## 留言板

 引用本文: 赵伟东, 杨亚平. 扁球壳在均布压力与均匀温度场联合作用下的屈曲[J]. 应用数学和力学, 2015, 36(3): 262-273.
ZHAO Wei-dong, YANG Ya-ping. Buckling of Shallow Spherical Shells Under Uniform Pressure in Uniform Temperature Field[J]. Applied Mathematics and Mechanics, 2015, 36(3): 262-273. doi: 10.3879/j.issn.1000-0887.2015.03.004
 Citation: ZHAO Wei-dong, YANG Ya-ping. Buckling of Shallow Spherical Shells Under Uniform Pressure in Uniform Temperature Field[J]. Applied Mathematics and Mechanics, 2015, 36(3): 262-273.

• 中图分类号: TU43

## Buckling of Shallow Spherical Shells Under Uniform Pressure in Uniform Temperature Field

• 摘要: 根据扁壳几何非线性理论，推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件，采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时，上、下临界荷载都随几何参数增加而增加.给定几何参数时，考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加，会使下临界荷载略有减小.均匀变温会使临界几何参数改变.
•  [1] von Karman T, Tsien H S. The buckling of spherical shells by external pressure[J].Journal of the Aeronautical Sciences,1939,6(2): 43-50. [2] Weinitschke H J. On the stability problem for shallow spherical shells[J].J Math Phys,1959,38(4): 209-231. [3] 沃耳密耳 A C. 柔韧板与柔韧壳[M]. 卢文达, 黄择言, 卢鼎霍 译. 北京: 科学出版社, 1959.(Wolmil A C. Flexible Plate and Flexible Shell [M]. LU Wen-da, HUANG Ce-yan, LU Ding-huo transl. Beijing: Science Press, 1959.(in Chinese)) [4] 胡海昌. 球面扁薄圆壳的跳跃问题[J]. 物理学报, 1954,10(2): 105-131.(HU Hai-chang. On the snapping of a thin spherical cap[J].Acta Physica Sinica,1954,10(2): 105-131.(in Chinese)) [5] 罗祖道, 聂徳耀, 刘汉东, 刘习文, 史建勋. 双层金属球面扁壳的热稳定性[J]. 力学学报, 1966,9(1): 1-13.(LUO Zu-dao, NIE De-yao, LIU Han-dong, LIU Xi-wen, SHI Jian-xun. Thermal snap-through buckling of a bimetallic shallow spherical shell[J].Acta Mechanica Sinica,1966,9(1): 1-13.(in Chinese)) [6] 叶开沅. 柔韧构件研究在中国的进展[J]. 力学进展, 1983,13(2): 125-134.(YE Kai-yuan. The development of investigations of flexible structural elements in China[J].Advances in Mechanics,1983,13(2): 125-134.(in Chinese)) [7] 叶开沅, 宋卫平. 均布压力作用下圆底扁薄球壳的轴对称屈曲[J]. 兰州大学学报(自然科学版), 1987,23(2): 18-27.(YE Kai-yuan, SONG Wei-ping. Axisymmetrical buckling of thin shallow circular spherical shells under the action of uniform pressure[J].Journal of Lanzhou University(Natural Science), 1987,23(2): 18-27.(in Chinese)) [8] 顾淑贤. 扁球壳在对称线布荷载作用下的稳定性问题[J]. 固体力学学报, 1988,9(1): 39-48.(GU Shu-xian. An approach to the nonlinear stability of shallow shells with a symmetrically distributed line load[J].Acta Mechanica Solida Sinica,1988,9(1): 39-48.(in Chinese)) [9] 严圣平. 扁球壳在均布压力作用下的非线性弯曲问题[J]. 应用力学学报, 1988,5(3): 21-29.(YAN Sheng-ping. Non-linear bending of a shallow spherical shell under uniformly distributed pressure[J].Chinese Journal of Applied Mechanics,1988,5(3): 21-29.(in Chinese)) [10] 刘人怀, 成振强. 集中载荷作用下开顶扁球壳的非线性稳定问题[J]. 应用数学和力学, 1988,9(2): 95-106.(LIU Ren-huai, CHENG Zhen-qiang. On the nonlinear stability of a truncated shallow spherical shell under a concentrated load[J].Applied Mathematics and Mechanics,1988,9(2): 95-106.(in Chinese)) [11] 严圣平. 均布载荷作用下变厚度开顶扁球壳的非线性稳定问题[J]. 应用数学和力学, 1997,18(10): 947-952.(YAN Sheng-ping. Nonlinear stability of truncated shallow spherical shell with variable thickness under uniformly distributed load[J].Applied Mathematics and Mechanics,1997,18(10): 947-952.(in Chinese)) [12] 王璠, 刘人怀. 复合材料层合开顶扁球壳的非线性动态屈曲[J]. 固体力学学报, 2001,22(3): 309-314.(WANG Fan, LIU Ren-huai. Nonlinear dynamic buckling of symmetrically lyminated truncated spherical shell[J].Acta Mechanica Solida Sinica,2001,22(3): 309-314.(in Chinese)) [13] 朱永安, 王璠, 刘人怀. 考虑横向剪切的对称圆柱正交异性层合扁球壳的热屈曲[J]. 应用数学和力学, 2008,29(3): 263-271.(ZHU Yong-an, WANG Fan, LIU Ren-huai. Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear[J].Applied Mathematics and Mechanics,2008,29(3): 263-271.(in Chinese)) [14] 李善倾, 袁鸿. 简支梯形底扁球壳自由振动问题的准Green函数方法[J]. 应用数学和力学, 2010,31(5): 602-608.(LI Shan-qing, YUAN Hong. Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell[J].Applied Mathematics and Mechanics,2010,31(5): 602-608.(in Chinese)) [15] Panda S K, Singh B N. Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel[J].International Journal of Mechanics and Materials in Design,2010,6(2): 175-188. [16] Boroujerdy M S, Eslami M R. Nonlinear axisymmetric thermomechanical response of piezo-FGM shallow spherical shells[J].Arch Appl Mech,2013,83(12): 1681-1693. [17] 张平, 周丽, 邱涛. 用于自适应进气道的扁薄球壳双稳态特性分析[J]. 工程力学, 2013,30(10): 264-271.(ZHANG Ping, ZHOU Li, QIU Tao. Analysis of bi-stable behavior of shallow thin spherical shell applied in adaptive inlet[J].Engineering Mechanics,2013,30(10): 264-271.(in Chinese)) [18] 赵伟东. 圆薄板及扁球壳轴对称非线性强迫振动[D]. 硕士学位论文. 兰州: 兰州理工大学, 2007.(ZHAO Wei-dong. Nonlinear forced axisymmetric vibrations of thin circular plate and shallow spherical shell[D]. Master Thesis. Lanzhou: Lanzhou University of Technology, 2007.(in Chinese)) [19] 赵伟东, 邱平, 吴晓, 甘文艳. 均布压力作用下扁球壳几何非线性自由振动[J]. 兰州理工大学学报, 2010,36(4): 168-171.(ZHAO Wei-dong, QIU Ping, WU Xiao, GAN Wen-yan. Geometrically nonlinear free vibration of a shallow spherical shell under uniform pressure[J].Journal of Lanzhou University of Technology,2010,36(4): 168-171.(in Chinese)) [20] 赵伟东, 黄永玉, 杨亚平. 弹性基础上压杆的横向非线性自由振动与屈曲[J]. 力学与实践, 2014,36(3):303-307.(ZHAO Wei-dong, HUANG Yong-yu, YANG Ya-ping. The transverse nonlinear free vibration and the buckling of a compressive bar on an elastic foundation[J].Mechanics in Engineering,2014,36(3): 303-307.(in Chinese)) [21] 冯仲齐. 扁球壳的大挠度弹塑性分析[J]. 西安冶金建筑学院学报, 1994,26(2): 117-122.(FENG Zhong-qi. Analysis of elastoplastic of shallow spherical shells with large deflection[J].Journal of Xi’an University of Architecture & Technology,1994,26(2): 117-122.(in Chinese))
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##### 出版历程
• 收稿日期:  2014-07-04
• 修回日期:  2015-01-29
• 刊出日期:  2015-03-15

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