工程力学 ›› 2018, Vol. 35 ›› Issue (12): 220-228.doi: 10.6052/j.issn.1000-4750.2017.09.0686

• 机械工程学科 • 上一篇    下一篇

功能梯度扁球壳在热-机械荷载作用下的屈曲分析

赵伟东1, 高士武1, 马宏伟1,2   

  1. 1. 青海大学土木工程学院, 西宁 810016;
    2. 东莞理工学院生态环境与建筑工程学院, 东莞 523808
  • 收稿日期:2017-09-06 修回日期:2018-01-03 出版日期:2018-12-14 发布日期:2018-12-14
  • 通讯作者: 赵伟东(1972-),男,甘肃人,副教授,硕士,硕导,主要从事结构非线性振动和结构屈曲分析研究(E-mail:zhwd.xbl@163.com). E-mail:zhwd.xbl@163.com
  • 作者简介:高士武(1985-),男,陕西人,讲师,硕士,主要从事计算力学与工程仿真研究(E-mail:swgao99e@163.com);马宏伟(1966-),男,山西人,长江学者特聘教授,博士,博导,主要从事结构损伤检测和加固,冲击动力学研究(E-mail:tmahw@jnu.edu.cn).
  • 基金资助:
    国家自然科学基金面上项目(11472146)

THERMOMECHANICAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED SHALLOW SPHERICAL SHELLS

ZHAO Wei-dong1, GAO Shi-wu1, MA Hong-wei1,2   

  1. 1. School of Civil Engineering, Qinghai University, Xining 810016, China;
    2. School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan 523808, China
  • Received:2017-09-06 Revised:2018-01-03 Online:2018-12-14 Published:2018-12-14

摘要: 基于经典壳理论,应用虚功原理和变分法推导了均匀变温场中的功能梯度圆底扁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。考虑固定夹紧边界条件,运用打靶法计算获得了球壳轴对称变形的数值结果。考察了材料体积分数指数、组分材料弹性模量和均匀变温场对壳体平衡路径,上、下临界荷载以及平衡构型的影响。数值结果表明,随材料体积分数指数的增加和组分材料弹性模量的减小,壳体上、下临界荷载均会显著减小。均匀升温,会使壳体上临界荷载显著增加,下临界荷载轻微减小。为方便工程设计人员进行几何、材料、荷载和变温参数的选取,给出了一个实用数表和一些实用的数值曲线。

关键词: 功能梯度材料, 圆底扁球壳, 均布压力, 均匀变温场, 屈曲, 打靶法

Abstract: Based on the classical shell theory, with the virtual work principle and the variational method, the displacement-type geometric nonlinear governing equations for functionally graded shallow circular spherical shells in uniform temperature field under uniform external pressure were derived. With the shooting method, the numerical results of the axisymmetric deformation of the shells in the clamped boundary condition were obtained. The effects of material volume fraction index, elasticity modulus of constituent materials and uniform temperature field on the equilibrium paths, the upper/lower critical loads and equilibrium configurations of the shells were investigated. The numerical results show that the upper/lower critical load of the shells decreases significantly with the increase of volume fraction index and the decrease of elasticity modulus of constituent materials. The rise of the uniform temperature brings obvious increase of the upper critical load and slight decrease of the lower critical load. A practical numerical table and some practical numerical curves are given for the convenience of designers to select geometry, material, load and temperature parameters.

Key words: functionally graded materials, shallow circular spherical shells, uniform pressure, uniform temperature field, buckling, shooting method

中图分类号: 

  • TB34
[1] von Kármán Th. Tsien H S. The buckling of spherical shells by external pressure[J]. Journal of the Aeronautical Sciences, 1939, 7(2):43-50.
[2] Weinitschke H J. On the stability problem for shallow spherical shells[J]. Journal of Mathematics and Physics, 1959, 38(4):209-231.
[3] 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 Kaiyuan, Song Weiping. 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)
[4] 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 Shengping. 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)
[5] 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.
[6] Li Q S, Liu J, Tang J. Buckling of shallow spherical shells including the effects of transverse shear deformation[J]. International Journal of Mechanical Sciences. 2003, 45(9):1519-1529.
[7] 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 Baosheng, Liu Jianghua, 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)
[8] 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)
[9] 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 Xuekun, Wang Hairen, 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)
[10] 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.
[11] 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 Nonlinear Mechanics, 2011, 46(9):1195-1204.
[12] 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.
[13] Boroujerdy M S, Eslami M R. Thermal buckling of piezo-FGM shallow spherical shells[J]. Meccanica, 2013, 48(4):887-899.
[14] Mao Y Q, Ai S G, Chen C P, et al. Nonlinear dynamic response and damage analysis for functionally graded metal shallow spherical shell under low-velocity impact[J]. Archive of Applied Mechanics, 2015, 85(11):1627-1647.
[15] 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 Weidong, Yang Yaping. Buckling of shallow spherical shells under uniform pressure in uniform temperature field[J]. Applied Mathematics and Mechanics, 2015, 36(3):262-273. (in Chinese)
[16] 邵玉龙, 段庆林, 李锡夔, 等. 功能梯度材料的二阶一致无网格法[J]. 工程力学, 2017, 34(3):15-21. Shao Yulong, Duan Qinglin, Li Xikui, et al. Quadratically consistent meshfree method for functionally graded materials[J]. Engineering Mechanics, 2017, 34(3):15-21. (in Chinese)
[17] 张鹏飞, 罗尧治, 杨超. 薄壳屈曲问题的有限质点法求解[J]. 工程力学, 2017, 34(2):12-20. Zhang Pengfei, Luo Yaozhi, Yang Chao. Buckling analysis of thin shell using the finite particle method[J]. Engineering Mechanics, 2017, 34(2):12-20. (in Chinese)
[18] 赵伟东, 高士武, 马宏伟. 扁球壳在热-机械荷载作用下的稳定性分析[J]. 应用数学和力学, 2017, 38(10):1146-1154. Zhao Weidong, Gao Shiwu, Ma Hongwei. Thermomechanical stability analysis of shallow spherical shells[J]. Applied Mathematics and Mechanics, 2017, 38(10):1146-1154. (in Chinese)
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