindrical shells with piezoelectric actuators. Composite Structures, 2002, 55: 13-22.
[65] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part I: prediction under axial compression. Composite Structures, 2008, 82: 346-361.
[66] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part II: prediction under external pressure. Composite Structures, 2008, 82: 362-370.
[67] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part III: prediction under torsion. Composite Structures, 2008, 82: 371-381.
[68] Reddy, J.N., Liu, C.F. A higher-order shear deformation theory of laminated elastic shells.International Journal of Engineering Sciences, 1985, 23: 319-330.
[69] Shen, H.-S. Postbuckling of shear deformable cross-ply laminated cylindrical shells under combined external pressure and axial compression. International Journal of Mechanical Sciences, 2001, 43: 2493-2523.
[70] Shen, H.-S. Postbuckling of shear deformable laminated cylindrical shells. Journal of Engineering Mechanics, ASCE, 2002, 128: 296-307.
[71] Shen, H.-S., Li, Q.S. Thermomechanical postbuckling of shear deformable laminated cylindrical shells with local geometric imperfections. International Journal of Mechanical Sciences, 2002, 39: 4525-4542.
[72] Shen, H.-S. Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments. Engineering Structures, 2003, 25: 487-497.
[73] Shen, H.-S. Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties. International Journal of Solids and Structures, 2004, 41: 1961-1974.
[74] Shen, H.-S. Postbuckling prediction of double-walled carbon nanotubes under hydrostatic pressure. International Journal of Solids and Structures, 2004, 41: 2643-2657.
[75] Shen, H.-S., Zhang, C.-L. Postbuckling prediction of axially loaded double-walled carbon nanotubes with temperature dependent properties and initial defects. Physical Review B 2006, 74: 035410, 1-16.
[76] Dow, M.B., Dexter, B.H. Development of stitched, braided and woven composite structures in the ACT program and at Langley Research Center (1985 to 1997) summary and bibliography. NASA/TP-97-206234.
[77] Kamiya, R., Cheeseman, B.A., Popper, P., Chou, T.W. Some recent advances in the fabrication and design of three-dimensional textile preforms. Composites Science and Technology, 2000, 60: 33-47.
[78]王波.三维编织复合材料力学行为研究[博士学位论文].西安:西北工业大学, 2003.
[79]陶肖明,冼杏娟,高冠勋.纺织结构复合材料.北京:科学出版社, 2001.
[80]杨朝坤.三维编织复合材料细观结构平均刚度及其压缩性能的研究[博士学位论文].天津:天津工业大学, 2003.
[81] Ko, F.K. Three-dimensional fabrics for composites-an introduction to the magna weave structure. Proceedings ICCM-4 Japan Society, Composite Material, Tokyo, Japan, 1982, pp. 1609.
[82] Li, W., Hammad, M., El-Shiekh, A. Structural analysis of 3-D braided performs for composites partI: the Four-step performs. Journal of Textile Institute, 1990, 81: 491-514.
[83] Ma, C.L., Yang, J.M., Chou, T.W. Elastic stiffness of three-dimensional braided textile structure composites. ASTM STP 893, Composite Materials: Testing and Design, Philadelphia, 1986, 404-421.
[84] Yang, J.M., Ma C.L., Chou T.W. Fiber inclination model of three dimensional textile structural composites. Journal of Composite Material, 1986, 20: 472-484.
[85] Sun H.Y., Qiao, X. Prediction of mechanical properties of three-dimensionally braided composites. Composites Science and Technology, 1997, 57: 623-629.
[86]孙慧玉.编织结构复合材料的力学性能预报和成型工艺研究[博士学位论文].南京:南京航空航天大学, 1996.
[87]吴德隆,郝兆平.五向编织结构复合材料的分析模型.宇航学报,1993, 14(3): 40-51.
[88] Wu, D.L. Three-cell model and 5D braided structural composites. Composites Science and Technology, 1996, 56: 225-233.
[89] Chen, L., Tao, X.M., Choy, C.L. On the microstructure of three-dimensional braided performs. Composite Science and Technology, 1999, 59: 391-404.
[90] Chen, L., Tao, X.M., Choy, C.L. A study on the microstructure of three-dimensional braids, Eleventh International Conference on Composite Materials, p. 317-327, Australia, July, 1997.
[91]陈利.三维编织复合材料的细观结构及其弹性性能分析[博士学位论文].天津:天津纺织工学院, 1998.
[92] Whitney, T.J, Chou T.W. Modeling of 3-D angle-interlock textile structural composite. Journal of Composite Material, 1989, 23: 890-911.
[93] Crane, R.M., Camponeschi, E.T. Experimental and analytical characterization of multi- dimensionally braided graphite/epoxy composites. Experiment Mechanics, 1986, 19: 259-266.
[94] Yasar, B. Analysis of braided composite laminate. M.S. thesis, the University of Taxas at Arlington, 2003.
[95]梁军.三维编织复合材料力学性能的细观研究[博士学位论文].哈尔滨:哈尔滨工业大学, 1996.
[96]梁军,杜善义.一种含特定微型纹缺陷三维编织复合材料弹性常数预报方法.复合材料学报,1997, 14(1): 101-107.
[97]梁军,陈晓峰等.多向编织复合材料的力学性能研究.力学进展, 1999, 29(2): 197-210.
[98] Chou, T.W. Microstructural Design of Fiber Composites. Cambridge University Press 1992.
[99] Feder, E. Algorithmic problems in the braid group. Ph.D. thesis, the City University of New York,2003.
[100] Mohajerjasbi, S. Modeling and analysis of 4-step 3-D cartesian braiding composites including axial yarns. Proceedings of the 36th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics, and Materials Conference and AIAA/ASME Adaptive Structure Forum. 1995, 8-16.
[101] Li, J., Pu, S., Chen, A.E. Construction and geometry of 6-step braided performs for composites. 39th international SAMPE Symposium, April, 1994, 826-833.
[102] Hiroyuki, H., Asami, N., Akihiro, F., Zenichiro, M. CAE in integrated braided composite. Science and Engineering of Composite Materials. 1995, 4: 109-120.
[103] Walrath, D.E., Adeams, D.F. Finite element micromechanics and minimechanics modeling of a three-dimensional carbon-carbon composite material. ADA 168050, 1995.
[104]赫晓东.编织复合材料的细观计算力学研究[博士学位论文].哈尔滨:哈尔滨工业大学, 1992.
[105] Whyte, D.E., Pastore, C.M., Ko, F.K. A fabric geometry model for 3-D braid reinforced FP/Al-Li composites. Inter SAMPE Metal Cont, Competitive Advances in Metals/Metal Processing, Cherry Hill, Aug. 1997, 18-21.
[106] Lei, C., Wang, A.S., Ko, F.K. A finite cell model for 3D braided composites. ASME Winter Annual Meeting, Chicago USA, 1988.
[107] Whitcomb, J.D. Three-dimensional stress analysis of plain weave composites. in: 3rd Symposium on Composite Materials: Fatigue and Fracture, ASTM, USA, Oct. 1989.
[108]庞宝君.三维多向编织复合材料力学性能预报与优化设计研究[博士学位论文].哈尔滨:哈尔滨工业大学, 1997.
[109]张文毅,姚振汉,姚学锋,曹艳平.编织复合材料的一种数值模型.工程力学, 2004, 21(3): 55-60.
[110]燕瑛.编织复合材料弹性性能的细观力学模型.力学学报, 1997, 29(4): 429-438.
[111]徐孝诚,孙德海,黄小平.三维编织复合材料细观结构的几何学分析.强度与环境, 1999, 26(2): 37-43.
[112]陈利,李嘉禄,李学明.三维四步法圆形编制结构分析.复合材料学报, 2003, 20(2): 76-80.
[113] Wang, Y.Q., Wang, A.S.D. Spatial distribution of yarns and mechanical properties in 3D braided tubular composites applied. Composite Materials, 1997, 4: 121-132.
[114] Sun, X.K. Micro-geometry of 3-D braided tubular preform. Journal of Composite Materials 2004, 38: 791-98.
[115]马文锁,冯伟.三维管状编织复合材料及其构件可变微单元几何分析模型.复合材料学报, 2005, 22(5): 162-171.
[116]柴雅凌.矩形和圆形三维编织预制件中纱线的拓朴学结构.纤维复合材料, 1996, 1: 23-30.
[1] Khot, N.S., Venkaya, V.B. Effect of fiber orientation on initial postbuckling behavior and imperfection sensitivity of composite cylindrical shells. AFFDL-TR-70-125, 1970.
[2] Tennyson, R.C., Muggeridge, D.B. Buckling of laminated anisotropic imperfect circular cylinders under axial compression. Journal of Spacecraft, 1973, 10: 143-148.
[3] Bisagni, C. Experimental buckling of thin composite cylinders. AIAA Journal, 1999, 37: 276-278.
[4] Chryssanthopoulos, M.K., Elghazouli, A.Y., Esong, I.E. Compression tests on anti-symmetric two-ply GFRP cylinders. Composites: Part B, 1999, 30: 335-350.
[5]武兰河.加权残数法分析前屈曲变形对复合材料层迭圆柱壳屈曲载荷的影响.石家庄铁道学院学报, 1997, 10(1): 40-47.
[6]李媛,利凤祥,李越森,王锟,胡春波.复合材料壳体轴压稳定性分析.固体火箭技术, 2004, 27(4): 280-284.
[7] Zhou,C.T. The computation of nonlinear instability for multi-layer composite cylindrical shells. Applied Mathematics and Mechanics, 1986, 7: 17-23.
[8] Hilburger, M.W., Starnes Jr. JH. Effects of imperfections of the buckling response of compositeshells. Thin-Walled Structures, 2004, 42: 369-397.
[9] Geier, B., Meyer-Piening, H.R., Zimmermann, R. On the influence of laminate stacking on buckling of composite cylindrical shells subjected to axial compression. Composite Structures, 2002, 55: 467-474.
[10]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.华东船舶工业学院学报, 1999, 13(2): 42-46.
[11]张建武,徐延海,吴金松.反对称正交铺层剪切圆柱壳在轴压下的屈曲分析.上海交通大学学报, 2002, 36(3): 411-415.
[12] Mao, R.J., Williams, F.W. Nonlinear analysis of cross-ply thick cylindrical shells under axial compression. International Journal of Solids and Structures, 1998, 35: 2151-2171.
[13] Ye, J.Q., Soldatos, K.P. Three-dimensional buckling analysis of laminated hollow cylinders and cylindrical panels. International Journal of Solids and Structures, 1995, 32: 1949-1962.
[14] Iu, V.P., Chia, C.Y. Effect of transverse shear on nonlinear vibration and postbuckling of anti-symmetric cross-ply imperfect cylindrical shells. International Journal of Mechanical Science, 1988, 30: 705-718.
[15]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.导弹与航天运载技术, 2001, (2): 24-28.
[16] Han, B., Simitses, G.J. Analysis of anisotropic laminated cylindrical shells subjected to destabilizing loads, Part II: numerical results. Composite Structures, 1991, 19: 183-205.
[17] Tabiei, A., Simitses, G. Imperfection sensitivity of shear deformable moderately thick laminated cylindrical shells. Computers & Structures, 1997, 62: 165-174.
[18] Simitses, G.J., Anastasiadis, J.S. Buckling of axially-loaded, moderately-thick, cylindrical laminated shells. Composites Engineering, 1991, 1: 375-391.
[19] Reddy, J.N., Savoia, M. Layer-wise shell theory for postbuckling of laminated circular cylindrical shells. AIAA Journal, 1992, 30: 2148-2154.
[20] Eslami, M.R., Shariyat, M., Shakeri, M. Layerwise theory for dynamic buckling and postbuckling of laminated composite cylindrical shells. AIAA Journal, 1998, 36: 1874-1882.
[21] Eslami, M.R., Shariyat, M. A higher-order theory for dynamic buckling and postbuckling analysis of laminated cylindrical shells. ASME Journal of Pressure Vessel Technology, 1999, 121: 94-102.
[22] Weaver, P.M. The effect of extension/twist anisotropy on compression buckling in cylindrical shells. Composites: Part B, 2003, 34: 251-260.
[23] Weaver, P.M., Driesen, J.R., Roberts, P. The effect of flexural/twist anisotropy on compression buckling of quasi-isotropic laminated cylindrical shells. Composite Structures, 2002, 55: 195-204.
[24] Wong, K.F.W., Weaver, P.M. Approximate solution for the compression buckling of fully anisotropic cylindrical shells. AIAA Journal, 2005, 43: 2639-2645.
[25] Takano, A. Improvement of Flügge’s equations for buckling of moderately thick anisotropic cylindrical shells. AIAA Journal, 2008, 46: 903-911.
[26] Reddy, J.N., Liu, C.F. A higher-order shear deformation theory of laminated elastic shells. International Journal of Engineering Sciences, 1985, 23: 319-330.
[27] Donnell, L.H. Stability of thin walled tubes under torsion. NACA Report No. 479, 1933.
[28]沈惠申.板壳的后屈曲行为.上海:上海科学技术文献出版社, 2002.
[29] Shen, H.-S. Thermal buckling and postbuckling of laminated plates. In Analysis and Design of Plated Structures (eds. Shanmugam, N.E. and Wang, C.M.), Vol. 1 Stability, pp. 170-213, Woodhead Publishing Ltd, 2006.
[30] Batdorf, S.B. A simplified method of elastic-stability analysis for thin cylindrical shells. NACA TR-874, 1947.
[31] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part I: prediction under axial compression. Composite Structures, 2008, 82: 346-361.
[32] Simitses, G.J., Anastasiadis, S.J. Shear deformable theories for cylindrical laminates- equilibrium and buckling with applications. AIAA Journal, 1992, 30: 826-834.
[33] Fahadinia. M. Finite element analysis and experimental evaluation of buckling phenomena in laminate composite tubes and plates. PhD. Thesis, University of Missouri-Rolla, 1992.
[34] Arciniega, R.A., Goncalves, P.B., Reddy, J.N. Buckling and postbuckling analysis of laminated cylindrical shells using third-order shear deformable theory. International Journal of Structural Stability and Dynamics, 2004, 4: 293-312.
[35] Yuan, F.G., Hsieh, C.C. Three-dimensional wave propagation in composite cylindrical shells. Composite Structures, 1998, 42: 153-167.
[36] Li, Z.-M., Shen, H.-S. Postbuckling of shear deformable anisotropic laminated cylindrical shell under axial compression. International Journal of Structural Stability and Dynamics.(in press)
[1] Ouellette, P., Hoa, S.V., Sankar, T.S. Buckling of composite cylinders under external pressure. Polymer Composites, 1986, 7: 363-374.
[2] Smerdov, A.A. A computational study in optimum formulations of optimization problems on laminated cylindrical shells for buckling II, Shells under external pressure. Composites Science and Technology, 2000, 60: 2067-2076.
[3]周承倜,周建平.多层复合材料圆柱壳的非线性失稳计算.应用数学和力学, 1986, 7(1): 17-23.
[4]杜建科,田晓耕,沈亚鹏,陈汝训.复合材料燃烧室均布侧压下稳定性分析.固体火箭技术, 2002, 25(2): 18-21.
[5] Carvelli, V., Panzeri, N., Poggi, C. Buckling strength of GFRP under-water vehicles. Composite Part: B, 2001, 32: 89-101.
[6] Messager, T. Buckling of imperfect laminated cylinders under hydrostatic pressure. Composite Structures, 2001, 53: 301-307.
[7] Messager, T., Pyrz, M., Gineste, B., Chauchot, P. Optimal laminations of thin underwater composite cylindrical vessels. Composite Structures, 2002, 58: 529-537.
[8] Yousefpour, A. Design, analysis, manufacture, and test of composite pressure vessels and finite element analysis of metallic frame for deep ocean underwater vehicle applications. PhD. thesis, University of Hawaii, December, 2000.
[9] Chucheepsakul, S., Monprapussorny, T. Nonlinear buckling of marine elastica pipes transporting fluid. International Journal of Structural Stability and Dynamics, 2001, 1: 333-365.
[10]王永志,向锦武.复合材料旋转壳稳定性有限元分析和横向剪切变形的影响分析.复合材料学报, 2006, 23(4): 175-179.
[11]王震鸣.复合材料力学和复合材料结构力学.北京:机械工业出版社, pp.418-420, 1991.
[12] Han, B., Simitses, G.J. Analysis of anisotropic laminated cylindrical shells subjected todestabilizing loads, Part II: numerical results. Composite Structures, 1991, 19: 183-205.
[13] Simitses, G.J., Anastasiadis, J.S. Shear deformable theories for cylindrical laminates- equilibrium and buckling with applications. AIAA Journal, 1992, 30: 826-834.
[14] Simitses, G.J., Tabiei, A., Anastasiadis, J.S. Buckling of moderately thick laminated cylindrical shells under lateral pressure. Composites Engineering, 1993, 3: 409-417.
[15] Kasagi, A., Sridharan, S. Imperfection sensitivity of layered composite cylinders, ASCE Journal of Engineering Mechanics, 1995, 121: 810-818.
[16] Eslami, M.R., Shariyat, M., Shakeri, M. Layerwise theory for dynamic buckling and postbuckling of laminated cylindrical shells. AIAA Journal, 1998, 36: 1874-1882.
[17] Eslami, M.R., Shariyat, M. A higher-order theory for dynamic buckling and postbuckling analysis of laminated cylindrical shells. ASME Journal of Pressure Vessel Technology, 1999, 121: 94-102.
[18] Arciniega, R.A., Goncalves, P.B., Reddy, J.N. Buckling and postbuckling analysis of laminated cylindrical shells using third-order shear deformable theory. International Journal of Structural Stability and Dynamics, 2004, 4: 293-312.
[19]沈惠申.板壳的后屈曲行为.上海:上海科学技术文献出版社, 2002.
[20] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part II: prediction under external pressure. Composite Structures, 2008, 82: 362-370.
[21] Yuan, F.G., Hsieh, C.C. Three-dimensional wave propagation in composite cylindrical shells. Composite Structures, 1998, 42: 153-167.
[22] Li, Z.-M. Postbuckling of shear deformable anisotropic laminated cylindrical shell under external pressure in thermal environments. Mechanics of Composite Materials, 2007, 43: 535-560.
[1]周建钢,熊鹰.复合材料推进器.航海工程, 2004, 14(5): 33-35.
[2] Simitses G.J., Shaw, D., Sheinman, I. Stability of imperfect laminated cylinders: a comparison between theory and experiment. AIAA Journal, 1985, 23: 1086-1092.
[3] Wilkins, D.J., Love, T.S. Compression-torsion buckling test of laminated composite cylindrical shells. AIAA paper, pp. 74-379, 1974.
[4]周承倜,周建平.多层复合材料圆柱壳的非线性失稳计算.应用数学和力学, 1986, 7(1): 17-23.
[5] Tennyson, R.C. Buckling of laminated composite cylinders: a review. Composites, 1975, 6: 17-24.
[6] Huille, A., Yang, C., Pang, S.S. Buckling analysis of thick-walled composite pipe under torsion. ASME Journal of Pressure Vessel Technology, 1997, 119: 111-116.
[7] Shaw, D., Simitses G.J. Insability of laminated cylinders in torsion. ASME Journal of Applied Mechanics, 1984, 51: 188-190.
[8]黄晓东,茅人杰.具有力边条件的层合圆柱薄壳的扭转屈曲.上海交通大学学报, 2000, 34(8): 1146-1149.
[9] Mao, R., Lu, C.H. Buckling analysis of a laminated cylindrical shell under torsion subjected to mixed boundary conditions. International Journal of Solids and Structures, 1999, 36: 3821-3835.
[10] Tan, D. Torsional buckling analysis of thin and thick shells of revolution. International Journal of Solids and Structures, 2000, 37: 3055-3078.
[11] Park, H.C., Cho, C., Choi, Y. Torsional buckling analysis of composite cylinders. AIAA Journal, 2001, 39: 951-955.
[12] Tabiei, A., Simitses G.J. Buckling of moderately thick laminated cylindrical shells under torsion. AIAA Journal, 1994, 32: 639-647.
[13] Tabiei, A., Simitses, G.J. Torsional instability of moderately thick composite cylindrical shells by various shell theories. AIAA Journal, 1997, 37: 1243-1246.
[14] Batdorf, S.B. A simplified method of elastic-stability analysis for thin cylindrical shells. NACA TR-874, 1947.
[15] Loo, T.T. Effects of large deflections and imperfections on the elastic buckling of cylinders under torsion and axial compression. In: Proceedings of the 2nd US national congress on applied mechanics, pp. 345-357, 1954.
[16] Nash, W.A. Buckling of initially imperfect cylindrical shells subjected to torsion. ASME Journal of Applied Mechanics, 1957, 24: 125-130.
[17] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part III: prediction under torsion. Composite Structures, 2008, 82: 371-381.
[18]沈惠申.板壳的后屈曲行为.上海:上海科学技术文献出版社, 2002.
[19] Herakovich, C.T., Johnson, E.R. Buckling of composite cylinders under combined compression and torsion-theoretical/experimental correlation. Test Methods and Design Allowable for Fibrous Composites, ASTM STP 734, (ed. Chamis, C.C.) American Society for Testing Materials, Philadelphia, PA, pp. 341-360, 1981.
[20] Wu, C.H. Buckling of anisotropic circular shells. Ph.D. Dissertation, Case Western Reserve University, Cleveland, OH, 1971.
[21] Ambrose, H.S., Walter, R.,Goldie, B. Torsion tests of tubes, NACA TR-601, 1937.
[22] Derstine, M.S., Pindera, M.J., Bowles, D.E. Combined mechanical loading of composite tubes, NASA CR-183012, 1988.
[23] Yuan, F.G., Hsieh, C.C. Three-dimensional wave propagation in composite cylindrical shells. Composite Structures, 1998, 42: 153-167.
[24] Li, Z.-M., Shen, H.-S. Postbuckling of shear deformable anisotropic laminated cylindrical shell under torsion. Mechanics of Advanced Materials and Structures.(in press)
[1]何煌.编织复合材料圆柱壳的稳定性分析[硕士学位论文].长沙:国防科技大学, 2003.
[2]何煌,唐国金,蒋志刚,王可晟.编织复合材料圆柱壳蠕变屈曲分析,重庆交通学院学报, 2003, 22(4): 35-38.
[3]张雪丽,果立成,曾涛,吴林志,马力.三维编织复合材料圆柱壳的稳定性研究.哈尔滨工业大学学报, 2003, 35(2): 222-226.
[4] Tasi, J., Feldman, A., Stang, D.A. The buckling strength of filament-wound cylinders loaded in axial compression. NASA CR-266, 1965.
[5] Card, M.F. Experiments to determine the strength of filament-wound cylinders loaded in axial compression. NASA TN D-3522, 1966.
[6] Jensen, D.W., Pai, S.P. Influence of local fiber undulation on the global buckling of filament-wound cylinders. Journal of Reinforced Plastics and Composites, 1993, 12: 865-875.
[7] Pai, S.P., Jensen, D.W. Influence of fiber undulations on buckling of thin filament-wound cylinders in axial compression. Journal of Aerospace Engineering, 2001, 14: 12-20.
[8] Chyssanthopoulos, M.K., Elghazouli, A.Y., Esong, I.E. Validation of FE models for buckling analysis of woven GFRP shells. Composite Structures, 2000, 49: 355-367.
[9]张平,桂良进,范子杰.编织复合材料圆管准静态轴向压缩吸能特性的试验研究. 2007, 24(1): 144-150.
[10] Harte, A.M., Fleck, N.A. Deformation and failure mechanics of braided composite tubes in compression and torsion. Acta Materialia, 2000, 48: 1259-1271.
[11] Shu, C.Q., Anthony, M.W., Khaled, W.S., Venkatesh, A. Compressive response and failure of braided textile composites: Part 1-experiments. International Journal of Non-Linear Mechanics, 2004, 39: 635-648.
[12] Shu, C.Q., Anthony, M.W., Khaled, W.S., Venkatesh, A. Compressive response and failure of braided textile composites: Part 1-computations. International Journal of Non-Linear Mechanics, 2004, 39: 649-663.
[13] Wong, W.H., Ip, K.H., Tse, P.C. Buckling stresses of composite tubes under biaxial compressive loads. Experimental Mechanics, 1998, 38: 126-131.
[14] Kuo, W.S., Ko T.H., Shiah, Y.C. Compressive damage in three-axis woven thermoplastic composites. Journal of Thermoplastic Composite Materials 2006, 19: 357-373.
[15] Spagnoli, A., Elghazouli, A.Y., Chryssanthopoulos, M.K. Numerical simulation of glass-reinforced plastic cylinders under axial compression. Marine Structures, 2001, 14: 353-374.
[16] Zeng, T., Wu, L.Z. Post-buckling analysis of stiffened braided cylindrical shells under combined external pressure and axial compression. Composite Structures, 2003, 60: 455-466.
[17] Shen, H.-S., Chen, T.-Y. A boundary layer theory for the buckling of thin cylindrical shells under external pressure. Applied Mathematics and Mechanics, 1988, 9: 557-571.
[18] Shen, H.-S., Chen, T.-Y. A boundary layer theory for the buckling of thin cylindrical shells under axial compression. In: Advances in Applied Mathematics and Mechanics in China (eds. Chien, W.Z., Fu, Z.Z.), vol. 2, pp. 155-172, International Academic Publishers, Beijing, China, 1990.
[19] Shen, H.-S. Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and axial compression. Computers and Structures, 1997, 63: 335-348.
[20] Shen, H.-S., Li, Q.S. Thermomechanical postbuckling of shear deformable laminated cylindrical shells with local geometric imperfections. International Journal of Solids and Structures, 2002, 39: 4525-4542.
[21] Li, Z.-M. Nonlinear vibration analysis of 3D braided rectangular plates on elastic foundations. Journal of Ship Mechanics (in press).
[22]陶肖明,冼杏娟,高冠勋.纺织结构复合材料.北京:科学出版社, 2001.
[23] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal Composites Materials, 1968, 2: 380-404.
[24] Adams, D.F., Crane, D.A. Combined loading micromechanical analysis of a unidirectional composite. Composites, 1984, 15: 181-192.
[25] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, USA, 1991.
[26] Li, Z.-M., Shen, H.-S. Postbuckling analysis of three-dimensional textile composite cylindrical shells under axial compression in thermal environments. Composites Science and Technology, 2008, 68: 872-879.
[1] Rosenow, M.W.K. Wind angle effects in glass fibre reinforced polyester filament wound pipes. Composites, 1984, 15: 144-152.
[2] Ouellette, P., Hoa, S.V., Sankar, T.S. Buckling of composite cylinders under external pressure. Polymer Composites, 1986, 7: 363-374.
[3] Olivas, J.D., Ravi-Chandar, K., Bustillos, J., Craigie, L. Buckling of filament-wound cylindrical vessels subjected to external pressure. Journal of Pressure Vessel Technology ASME, 1996, 118: 216-220.
[4] Messager, T., Pyrz, M., Gineste, B., Chauchot, P. Optimal laminations of thin underwater composite cylindrical vessels. Composite Structures, 2002, 58: 529-537.
[5] Yousefpour, A., Ghasemi Nejhad, M.N. Design, analysis, manufacture, and test of APC-2/AS4 thermoplastic composite pressure vessels for deep water marine applications. Journal of Composite Materials, 2004, 38: 1701-1732.
[6] Calme, O., Bigaud, D., Hamelin, P. 3D braided composite rings under lateral compression. Composite Science and Technology, 2005, 65: 95-106.
[7]徐孝诚,马斌捷.三维四向整体编织复合材料圆筒壳体临界外压计算及试验验证.复合材料学报, 1999, 16(4): 136-141.
[8]谢禹均,邬柱,刘占民.混杂纤维缠绕圆柱壳外压稳定性与缠绕参数.复合材料学报, 1995, 12(1): 106-110.
[9]王晓华.纤维缠绕外压容器稳定性最佳铺层分析.抚顺石油学院学报, 1997, 17(4): 22-25.
[10]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.中国机械工程, 2007, 18(3): 286-290.
[11] Shen, H.-S. The effects of hygrothermal conditions on the postbuckling analysis of shear deformable laminated cylindrical shells. International Journal of Solids and Structures, 2001, 38: 6357-6380.
[12] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal Composites Materials, 1968, 2: 380-404.
[13] Adams, D.F., Crane DA. Combined loading micromechanical analysis of a unidirectional composite. Composites, 1984, 15: 181-192.
[14] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, 1991.
[15]李志敏,沈惠申.三维编织复合材料圆柱壳外压下的屈曲分析.固体力学学报, 2008, 29(1): 52-58.
[1] Harte, A.M., Fleck, N.A. Deformation and failure mechanics of braided composite tubes in compression and torsion. Acta Materialia, 2000, 48: 1259-1271.
[2] Wall, L.D., Jr, Card, M.F. Torsional shear strength of filament-wound glass-epoxy tubes. NASA TN D-6140, 1971.
[3] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal of Composites Materials, 1968, 2: 380-404.
[4] Karamia, G., Garnichb, M. Micromechanical study of thermoelastic behavior of composites with periodic fiber waviness. Composites: Part B, 2005, 36: 241-248.
[5] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, USA, 1991.
[6] Li, Z.-M., Shen, H.-S. Postbuckling analysis of 3D braided composite cylindrical shells under torsion in thermal environments. Composite Structures.(in press)
[1] Chucheepsakul, S., Monprapussorny, T. Nonlinear buckling of marine elastica pipes transporting fluid. International Journal of Structural Stability and Dynamics, 2001, 1: 333-365.
[2] Weingarten, V.I., Seide, P. Elastic stability of thin-walled cylindrical and conical shells under combined external pressure and axial compression. AIAA Journal, 1965, 3:913-920.
[3] Yousefpour, A., Ghasemi Nejhad, M.N. Design, analysis, manufacture, and test of APC-2/AS4 thermoplastic composite pressure vessels for deep water marine applications. Journal of Composite Materials, 2004, 38:1701-1732.
[4] Mouritz, A.P., Gellert, E., Burchill, P., Challis, K. Review of advanced composite structures for naval ships and submarines. Composites Structures, 2001, 53: 21-41.
[5] Kaddour, A.S., Soden, P.D., Hinton, M.J. Failure of±55 degree filament wound glass/epoxy composite tubes under biaxial compression. Journal of Composite Materials, 1998, 32:1618-1645.
[6] Dong, L., Mistry, J. An experimental study of the failure of composite cylinder subjected to combined external pressure and axial compression. Composite Structures, 1998, 40: 81-94.
[7] Mistry, J., Gibson, A.G., Wu, Y.S. Failure of composite cylinders under combined external pressure and axial loading. Composite Structures, 1992, 22:193-200.
[8] Mistry, J. Theoretical investigation into the effect the winding angle of the fibres on the strength of filament wound GRP pipes subjected to combined external pressure and axial compression. Composite Structures, 1992, 20: 83-90.
[9] Zeng T., Wu, L.Z. Post-buckling analysis of stiffened braided cylindrical shells under combined external pressure and axial compression. Composite Structures, 2003, 60: 455-466.
[10] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal Composites Materials, 1968, 2: 380-404.
[11] Adams, D.F., Crane, D.A. Combined loading micromechanical analysis of a unidirectional composite. Composites, 1984, 15: 181-192.
[12] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, USA, 1991.
[13] Li, Z.-M., Shen, H.-S. Postbuckling analysis of 3D braided composite cylindrical shells under combined external pressure and axial compression in thermal environments. International Journal of Mechanical Sciences, 2008, 50: 719-731.
[2] Sharpe, R. Jane’s fighting ships 1999-2000. Coulsdon, UK: Jane’s Information Group Limited, 1999.
[3]蔡斌.复合材料在船艇工业中的应用.功能高分子材料, 2003, 16(1): 113-119.
[4] Chucheepsakul, S., Monprapussorny, T. Nonlinear buckling of marine elastica pipes transporting fluid. International Journal of Structural Stability and Dynamics, 2001, 1: 333-365.
[5]曾锐,昂海松.“天使鸟”号地效翼艇的设计与试航.兵工学报, 2006, 27: 380-384.
[6] Macander, A. An X-D braided composite marine propeller. In: Proceedings of the 10th DOD/NASA/FAA Conference on Fibrous Composites in Structural Design. pp.19-53, 1994.
[7] Macander A. Multidimensionally braided composite marine propeller. Proceedings of 3-D Composite Materials. NASA Conference Publication 2420. pp. 171-183, 1986.
[8] Pegg, R.L., Reyes, H. Composites promise navy weight, tactical advantages. Sea Technology.1986, 27: 31-35.
[9]朱孝信.舰船用高技术新材料的发展.材料开发与应用, 1999, 14(1): 24-30.
[10]邱建新.玻璃钢材料在船舶结构设计中应注意的问题.中国水运, 2007, 5(1): 8-9.
[11] Carvelli, V., Panzeri, N., Poggi, C. Buckling strength of GFRP under-water vehicles. Composite Part: B, 2001, 32: 89-101.
[12] Yousefpour, A., Ghasemi Nejhad, M.N. Design, analysis, manufacture, and test of APC-2/AS4 thermoplastic composite pressure vessels for deep water marine applications. Journal of Composite Materials, 2004, 38: 1701-1732.
[13]中科院力学所.加筋圆柱曲板与圆柱壳.北京:科学出版社, 1983.
[14] Bernitsas, M. M. Riser top tension and riser buckling loads. Computer Methods for Offshore Structures, ASME, New York, pp.101-109, 1980.
[15] Bernitsas, M.M., Kokkinis, T. Buckling of columns with nonmovable boundaries, Journal of Engineering Structures, ASCE, 1983, 105: 2113-2128.
[16] Bernitsas, M.M., Kokkinis, T. Buckling of columns with movable boundaries. Journal of Structural Engineering, ASCE, 1983, 11: 351-370.
[17] Bernitsas, M.M., Kokkinis, T. Asymptotic behavior of heavy column and riser stability boundaries. Journal of Applied Mechanics, ASME, 1984, 51: 560-565.
[18] Vaz, M. A., Patel, M. H. Analysis of drill strings in vertical and deviated holes using the Galerkin technique. Engineering Structures, 1995, 17: 437-442.
[19] Donnell, L.H. A new theory for the buckling of thin cylinders under axial compression and bending. Transaction ASME, 1934, 56: 775-806.
[20] Karman, T.V., Tsien, H.S. The buckling of spherical shell by external pressure. Journal of Aeronaut Science, 1937, 7: 43-50.
[21] Karman, T.V., Tsien, H.S. The buckling of thin cylindrical shell under axial compression. Journal of Aeronaut Science, 1941, 8: 303-312.
[22] Karman, T.V., Tsien, H.S. A theory for the buckling of thin shells. Journal of Aeronaut Science, 1942, 9: 373-384.
[23] Stein, M. The effect on the buckling of perfect cylinders of prebuckling deformations and stresses induced by edge support. NASA TN D-1510, 1962.
[24] Stein, M. The influence of pre-buckling deformations and stresses on the buckling of perfect cylinders. NASA TR-190, 1964.
[25] Koiter, W.T. On the stability of elastic equilibrium (in Dutch). PhD Thesis, Delft, H. J. Paris, Amsterdam; also NASA TTF-10, 833, 1967.
[26] Koiter, W.T. Elastic stability and postbuckling behavior. In Nonlinear Problems (ed. by Langer, R.E.) University of Wisconsin Press, 1963.
[27] Budiansky, B., Hutchinson, J.W. A survey of some buckling problems. AIAA Journal, 1966, 4: 1505-1510.
[28] Babcock, C.D. Shell stability. Journal of Applied Mechanics, 1983, 50: 935-940.
[29] Simitses, G.J. Buckling and postbuckling of imperfect cylindrical shells: a review. ASME, Applied Mechanics Reviews, 1986, 39: 1517-1524.
[30] Simitses, G.J., Anastasiadis, J.S. Shear deformable theories for cylindrical laminates- equilibrium and buckling with applications. AIAA Journal, 1992, 30: 826-834.
[31] Simitses, G.J., Tabiei, A., Anastasiadis, J.S. Buckling of moderately thick laminated cylindrical shells under lateral pressure. Composites Engineering, 1993, 3: 409-417.
[32] Teng, J.G. Buckling of thin shells: recent advances and trends. Applied Mechanics Reviews, 1996, 49: 263-274.
[33]王俊奎,王虎.复合材料薄壁壳体的稳定性.航空学报, 1991, 12(12): 598-605.
[34]杜启端.现代薄壳非线性稳定性理论的发展和应用.强度与环境, 2002, 29(1): 41-58.
[35]白雪飞,郭日修.近代弹性稳定性理论的几个重要分支.海军工程大学学报, 2004, 16(3):40-46.
[36]周利,黄义.薄壳非线性稳定理论的最新发展.建筑钢结构进展, 2006, 8(4): 23-32.
[37]陈铁云,沈惠申.结构的屈曲.上海:上海科学技术文献出版社, 1993.
[38]沈惠申.板壳后屈曲行为.上海:上海科学技术出版社, 2002.
[39] Tielemann, W.F., Esslinger, M.E. On the postbuckling behavior of thin-walled, axially compressed circular cylinders of finite length. Proceedings of Symposium of the Theory of Shells (ed. by Muster, D.), 1967, pp. 433-479, University of Houston.
[40] Yamaki, N., Otomo, K., Matsuda, K. Experiments on the postbuckling behavior of circular cylindrical shells under compression. Experimental Mechanics, 1975, 15: 23-28.
[41] Yamaki, N. Elastic stability of circular cylindrical shells. Elsevier Science Publishers, B.V., 1984.
[42] Tennyson, R.C., Muggeridge, D.B. Buckling of laminated anisotropic imperfect circular cylinders under axial compression. Journal of Spacecraft, 1973, 10: 143-148.
[43] Katz, L. Compression tests on integrally stiffened cylinders. NASA TM X-55315.
[44] Seleim, S.S., Roorda, J. Theoretical and experimental results on the post-buckling of ring-stiffened cylinders. Mechanics of Structures and Machines, 1987, 15: 69-87.
[45] Tennyson, R.C. Buckling of laminated composite cylinders: a review. Composites, 1975, 6: 17-24.
[46] Yamaki, N. Postbuckling and imperfection sensitivity of circular cylindrical shells under compression. In Theoretical and Applied Mechanics (ed. by Koiter, W.T.), pp. 461-476, North-Holland Publishing Co, 1976.
[47]沈惠申.近海平台管状构件弹性稳定性[博士学位论文].上海:上海交通大学, 1986.
[48]沈惠申,陈铁云.圆柱薄壳在外压作用下屈曲的边界层理论.应用数学和力学, 1988, 9: 515-527.
[49] Shen, H.-S., Chen, T.-Y. A Boundary layer theory for the buckling of thin cylindrical shells under axial compression. In Advances in Applied Mathematics and Mechanics in China (eds. Chien, W.Z. and Fu, Z.Z.), 1990, Vol. 2, pp 155-172, International Academic Publishers.
[50] Shen, H.-S., Chen, T.-Y. Buckling and postbuckling behaviour of cylindrical shells under combined external pressure and axial compression. Thin-Walled Structures, 1991, 12: 321-334.
[51] Stum, R.G. A study of the collapsing pressure of thin-walled cylinders. Engineering Experimental Statistics, Bull. No. 329, University Illinois, 1941.
[52] Weigarten, V.I., Seide, P. Elastic stability of thin-walled cylindrical and concial shells under combined external pressure and axial compression. AIAA Journal, 1965, 3: 913-920.
[53] Winderburg, D.F., Trilling, C. Collapse by instability of thin cylindrical shells under externalpressure. Transaction ASME, 1934, 56: 819-825.
[54] Yamaki, N., Otomo, K.. Experiments on the postbuckling behavior of circular cylindrical shells under hydrostatic pressure. Experimental Mechanics, 1973, 13: 299-304.
[55]沈惠申,周频,陈铁云.加肋圆柱壳在轴压作用下的屈曲和后屈曲.应用数学和力学, 1991, 12: 1127-1139.
[56] Shen, H.-S. Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and axial compression. Computers and Structures, 1997, 63: 335-348.
[57] Shen, H.-S. Postbuckling analysis of stiffened laminated cylindrical shells under combined external liquid pressure and axial compression. Engineering Structures, 1998, 20: 738-751.
[58] Shen, H.-S. Thermal postbuckling analysis of imperfect stiffened laminated cylindrical shells. International Journal of Non-linear Mechanics, 1997, 32: 259-275.
[59] Shen, H.-S. Thermomechanical postbuckling of stiffened laminated cylindrical shell. Journal of Engineering Mechanics, 1997, 123: 433-443.
[60] Shen, H.-S. Thermomechanical postbuckling of composite laminated cylindrical shells with local geometric imperfections. International Journal of Solids and Structures, 1999, 36: 597-617.
[61] Shen, H.-S. Hygrothermal effects on the post-buckling of composite laminated cylindrical shells. Composites Science and Technology, 2000, 60: 1227-1240.
[62]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.应用数学和力学, 2001, 22: 228-238.
[63] Shen, H.-S. Postbuckling analysis of axially-loaded laminated cylindrical shells with piezoelectric actuators. European Journal of Mechanics A-Solids, 2001, 20: 1007-1022.
[64] Shen, H.-S. Thermal postbuckling analysis of laminated cylindrical shells with piezoelectric actuators. Composite Structures, 2002, 55: 13-22.
[65] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part I: prediction under axial compression. Composite Structures, 2008, 82: 346-361.
[66] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part II: prediction under external pressure. Composite Structures, 2008, 82: 362-370.
[67] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part III: prediction under torsion. Composite Structures, 2008, 82: 371-381.
[68] Reddy, J.N., Liu, C.F. A higher-order shear deformation theory of laminated elastic shells.International Journal of Engineering Sciences, 1985, 23: 319-330.
[69] Shen, H.-S. Postbuckling of shear deformable cross-ply laminated cylindrical shells under combined external pressure and axial compression. International Journal of Mechanical Sciences, 2001, 43: 2493-2523.
[70] Shen, H.-S. Postbuckling of shear deformable laminated cylindrical shells. Journal of Engineering Mechanics, ASCE, 2002, 128: 296-307.
[71] Shen, H.-S., Li, Q.S. Thermomechanical postbuckling of shear deformable laminated cylindrical shells with local geometric imperfections. International Journal of Mechanical Sciences, 2002, 39: 4525-4542.
[72] Shen, H.-S. Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments. Engineering Structures, 2003, 25: 487-497.
[73] Shen, H.-S. Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties. International Journal of Solids and Structures, 2004, 41: 1961-1974.
[74] Shen, H.-S. Postbuckling prediction of double-walled carbon nanotubes under hydrostatic pressure. International Journal of Solids and Structures, 2004, 41: 2643-2657.
[75] Shen, H.-S., Zhang, C.-L. Postbuckling prediction of axially loaded double-walled carbon nanotubes with temperature dependent properties and initial defects. Physical Review B 2006, 74: 035410, 1-16.
[76] Dow, M.B., Dexter, B.H. Development of stitched, braided and woven composite structures in the ACT program and at Langley Research Center (1985 to 1997) summary and bibliography. NASA/TP-97-206234.
[77] Kamiya, R., Cheeseman, B.A., Popper, P., Chou, T.W. Some recent advances in the fabrication and design of three-dimensional textile preforms. Composites Science and Technology, 2000, 60: 33-47.
[78]王波.三维编织复合材料力学行为研究[博士学位论文].西安:西北工业大学, 2003.
[79]陶肖明,冼杏娟,高冠勋.纺织结构复合材料.北京:科学出版社, 2001.
[80]杨朝坤.三维编织复合材料细观结构平均刚度及其压缩性能的研究[博士学位论文].天津:天津工业大学, 2003.
[81] Ko, F.K. Three-dimensional fabrics for composites-an introduction to the magna weave structure. Proceedings ICCM-4 Japan Society, Composite Material, Tokyo, Japan, 1982, pp. 1609.
[82] Li, W., Hammad, M., El-Shiekh, A. Structural analysis of 3-D braided performs for composites partI: the Four-step performs. Journal of Textile Institute, 1990, 81: 491-514.
[83] Ma, C.L., Yang, J.M., Chou, T.W. Elastic stiffness of three-dimensional braided textile structure composites. ASTM STP 893, Composite Materials: Testing and Design, Philadelphia, 1986, 404-421.
[84] Yang, J.M., Ma C.L., Chou T.W. Fiber inclination model of three dimensional textile structural composites. Journal of Composite Material, 1986, 20: 472-484.
[85] Sun H.Y., Qiao, X. Prediction of mechanical properties of three-dimensionally braided composites. Composites Science and Technology, 1997, 57: 623-629.
[86]孙慧玉.编织结构复合材料的力学性能预报和成型工艺研究[博士学位论文].南京:南京航空航天大学, 1996.
[87]吴德隆,郝兆平.五向编织结构复合材料的分析模型.宇航学报,1993, 14(3): 40-51.
[88] Wu, D.L. Three-cell model and 5D braided structural composites. Composites Science and Technology, 1996, 56: 225-233.
[89] Chen, L., Tao, X.M., Choy, C.L. On the microstructure of three-dimensional braided performs. Composite Science and Technology, 1999, 59: 391-404.
[90] Chen, L., Tao, X.M., Choy, C.L. A study on the microstructure of three-dimensional braids, Eleventh International Conference on Composite Materials, p. 317-327, Australia, July, 1997.
[91]陈利.三维编织复合材料的细观结构及其弹性性能分析[博士学位论文].天津:天津纺织工学院, 1998.
[92] Whitney, T.J, Chou T.W. Modeling of 3-D angle-interlock textile structural composite. Journal of Composite Material, 1989, 23: 890-911.
[93] Crane, R.M., Camponeschi, E.T. Experimental and analytical characterization of multi- dimensionally braided graphite/epoxy composites. Experiment Mechanics, 1986, 19: 259-266.
[94] Yasar, B. Analysis of braided composite laminate. M.S. thesis, the University of Taxas at Arlington, 2003.
[95]梁军.三维编织复合材料力学性能的细观研究[博士学位论文].哈尔滨:哈尔滨工业大学, 1996.
[96]梁军,杜善义.一种含特定微型纹缺陷三维编织复合材料弹性常数预报方法.复合材料学报,1997, 14(1): 101-107.
[97]梁军,陈晓峰等.多向编织复合材料的力学性能研究.力学进展, 1999, 29(2): 197-210.
[98] Chou, T.W. Microstructural Design of Fiber Composites. Cambridge University Press 1992.
[99] Feder, E. Algorithmic problems in the braid group. Ph.D. thesis, the City University of New York,2003.
[100] Mohajerjasbi, S. Modeling and analysis of 4-step 3-D cartesian braiding composites including axial yarns. Proceedings of the 36th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics, and Materials Conference and AIAA/ASME Adaptive Structure Forum. 1995, 8-16.
[101] Li, J., Pu, S., Chen, A.E. Construction and geometry of 6-step braided performs for composites. 39th international SAMPE Symposium, April, 1994, 826-833.
[102] Hiroyuki, H., Asami, N., Akihiro, F., Zenichiro, M. CAE in integrated braided composite. Science and Engineering of Composite Materials. 1995, 4: 109-120.
[103] Walrath, D.E., Adeams, D.F. Finite element micromechanics and minimechanics modeling of a three-dimensional carbon-carbon composite material. ADA 168050, 1995.
[104]赫晓东.编织复合材料的细观计算力学研究[博士学位论文].哈尔滨:哈尔滨工业大学, 1992.
[105] Whyte, D.E., Pastore, C.M., Ko, F.K. A fabric geometry model for 3-D braid reinforced FP/Al-Li composites. Inter SAMPE Metal Cont, Competitive Advances in Metals/Metal Processing, Cherry Hill, Aug. 1997, 18-21.
[106] Lei, C., Wang, A.S., Ko, F.K. A finite cell model for 3D braided composites. ASME Winter Annual Meeting, Chicago USA, 1988.
[107] Whitcomb, J.D. Three-dimensional stress analysis of plain weave composites. in: 3rd Symposium on Composite Materials: Fatigue and Fracture, ASTM, USA, Oct. 1989.
[108]庞宝君.三维多向编织复合材料力学性能预报与优化设计研究[博士学位论文].哈尔滨:哈尔滨工业大学, 1997.
[109]张文毅,姚振汉,姚学锋,曹艳平.编织复合材料的一种数值模型.工程力学, 2004, 21(3): 55-60.
[110]燕瑛.编织复合材料弹性性能的细观力学模型.力学学报, 1997, 29(4): 429-438.
[111]徐孝诚,孙德海,黄小平.三维编织复合材料细观结构的几何学分析.强度与环境, 1999, 26(2): 37-43.
[112]陈利,李嘉禄,李学明.三维四步法圆形编制结构分析.复合材料学报, 2003, 20(2): 76-80.
[113] Wang, Y.Q., Wang, A.S.D. Spatial distribution of yarns and mechanical properties in 3D braided tubular composites applied. Composite Materials, 1997, 4: 121-132.
[114] Sun, X.K. Micro-geometry of 3-D braided tubular preform. Journal of Composite Materials 2004, 38: 791-98.
[115]马文锁,冯伟.三维管状编织复合材料及其构件可变微单元几何分析模型.复合材料学报, 2005, 22(5): 162-171.
[116]柴雅凌.矩形和圆形三维编织预制件中纱线的拓朴学结构.纤维复合材料, 1996, 1: 23-30.
[1] Khot, N.S., Venkaya, V.B. Effect of fiber orientation on initial postbuckling behavior and imperfection sensitivity of composite cylindrical shells. AFFDL-TR-70-125, 1970.
[2] Tennyson, R.C., Muggeridge, D.B. Buckling of laminated anisotropic imperfect circular cylinders under axial compression. Journal of Spacecraft, 1973, 10: 143-148.
[3] Bisagni, C. Experimental buckling of thin composite cylinders. AIAA Journal, 1999, 37: 276-278.
[4] Chryssanthopoulos, M.K., Elghazouli, A.Y., Esong, I.E. Compression tests on anti-symmetric two-ply GFRP cylinders. Composites: Part B, 1999, 30: 335-350.
[5]武兰河.加权残数法分析前屈曲变形对复合材料层迭圆柱壳屈曲载荷的影响.石家庄铁道学院学报, 1997, 10(1): 40-47.
[6]李媛,利凤祥,李越森,王锟,胡春波.复合材料壳体轴压稳定性分析.固体火箭技术, 2004, 27(4): 280-284.
[7] Zhou,C.T. The computation of nonlinear instability for multi-layer composite cylindrical shells. Applied Mathematics and Mechanics, 1986, 7: 17-23.
[8] Hilburger, M.W., Starnes Jr. JH. Effects of imperfections of the buckling response of compositeshells. Thin-Walled Structures, 2004, 42: 369-397.
[9] Geier, B., Meyer-Piening, H.R., Zimmermann, R. On the influence of laminate stacking on buckling of composite cylindrical shells subjected to axial compression. Composite Structures, 2002, 55: 467-474.
[10]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.华东船舶工业学院学报, 1999, 13(2): 42-46.
[11]张建武,徐延海,吴金松.反对称正交铺层剪切圆柱壳在轴压下的屈曲分析.上海交通大学学报, 2002, 36(3): 411-415.
[12] Mao, R.J., Williams, F.W. Nonlinear analysis of cross-ply thick cylindrical shells under axial compression. International Journal of Solids and Structures, 1998, 35: 2151-2171.
[13] Ye, J.Q., Soldatos, K.P. Three-dimensional buckling analysis of laminated hollow cylinders and cylindrical panels. International Journal of Solids and Structures, 1995, 32: 1949-1962.
[14] Iu, V.P., Chia, C.Y. Effect of transverse shear on nonlinear vibration and postbuckling of anti-symmetric cross-ply imperfect cylindrical shells. International Journal of Mechanical Science, 1988, 30: 705-718.
[15]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.导弹与航天运载技术, 2001, (2): 24-28.
[16] Han, B., Simitses, G.J. Analysis of anisotropic laminated cylindrical shells subjected to destabilizing loads, Part II: numerical results. Composite Structures, 1991, 19: 183-205.
[17] Tabiei, A., Simitses, G. Imperfection sensitivity of shear deformable moderately thick laminated cylindrical shells. Computers & Structures, 1997, 62: 165-174.
[18] Simitses, G.J., Anastasiadis, J.S. Buckling of axially-loaded, moderately-thick, cylindrical laminated shells. Composites Engineering, 1991, 1: 375-391.
[19] Reddy, J.N., Savoia, M. Layer-wise shell theory for postbuckling of laminated circular cylindrical shells. AIAA Journal, 1992, 30: 2148-2154.
[20] Eslami, M.R., Shariyat, M., Shakeri, M. Layerwise theory for dynamic buckling and postbuckling of laminated composite cylindrical shells. AIAA Journal, 1998, 36: 1874-1882.
[21] Eslami, M.R., Shariyat, M. A higher-order theory for dynamic buckling and postbuckling analysis of laminated cylindrical shells. ASME Journal of Pressure Vessel Technology, 1999, 121: 94-102.
[22] Weaver, P.M. The effect of extension/twist anisotropy on compression buckling in cylindrical shells. Composites: Part B, 2003, 34: 251-260.
[23] Weaver, P.M., Driesen, J.R., Roberts, P. The effect of flexural/twist anisotropy on compression buckling of quasi-isotropic laminated cylindrical shells. Composite Structures, 2002, 55: 195-204.
[24] Wong, K.F.W., Weaver, P.M. Approximate solution for the compression buckling of fully anisotropic cylindrical shells. AIAA Journal, 2005, 43: 2639-2645.
[25] Takano, A. Improvement of Flügge’s equations for buckling of moderately thick anisotropic cylindrical shells. AIAA Journal, 2008, 46: 903-911.
[26] Reddy, J.N., Liu, C.F. A higher-order shear deformation theory of laminated elastic shells. International Journal of Engineering Sciences, 1985, 23: 319-330.
[27] Donnell, L.H. Stability of thin walled tubes under torsion. NACA Report No. 479, 1933.
[28]沈惠申.板壳的后屈曲行为.上海:上海科学技术文献出版社, 2002.
[29] Shen, H.-S. Thermal buckling and postbuckling of laminated plates. In Analysis and Design of Plated Structures (eds. Shanmugam, N.E. and Wang, C.M.), Vol. 1 Stability, pp. 170-213, Woodhead Publishing Ltd, 2006.
[30] Batdorf, S.B. A simplified method of elastic-stability analysis for thin cylindrical shells. NACA TR-874, 1947.
[31] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part I: prediction under axial compression. Composite Structures, 2008, 82: 346-361.
[32] Simitses, G.J., Anastasiadis, S.J. Shear deformable theories for cylindrical laminates- equilibrium and buckling with applications. AIAA Journal, 1992, 30: 826-834.
[33] Fahadinia. M. Finite element analysis and experimental evaluation of buckling phenomena in laminate composite tubes and plates. PhD. Thesis, University of Missouri-Rolla, 1992.
[34] Arciniega, R.A., Goncalves, P.B., Reddy, J.N. Buckling and postbuckling analysis of laminated cylindrical shells using third-order shear deformable theory. International Journal of Structural Stability and Dynamics, 2004, 4: 293-312.
[35] Yuan, F.G., Hsieh, C.C. Three-dimensional wave propagation in composite cylindrical shells. Composite Structures, 1998, 42: 153-167.
[36] Li, Z.-M., Shen, H.-S. Postbuckling of shear deformable anisotropic laminated cylindrical shell under axial compression. International Journal of Structural Stability and Dynamics.(in press)
[1] Ouellette, P., Hoa, S.V., Sankar, T.S. Buckling of composite cylinders under external pressure. Polymer Composites, 1986, 7: 363-374.
[2] Smerdov, A.A. A computational study in optimum formulations of optimization problems on laminated cylindrical shells for buckling II, Shells under external pressure. Composites Science and Technology, 2000, 60: 2067-2076.
[3]周承倜,周建平.多层复合材料圆柱壳的非线性失稳计算.应用数学和力学, 1986, 7(1): 17-23.
[4]杜建科,田晓耕,沈亚鹏,陈汝训.复合材料燃烧室均布侧压下稳定性分析.固体火箭技术, 2002, 25(2): 18-21.
[5] Carvelli, V., Panzeri, N., Poggi, C. Buckling strength of GFRP under-water vehicles. Composite Part: B, 2001, 32: 89-101.
[6] Messager, T. Buckling of imperfect laminated cylinders under hydrostatic pressure. Composite Structures, 2001, 53: 301-307.
[7] Messager, T., Pyrz, M., Gineste, B., Chauchot, P. Optimal laminations of thin underwater composite cylindrical vessels. Composite Structures, 2002, 58: 529-537.
[8] Yousefpour, A. Design, analysis, manufacture, and test of composite pressure vessels and finite element analysis of metallic frame for deep ocean underwater vehicle applications. PhD. thesis, University of Hawaii, December, 2000.
[9] Chucheepsakul, S., Monprapussorny, T. Nonlinear buckling of marine elastica pipes transporting fluid. International Journal of Structural Stability and Dynamics, 2001, 1: 333-365.
[10]王永志,向锦武.复合材料旋转壳稳定性有限元分析和横向剪切变形的影响分析.复合材料学报, 2006, 23(4): 175-179.
[11]王震鸣.复合材料力学和复合材料结构力学.北京:机械工业出版社, pp.418-420, 1991.
[12] Han, B., Simitses, G.J. Analysis of anisotropic laminated cylindrical shells subjected todestabilizing loads, Part II: numerical results. Composite Structures, 1991, 19: 183-205.
[13] Simitses, G.J., Anastasiadis, J.S. Shear deformable theories for cylindrical laminates- equilibrium and buckling with applications. AIAA Journal, 1992, 30: 826-834.
[14] Simitses, G.J., Tabiei, A., Anastasiadis, J.S. Buckling of moderately thick laminated cylindrical shells under lateral pressure. Composites Engineering, 1993, 3: 409-417.
[15] Kasagi, A., Sridharan, S. Imperfection sensitivity of layered composite cylinders, ASCE Journal of Engineering Mechanics, 1995, 121: 810-818.
[16] Eslami, M.R., Shariyat, M., Shakeri, M. Layerwise theory for dynamic buckling and postbuckling of laminated cylindrical shells. AIAA Journal, 1998, 36: 1874-1882.
[17] Eslami, M.R., Shariyat, M. A higher-order theory for dynamic buckling and postbuckling analysis of laminated cylindrical shells. ASME Journal of Pressure Vessel Technology, 1999, 121: 94-102.
[18] Arciniega, R.A., Goncalves, P.B., Reddy, J.N. Buckling and postbuckling analysis of laminated cylindrical shells using third-order shear deformable theory. International Journal of Structural Stability and Dynamics, 2004, 4: 293-312.
[19]沈惠申.板壳的后屈曲行为.上海:上海科学技术文献出版社, 2002.
[20] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part II: prediction under external pressure. Composite Structures, 2008, 82: 362-370.
[21] Yuan, F.G., Hsieh, C.C. Three-dimensional wave propagation in composite cylindrical shells. Composite Structures, 1998, 42: 153-167.
[22] Li, Z.-M. Postbuckling of shear deformable anisotropic laminated cylindrical shell under external pressure in thermal environments. Mechanics of Composite Materials, 2007, 43: 535-560.
[1]周建钢,熊鹰.复合材料推进器.航海工程, 2004, 14(5): 33-35.
[2] Simitses G.J., Shaw, D., Sheinman, I. Stability of imperfect laminated cylinders: a comparison between theory and experiment. AIAA Journal, 1985, 23: 1086-1092.
[3] Wilkins, D.J., Love, T.S. Compression-torsion buckling test of laminated composite cylindrical shells. AIAA paper, pp. 74-379, 1974.
[4]周承倜,周建平.多层复合材料圆柱壳的非线性失稳计算.应用数学和力学, 1986, 7(1): 17-23.
[5] Tennyson, R.C. Buckling of laminated composite cylinders: a review. Composites, 1975, 6: 17-24.
[6] Huille, A., Yang, C., Pang, S.S. Buckling analysis of thick-walled composite pipe under torsion. ASME Journal of Pressure Vessel Technology, 1997, 119: 111-116.
[7] Shaw, D., Simitses G.J. Insability of laminated cylinders in torsion. ASME Journal of Applied Mechanics, 1984, 51: 188-190.
[8]黄晓东,茅人杰.具有力边条件的层合圆柱薄壳的扭转屈曲.上海交通大学学报, 2000, 34(8): 1146-1149.
[9] Mao, R., Lu, C.H. Buckling analysis of a laminated cylindrical shell under torsion subjected to mixed boundary conditions. International Journal of Solids and Structures, 1999, 36: 3821-3835.
[10] Tan, D. Torsional buckling analysis of thin and thick shells of revolution. International Journal of Solids and Structures, 2000, 37: 3055-3078.
[11] Park, H.C., Cho, C., Choi, Y. Torsional buckling analysis of composite cylinders. AIAA Journal, 2001, 39: 951-955.
[12] Tabiei, A., Simitses G.J. Buckling of moderately thick laminated cylindrical shells under torsion. AIAA Journal, 1994, 32: 639-647.
[13] Tabiei, A., Simitses, G.J. Torsional instability of moderately thick composite cylindrical shells by various shell theories. AIAA Journal, 1997, 37: 1243-1246.
[14] Batdorf, S.B. A simplified method of elastic-stability analysis for thin cylindrical shells. NACA TR-874, 1947.
[15] Loo, T.T. Effects of large deflections and imperfections on the elastic buckling of cylinders under torsion and axial compression. In: Proceedings of the 2nd US national congress on applied mechanics, pp. 345-357, 1954.
[16] Nash, W.A. Buckling of initially imperfect cylindrical shells subjected to torsion. ASME Journal of Applied Mechanics, 1957, 24: 125-130.
[17] Shen, H.-S. Boundary layer theory for the buckling and postbuckling of an anisotropic laminated cylindrical shell, Part III: prediction under torsion. Composite Structures, 2008, 82: 371-381.
[18]沈惠申.板壳的后屈曲行为.上海:上海科学技术文献出版社, 2002.
[19] Herakovich, C.T., Johnson, E.R. Buckling of composite cylinders under combined compression and torsion-theoretical/experimental correlation. Test Methods and Design Allowable for Fibrous Composites, ASTM STP 734, (ed. Chamis, C.C.) American Society for Testing Materials, Philadelphia, PA, pp. 341-360, 1981.
[20] Wu, C.H. Buckling of anisotropic circular shells. Ph.D. Dissertation, Case Western Reserve University, Cleveland, OH, 1971.
[21] Ambrose, H.S., Walter, R.,Goldie, B. Torsion tests of tubes, NACA TR-601, 1937.
[22] Derstine, M.S., Pindera, M.J., Bowles, D.E. Combined mechanical loading of composite tubes, NASA CR-183012, 1988.
[23] Yuan, F.G., Hsieh, C.C. Three-dimensional wave propagation in composite cylindrical shells. Composite Structures, 1998, 42: 153-167.
[24] Li, Z.-M., Shen, H.-S. Postbuckling of shear deformable anisotropic laminated cylindrical shell under torsion. Mechanics of Advanced Materials and Structures.(in press)
[1]何煌.编织复合材料圆柱壳的稳定性分析[硕士学位论文].长沙:国防科技大学, 2003.
[2]何煌,唐国金,蒋志刚,王可晟.编织复合材料圆柱壳蠕变屈曲分析,重庆交通学院学报, 2003, 22(4): 35-38.
[3]张雪丽,果立成,曾涛,吴林志,马力.三维编织复合材料圆柱壳的稳定性研究.哈尔滨工业大学学报, 2003, 35(2): 222-226.
[4] Tasi, J., Feldman, A., Stang, D.A. The buckling strength of filament-wound cylinders loaded in axial compression. NASA CR-266, 1965.
[5] Card, M.F. Experiments to determine the strength of filament-wound cylinders loaded in axial compression. NASA TN D-3522, 1966.
[6] Jensen, D.W., Pai, S.P. Influence of local fiber undulation on the global buckling of filament-wound cylinders. Journal of Reinforced Plastics and Composites, 1993, 12: 865-875.
[7] Pai, S.P., Jensen, D.W. Influence of fiber undulations on buckling of thin filament-wound cylinders in axial compression. Journal of Aerospace Engineering, 2001, 14: 12-20.
[8] Chyssanthopoulos, M.K., Elghazouli, A.Y., Esong, I.E. Validation of FE models for buckling analysis of woven GFRP shells. Composite Structures, 2000, 49: 355-367.
[9]张平,桂良进,范子杰.编织复合材料圆管准静态轴向压缩吸能特性的试验研究. 2007, 24(1): 144-150.
[10] Harte, A.M., Fleck, N.A. Deformation and failure mechanics of braided composite tubes in compression and torsion. Acta Materialia, 2000, 48: 1259-1271.
[11] Shu, C.Q., Anthony, M.W., Khaled, W.S., Venkatesh, A. Compressive response and failure of braided textile composites: Part 1-experiments. International Journal of Non-Linear Mechanics, 2004, 39: 635-648.
[12] Shu, C.Q., Anthony, M.W., Khaled, W.S., Venkatesh, A. Compressive response and failure of braided textile composites: Part 1-computations. International Journal of Non-Linear Mechanics, 2004, 39: 649-663.
[13] Wong, W.H., Ip, K.H., Tse, P.C. Buckling stresses of composite tubes under biaxial compressive loads. Experimental Mechanics, 1998, 38: 126-131.
[14] Kuo, W.S., Ko T.H., Shiah, Y.C. Compressive damage in three-axis woven thermoplastic composites. Journal of Thermoplastic Composite Materials 2006, 19: 357-373.
[15] Spagnoli, A., Elghazouli, A.Y., Chryssanthopoulos, M.K. Numerical simulation of glass-reinforced plastic cylinders under axial compression. Marine Structures, 2001, 14: 353-374.
[16] Zeng, T., Wu, L.Z. Post-buckling analysis of stiffened braided cylindrical shells under combined external pressure and axial compression. Composite Structures, 2003, 60: 455-466.
[17] Shen, H.-S., Chen, T.-Y. A boundary layer theory for the buckling of thin cylindrical shells under external pressure. Applied Mathematics and Mechanics, 1988, 9: 557-571.
[18] Shen, H.-S., Chen, T.-Y. A boundary layer theory for the buckling of thin cylindrical shells under axial compression. In: Advances in Applied Mathematics and Mechanics in China (eds. Chien, W.Z., Fu, Z.Z.), vol. 2, pp. 155-172, International Academic Publishers, Beijing, China, 1990.
[19] Shen, H.-S. Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and axial compression. Computers and Structures, 1997, 63: 335-348.
[20] Shen, H.-S., Li, Q.S. Thermomechanical postbuckling of shear deformable laminated cylindrical shells with local geometric imperfections. International Journal of Solids and Structures, 2002, 39: 4525-4542.
[21] Li, Z.-M. Nonlinear vibration analysis of 3D braided rectangular plates on elastic foundations. Journal of Ship Mechanics (in press).
[22]陶肖明,冼杏娟,高冠勋.纺织结构复合材料.北京:科学出版社, 2001.
[23] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal Composites Materials, 1968, 2: 380-404.
[24] Adams, D.F., Crane, D.A. Combined loading micromechanical analysis of a unidirectional composite. Composites, 1984, 15: 181-192.
[25] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, USA, 1991.
[26] Li, Z.-M., Shen, H.-S. Postbuckling analysis of three-dimensional textile composite cylindrical shells under axial compression in thermal environments. Composites Science and Technology, 2008, 68: 872-879.
[1] Rosenow, M.W.K. Wind angle effects in glass fibre reinforced polyester filament wound pipes. Composites, 1984, 15: 144-152.
[2] Ouellette, P., Hoa, S.V., Sankar, T.S. Buckling of composite cylinders under external pressure. Polymer Composites, 1986, 7: 363-374.
[3] Olivas, J.D., Ravi-Chandar, K., Bustillos, J., Craigie, L. Buckling of filament-wound cylindrical vessels subjected to external pressure. Journal of Pressure Vessel Technology ASME, 1996, 118: 216-220.
[4] Messager, T., Pyrz, M., Gineste, B., Chauchot, P. Optimal laminations of thin underwater composite cylindrical vessels. Composite Structures, 2002, 58: 529-537.
[5] Yousefpour, A., Ghasemi Nejhad, M.N. Design, analysis, manufacture, and test of APC-2/AS4 thermoplastic composite pressure vessels for deep water marine applications. Journal of Composite Materials, 2004, 38: 1701-1732.
[6] Calme, O., Bigaud, D., Hamelin, P. 3D braided composite rings under lateral compression. Composite Science and Technology, 2005, 65: 95-106.
[7]徐孝诚,马斌捷.三维四向整体编织复合材料圆筒壳体临界外压计算及试验验证.复合材料学报, 1999, 16(4): 136-141.
[8]谢禹均,邬柱,刘占民.混杂纤维缠绕圆柱壳外压稳定性与缠绕参数.复合材料学报, 1995, 12(1): 106-110.
[9]王晓华.纤维缠绕外压容器稳定性最佳铺层分析.抚顺石油学院学报, 1997, 17(4): 22-25.
[10]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.中国机械工程, 2007, 18(3): 286-290.
[11] Shen, H.-S. The effects of hygrothermal conditions on the postbuckling analysis of shear deformable laminated cylindrical shells. International Journal of Solids and Structures, 2001, 38: 6357-6380.
[12] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal Composites Materials, 1968, 2: 380-404.
[13] Adams, D.F., Crane DA. Combined loading micromechanical analysis of a unidirectional composite. Composites, 1984, 15: 181-192.
[14] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, 1991.
[15]李志敏,沈惠申.三维编织复合材料圆柱壳外压下的屈曲分析.固体力学学报, 2008, 29(1): 52-58.
[1] Harte, A.M., Fleck, N.A. Deformation and failure mechanics of braided composite tubes in compression and torsion. Acta Materialia, 2000, 48: 1259-1271.
[2] Wall, L.D., Jr, Card, M.F. Torsional shear strength of filament-wound glass-epoxy tubes. NASA TN D-6140, 1971.
[3] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal of Composites Materials, 1968, 2: 380-404.
[4] Karamia, G., Garnichb, M. Micromechanical study of thermoelastic behavior of composites with periodic fiber waviness. Composites: Part B, 2005, 36: 241-248.
[5] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, USA, 1991.
[6] Li, Z.-M., Shen, H.-S. Postbuckling analysis of 3D braided composite cylindrical shells under torsion in thermal environments. Composite Structures.(in press)
[1] Chucheepsakul, S., Monprapussorny, T. Nonlinear buckling of marine elastica pipes transporting fluid. International Journal of Structural Stability and Dynamics, 2001, 1: 333-365.
[2] Weingarten, V.I., Seide, P. Elastic stability of thin-walled cylindrical and conical shells under combined external pressure and axial compression. AIAA Journal, 1965, 3:913-920.
[3] Yousefpour, A., Ghasemi Nejhad, M.N. Design, analysis, manufacture, and test of APC-2/AS4 thermoplastic composite pressure vessels for deep water marine applications. Journal of Composite Materials, 2004, 38:1701-1732.
[4] Mouritz, A.P., Gellert, E., Burchill, P., Challis, K. Review of advanced composite structures for naval ships and submarines. Composites Structures, 2001, 53: 21-41.
[5] Kaddour, A.S., Soden, P.D., Hinton, M.J. Failure of±55 degree filament wound glass/epoxy composite tubes under biaxial compression. Journal of Composite Materials, 1998, 32:1618-1645.
[6] Dong, L., Mistry, J. An experimental study of the failure of composite cylinder subjected to combined external pressure and axial compression. Composite Structures, 1998, 40: 81-94.
[7] Mistry, J., Gibson, A.G., Wu, Y.S. Failure of composite cylinders under combined external pressure and axial loading. Composite Structures, 1992, 22:193-200.
[8] Mistry, J. Theoretical investigation into the effect the winding angle of the fibres on the strength of filament wound GRP pipes subjected to combined external pressure and axial compression. Composite Structures, 1992, 20: 83-90.
[9] Zeng T., Wu, L.Z. Post-buckling analysis of stiffened braided cylindrical shells under combined external pressure and axial compression. Composite Structures, 2003, 60: 455-466.
[10] Shapery, R.A. Thermal expansion coefficient of composite materials based on energy principles. Journal Composites Materials, 1968, 2: 380-404.
[11] Adams, D.F., Crane, D.A. Combined loading micromechanical analysis of a unidirectional composite. Composites, 1984, 15: 181-192.
[12] Lee, M.S. International Encyclopedia of Composites. Vol.6, VHC Publishers, New York, USA, 1991.
[13] Li, Z.-M., Shen, H.-S. Postbuckling analysis of 3D braided composite cylindrical shells under combined external pressure and axial compression in thermal environments. International Journal of Mechanical Sciences, 2008, 50: 719-731.