Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity
Axisymmetric buckling of a spherical shell embedded in an elastic medium under uniaxial stress at infinity
复制标题
无穷远单轴应力下嵌入弹性介质的球壳的轴对称屈曲
DOI：
10.1093/qjmam/hbn018
复制
发表时间：
2008
影响因子：
0.9
通讯作者：
D. Allwright
中科院分区：
文献类型：
--
作者：
G. Jones;S. Chapman;D. Allwright
研究了与无限线弹性介质完美结合的线弹性薄球壳问题。在矩阵无穷远处施加恒定轴对称应力场，用调和势函数计算壳层和矩阵中的位移场和应力场。为了检验该解的稳定性，考虑了受这种变形的壳的屈曲问题。利用Koiter的非线性浅壳理论，将屈曲模式限制为轴对称的屈曲模式，并使用瑞利？Ritz方法通过展开无穷级数的Legendre函数的屈曲模式，确定了无穷级数中系数的特征值问题。该系统被截断并进行数值求解，以分析壳体在屈曲过程中的行为，并确定两种情况下的临界屈曲应力，即壳体是空心的，无穷远处的应力是单轴的或径向的。
The problem of a thin spherical linearly elastic shell perfectly bonded to an infinite linearly elastic medium is considered. A constant axisymmetric stress field is applied at infinity in the matrix, and the displacement and stress fields in the shell and matrix are evaluated by means of harmonic potential functions. In order to examine the stability of this solution, the buckling problem of a shell which experiences this deformation is considered. Using Koiter's nonlinear shallow shell theory, restricting buckling patterns to those which are axisymmetric and using the Rayleigh?Ritz method by expanding the buckling patterns in an infinite series of Legendre functions, an eigenvalue problem for the coefficients in the infinite series is determined. This system is truncated and solved numerically in order to analyse the behaviour of the shell as it undergoes buckling and to identify the critical buckling stress in two cases, namely, where the shell is hollow and the stress at infinity is either uniaxial or radial.