复合材料层合扁球壳的非线性热屈曲
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摘要
现代复合材料自60年代用作工程结构材料以来已取得很大成就。先进复合材料作为一种比较理想的结构材料和功能材料,具有许多独特的优点和重要的实用价值,其在工程中的应用多为板壳的形式。复合材料层合扁球壳在工程中应用广泛,且受力情况复杂,其力学性能的研究日益受到重视,由于非线性数学问题求解的困难,对复合材料层合扁球壳屈曲问题的研究比较有限,尤其是热屈曲问题。本文研究了复合材料层合扁球壳的非线性热屈曲问题,为复合材料层合扁球壳在工程中的应用提供一些有价值的参考。
本文首先回顾了国内外学者在板壳热屈曲问题方面所做过的主要工作,分析了研究的范围和方法。随后在几何非线性的基础上,考虑了横向剪切的影响,建立了复合材料层合扁球壳在均布荷载和温度场联合作用下的热屈曲控制方程。第三章中,对热屈曲控制方程在固定夹支、可移夹支、可移简支、不可移简支四种边界条件下采用修正迭代法进行了求解,求得了考虑温度场影响的非线性荷载—挠度关系式,临界屈曲荷载的解析表达式和临界几何参数的解析表达式,并用数值算例分析了几何参数,材料参数对临界荷载的影响,重点分析温度场的变化对临界荷载的影响,并对结果进行比较和分析。结果表明,热弯矩和热膜力的变化对临界荷载和临界几何参数有显著的影响。
Composite materials have been widely applied as engineering structure materials since 1960s. As excellent engineering materials and function materials , advanced composite materials have many unique merits and important practical values. Composite materials are widely used as plates and shells in engineering. The lanminated composite shallow spherical shells are widely applied in engineering, which are always under complicated loads. The research on the mechanical properties of lanminated composite shallow spherical shells is paid more and more attention. Because of the difficulty of solving nonlinear mathematical problems, there is only several research on buckling of lanminated composite shallow spherical shells, especially on thermal buckling of lanminated composite shallow spherical shells. The nonlinear thermal buckling of lanminated composite shallow spherical shell is studied in this paper, some valuable references are provided for the application of lanminated composite shallow spherical shells in engineering.In chapter one, the major work that both domestic and foreign scholars have done on thermal buckling of plates and shells is reviewed. The range of research and the methods of research are analyzed. In chapter two, the governing equation of thermal buckling is established based on nonlinear geometry, the effects of transverse shear deformation are taken into accounted. Finally, the governing equation is solved by the modified interation method in four types of boundary conditions which are immovably clamped supports, movably clamped supports, movably simply supports and immovably simply supports. The relationship between load and deformation, the analytical expression of critical load and the analytical expression of critical geometrical parameter under temperature are obtained. The effect of geometric parameters, the material parameters and the variation of temperature fields on critical load is analyzed, and the result is compared. The results show that the thermal moment and the thermal membrane force have remarkable effects on the critical loads and the critical geometrical
parameter.
本文首先回顾了国内外学者在板壳热屈曲问题方面所做过的主要工作,分析了研究的范围和方法。随后在几何非线性的基础上,考虑了横向剪切的影响,建立了复合材料层合扁球壳在均布荷载和温度场联合作用下的热屈曲控制方程。第三章中,对热屈曲控制方程在固定夹支、可移夹支、可移简支、不可移简支四种边界条件下采用修正迭代法进行了求解,求得了考虑温度场影响的非线性荷载—挠度关系式,临界屈曲荷载的解析表达式和临界几何参数的解析表达式,并用数值算例分析了几何参数,材料参数对临界荷载的影响,重点分析温度场的变化对临界荷载的影响,并对结果进行比较和分析。结果表明,热弯矩和热膜力的变化对临界荷载和临界几何参数有显著的影响。
Composite materials have been widely applied as engineering structure materials since 1960s. As excellent engineering materials and function materials , advanced composite materials have many unique merits and important practical values. Composite materials are widely used as plates and shells in engineering. The lanminated composite shallow spherical shells are widely applied in engineering, which are always under complicated loads. The research on the mechanical properties of lanminated composite shallow spherical shells is paid more and more attention. Because of the difficulty of solving nonlinear mathematical problems, there is only several research on buckling of lanminated composite shallow spherical shells, especially on thermal buckling of lanminated composite shallow spherical shells. The nonlinear thermal buckling of lanminated composite shallow spherical shell is studied in this paper, some valuable references are provided for the application of lanminated composite shallow spherical shells in engineering.In chapter one, the major work that both domestic and foreign scholars have done on thermal buckling of plates and shells is reviewed. The range of research and the methods of research are analyzed. In chapter two, the governing equation of thermal buckling is established based on nonlinear geometry, the effects of transverse shear deformation are taken into accounted. Finally, the governing equation is solved by the modified interation method in four types of boundary conditions which are immovably clamped supports, movably clamped supports, movably simply supports and immovably simply supports. The relationship between load and deformation, the analytical expression of critical load and the analytical expression of critical geometrical parameter under temperature are obtained. The effect of geometric parameters, the material parameters and the variation of temperature fields on critical load is analyzed, and the result is compared. The results show that the thermal moment and the thermal membrane force have remarkable effects on the critical loads and the critical geometrical
parameter.
引文
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[12] R.-H. Liu, F. Wang, Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells. Archive of Applied Mechancs, 1998, 375-384
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[32] Gellatly. RA.Bijlaad. PP, and Gallagher, RH. Thermal Stress and Instability of Sandwich Cylinders On Rigid Supports. J Aircraft, 1965,2(1), 44-48.
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Cylindrical Shells." Composite Eng, 1989,Vol 1 .No3,1991, pp 183-192.
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[41] Patel, B.P.; Shukla, K.K.; Nath, Y. Thermal buckling of laminated cross-ply oval cylindrical shells, Composite Structures, 2004, 65(2), 217-229.
[42] Li Shirong, Cheng Changjun, Analysis of thermal post-buckling of heated elastic rods, Applied Mathematics and Mechanics-English Edition, 2000, 21 (2): 133-140.
[43] Li Shirong, Zhou Youhe, Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates, Journal of Sound and Vibration, 2001, 248 (2): 379-386.
[44] Li Shirong, Zhou Youhe, Song Xi, Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass, Journal of Sound And Vibration, 2002, 251(1): 141-152.
[45] Li Shirong, Zhou Youhe, Zheng Xiaojing Thermal post-buckling of a heated elastic rod with pinned-fixed ends, Journal of Thermal Stresses, 2002, 25 (1): 45-56.
[46] Li Shirong, Zhou Youhe, Nonlinear vibration of heated orthotropic annular plates with immovably hinged edges, Journal of Thermal Stresses, 2003, 26 (7): 691-700.
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[59] Thornton E A, Thermal Buckling of Plates and Shells. Appl Mech Rev, 1993,146(10):485-506
[2] 竹内洋一朗,《热应力》(郭廷玮,李安定译),中国科学出版社,北京(1977),358—378.
[3] 刘人怀,考虑横向剪切的对称层合圆柱正交异性扁球壳的非线性稳定问题.中国科学A辑,1991
[4] 刘人怀,考虑横向剪切的对称层合圆柱正交异性中心开孔扁球壳的非线性屈曲.暨南大学学报,1994,15(1)
[5] 刘人怀,对称圆柱正交异性层合扁球壳的非线性稳定问题.应用数学和力学,1991,12(3)
[6] 刘人怀,王璠,复合材料层合扁球壳的非线性强迫振动.力学学报,1997,29(2),236-241
[7] 王璠,刘人怀,复合材料层合开顶扁球壳的非线性动态屈曲.固体力学学报,2001,22(3)
[8] 王璠,开孔复合材料扁球壳的非线性动态响应.哈尔滨工业大学学报,2000,32(1)
[9] 王璠,刘人怀,复合材料层合开顶扁球壳的非线性振动屈曲.第九界全国复合材料学术会议论文集,1996
[10] 王璠,肖潭,刘人怀,阻尼对层合复合材料中心开口扁球壳非线性振动的影响.应用力学与实践,2000,35-43
[11] 王璠,剪切刚度对复合材料层合扁球壳非线性振动屈曲的影响.强度与环境,2001,1
[12] R.-H. Liu, F. Wang, Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells. Archive of Applied Mechancs, 1998, 375-384
[13] Whitney, JM. and Ashton. JE. Effect of Enviroment on the Elastic Response of Layered Composite Plates. ALAA J, 1971,9(9),1708-1713
[14] Flagg.DI. and Vinson. JR. Hygrothermal Effects on the Buckling of Laminated Composite Plates. Fibre Sci and Tech,1978,11,3 53-365.
[15] Whiteney, JM. Structural Analysis of Laminate Anisotropic Plates. Technomic Publishing, Lancaster, PA, 1987
[16] Tauchert.TR. Thermal Buckling of Thick Antisymmetric Angle-Ply Lanminates.J Thermal stress, 1987,10,113-124
[17] Tauchert.TR. and Huang, NN. Thermal Buckling of Symmetric Angle-Ply Lanminated Plates. IH Marshall(editor), composite structures 4(4th ICCs),Paisley, Scotland. London: Elsevier, 1987,1.424-1.435.
[18] Chen. LW, and Chen. LY, Thermal Buckling of Laminated Composite Plates.J Thermal Stresses, 1987,10,345-356
[19] Chen. LW. and Chen..Thermal Buckling of Laminated Cylindrical Plates. Composite Struct. 1987,8,189-206
[20] Chen. LW, and Chen..Thermal Buckling Behavior of Laminated Composite Plates with Tempretature-Dependent Properties. Composite Structures, 1989,13,275-287
[21] Chandrashekhara, K. Buckling of Multilayered Composite Plates Under Uniform Temperature Field. B.Birman. and D. Hui(editors). Thermal Effects on structures and Materials. New York: ASME, 1991,29-33.
[22] Huang,NN, and Tauchert,TR. Thermal Buckling of Clamped Symmetric Laminated Plates. Impact and Buckong of Structures Vol ASME AD-V20.AMD-V114. 1990, (53-59).
[23] Sun, LX. And Hsu,TR. Thermal Buckling of Laminated Composite Plates with Transverse Shear Deformation. Comput Struct. 1990,36(5),883-889.
[24] Chang, J. and Leu, S. Thermal Bucking Analysis of Antisymmetric Angle-Ply Laminates Based on a I lingher-Order Displacement Field. Composites Sci and Tech. 1991,41.109-128
[25] Thangaratnam. KR. Palaninathan, and Ramachandran, J. Thermal Buckling of Composite Laminated Plates. Comput Struct, 1989,32(5), 1127-1124.
[26] Chen, LW, and Chen. LY. Thermal Buckling Analysis of Composite Lanminated Plates by the Finite -Element Method. Composite Structures, 1989,12, 257-270.
[27] Chen, LW, and Chen. LY. Thermal Postbuckling Analysis of Composite Lanminated Plates by the Finite -Element Method. Composite Structures, 199012,257-270.
[28] Chang.J, and Shiao. F. Thermal Buckling Analysis of Isotropic and Composite Plates with a Hole. J Thermal Stresses. 1990, 13.315-332.
[29] Chang, J. FEM Analysis of Buckling and Thermal Buckling of Antisymmetric Angle-Ply Laminates According to Transverse Shear and Normal Deformable High Order Displacement Theory. Comput Struct, 1990,37(6), 925-946
[30] Birman, V, and Hui. D. Thermal Effects on Stuctures and Materials. AMD, 110. Papers presented at the Winter Annual Meetiong of ASME, Dallas,TX. 1990,November 25-30,1990
[31] Paley. M. and Aboudi. J. Inelastic Thermal Buckling of Metal Matrix Laminated Plates.J Thermal Stresses. 1991,14.479-497.
[32] Gellatly. RA.Bijlaad. PP, and Gallagher, RH. Thermal Stress and Instability of Sandwich Cylinders On Rigid Supports. J Aircraft, 1965,2(1), 44-48.
[33] Hoff, NJ. Buckling of Thin Cylindrical Shell Under Hoop Stresses Varying in Axial Direction. J Appl Mech, 24(3),405-412.
[34] Chang, LK, and Card. MF.Thermal Buckling in Stiffened Cylindrical Shells. AIAA/ASME 11th Structures. Structural Dynamics, and Materials Conferernce. (pp 260-172) New York;AIAA. ,1970
[35] Chang, LK, and Card. MF. Thermal Buckling Analysis For Stiffened Orthotropic Cylindrical Shells. NASA TN D-6332., 1971
[36] Gupta.Sd. and Wang,I.Thermal Buckling of Orthotropic Cylindrical Shells. Fibe Sci and Tech, 1973,6,39-45.
[37] Radhamohan,SK,and Venkataramana, J. Thermal Bucklong of Orthotropic Cylinderical Shells. AIAA J, 1975,4(8), 1437-1439.
[38] Wilcox,MW.,and Ma,S. Thermal Buckling of Antisymmetric Angle-Ply Composite Circular Cylindrical Shells. 30th AIAA/ASME/ASCE/AIIS/ASC Structures, Structural Dynamics and Materials Conference Vol AIAA Paper No 89-1172-CP,. 1989, April 3(pp 113-120).Also Ma,S-F and Wijcox,MW. "Thermal buckling of Antisymmetric Angle-Ply Laminated
Cylindrical Shells." Composite Eng, 1989,Vol 1 .No3,1991, pp 183-192.
[39] Thangaratnarn, RK, Palaninathan, and Ramachandran, J. Thermal Buckling of Laminated Composite Shells. AIAA J, 1990,28(5),859-860
[40] Birman,V. Thermal Dynamic Problems of Reinforced Composite Cylinders. J Appl Mech. 1990,57.941-947.
[41] Patel, B.P.; Shukla, K.K.; Nath, Y. Thermal buckling of laminated cross-ply oval cylindrical shells, Composite Structures, 2004, 65(2), 217-229.
[42] Li Shirong, Cheng Changjun, Analysis of thermal post-buckling of heated elastic rods, Applied Mathematics and Mechanics-English Edition, 2000, 21 (2): 133-140.
[43] Li Shirong, Zhou Youhe, Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates, Journal of Sound and Vibration, 2001, 248 (2): 379-386.
[44] Li Shirong, Zhou Youhe, Song Xi, Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass, Journal of Sound And Vibration, 2002, 251(1): 141-152.
[45] Li Shirong, Zhou Youhe, Zheng Xiaojing Thermal post-buckling of a heated elastic rod with pinned-fixed ends, Journal of Thermal Stresses, 2002, 25 (1): 45-56.
[46] Li Shirong, Zhou Youhe, Nonlinear vibration of heated orthotropic annular plates with immovably hinged edges, Journal of Thermal Stresses, 2003, 26 (7): 691-700.
[47] 李世荣,弹性圆板的热过屈曲.固体力学学报,1997,18(2)
[48] 李世荣,周又和,滕兆春,正交异性环板-刚性质量系统的大幅振动和热屈曲.振动工 程学报,2002,15(2)
[49] 李世荣,具有中心刚性质量的受热环板的非线性振动和热屈曲.应用数学和力学.1992,13(8).-745-751
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