扁球壳在热-机械荷载作用下的稳定性分析

赵伟东; 高士武; 马宏伟

doi:10.21656/1000-0887.370320

扁球壳在热-机械荷载作用下的稳定性分析

doi: 10.21656/1000-0887.370320

¹青海大学土木工程学院, 西宁 810016;²东莞理工学院, 广东东莞 523106

基金项目: 国家自然科学基金(面上项目)(11472146)；青海省科技厅国际合作项目(2014-HZ-822)

详细信息

作者简介:
作者简介：赵伟东(1972—)，男，副教授，硕士，硕士生导师（通讯作者. E-mail: zhwd.xbl@163.com）.

中图分类号: TU43
计量
- 文章访问数: 1193
- HTML全文浏览量: 216
- PDF下载量: 931
- 被引次数: 0
出版历程
- 收稿日期: 2016-10-20
- 修回日期: 2016-12-17
- 刊出日期: 2017-10-15

Thermomechanical Stability Analysis of Shallow Spherical Shells

¹School of Civil Engineering, Qinghai University, Xining 810016, P.R.China;²Dongguan University of Technology, Dongguan, Guangdong 523106, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(11472146)

摘要

摘要: 基于扁壳几何非线性理论，应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件，运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时，上临界荷载随几何参数的增加单调增加，下临界荷载在很小范围内随几何参数的增加而增加，之后随几何参数的增加而减小.给定几何参数时，考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加，使下临界荷载和临界几何参数显著减小.
- 扁球壳 /
- 打靶法 /
- 均布外侧压力 /
- 均匀变温场 /
- 稳定性
Abstract: Based on the geometric nonlinear theory for shallow shells, with the virtual work principle and the variational method, the displacement-type geometric nonlinear governing equations for shallow spherical shells in uniform temperature field under uniform external pressure were derived. With the shooting method, the numerical results of axisymmetric bending deformation of the shallow spherical shell in the immovable simply supported boundary condition were obtained. The critical geometric parameters were defined. The effects of various shell geometric parameters on the equilibrium paths and the critical loads were investigated. It is found that the upper critical load increases but the lower critical load first increases in a small range and then decreases with the geometric parameter in the range beyond its critical value. The effects of different values of the uniform temperature on the shell critical geometric parameter, the critical load and the equilibrium configurations were investigated under a given geometric parameter. Rise of the uniform temperature brings obvious increase of the upper critical load and obvious decrease of the lower critical load and the critical geometric parameter.
- shallow spherical shell /
- shooting method /
- uniform external pressure /
- uniform temperature field /
- stability

HTML全文

参考文献(16)

[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]	叶开沅, 刘人怀, 李思来, 等. 在对称线布载荷作用下的园底扁薄球壳的非线性稳定问题[J]. 兰州大学学报, 1965,18(2): 10-33.(YEH Kai-yuan, LIU Zen-huai, LI Szu-lai, et al. Nonlinear stabilities of thin circular shallow shells under actions of axisymmetrical uniformly distributed line loads[J]. Journal of Lanzhou University,1965,18(2): 10-33.((in Chinese))
[3]	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))
[4]	Liu R H, Wang F. Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells[J]. Archive of Applied Mechanics,1998,68(6): 375-384.
[5]	Shahsiah R, Eslami M R, Naj R. Thermal instability of functionally graded shallow spherical shell[J]. Journal of Thermal Stresses,2006,29(8): 771-790.
[6]	李斌, 董保胜, 刘江华, 等. 均布外压下弹性支撑扁球壳的非线性稳定性分析[J]. 西北工业大学学报, 2006,24(6): 795-799.(LI Bin, DONG Bao-sheng, LIU Jiang-hua, et al. Approximate critical load in analytic form of uniformly corroded shallow spherical shell under uniform external pressure[J]. Journal of Northwestern Polytechnical University,2006,24(6): 795-799.(in Chinese))
[7]	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): 291-300.
[8]	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.
[9]	徐加初，张勇. 爆炸冲击载荷作用下夹层开顶扁球壳的非线性动力稳定性分析[J]. 工程力学, 2011,28(1): 150-156.(XU Jia-chu, ZHANG Yong. Nonlinear dynamic stability analysis of truncated sand-wich shallow spherical shells subjected to explosive impacts[J]. Engineering Mechanics, 2011,28(1): 150-156.(in Chinese))
[10]	Bich D H, van Tung H. Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects[J]. International Journal of Non-Linear Mechanics,2011,46(9): 1195-1204.
[11]	Boroujerdy M S, Eslami M R. Nonlinear axisymmetric thermomechanical response of piezo-FGM shallow spherical shells[J]. Archive of Applied Mechanics,2013,83(12): 1681-1693.
[12]	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))
[13]	张平, 周丽, 邱涛, 等. 椭圆底扁薄球壳结构的双稳态力学行为[J]. 航空动力学报, 2014,29(2): 328-336.(ZHANG Ping, ZHOU Li, QIU Tao, et al. Bi-stable mechanical behavior of shallow thin spherical shell with elliptical bottom[J]. Journal of Aerospace Power,2014,29(2): 328-336.(in Chinese))
[14]	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 shell under uniform pressure and uniform temperature field[J]. Applied Mathematics and Mechanics,2015,36(3): 262-273.(in Chinese))
[15]	李忱, 田雪坤, 王海任，等. 薄球壳在均布外压与温度耦合作用下的热屈曲研究[J]. 应用数学和力学, 2015,36(9): 924-935.(LI Chen, TIAN Xue-kun, WANG Hai-ren, et al. Thermal buckling of thin spherical shells under interaction of uniform external pressure and uniform temperature[J]. Applied Mathematics and Mechanics,2015,36(9): 924-935.(in Chinese))
[16]	钱伟长, 叶开沅. 圆薄板大挠度问题[J]. 物理学报, 1954,10(3): 209-238.(CHIEN Wei-zang, YEH Kai-yuan. On the large deflection of circular plate[J]. Acta Physica Sinica,1954,10 (3): 209-238.(in Chinese))