一类可压缩的超弹性球壳的径向对称变形

将一类各向同性可压缩的超弹性材料组成的球壳的径向对称变形问题的数学模型归结为二阶非线性常微分方程的边值问题．求得了问题的参数型解析解，并给出了相应的数值模拟．描述了球壳的内外表面分别受压时，球壳静态有限变形的机理，即当外压大于内压时，球壳处于压缩状态；而当外压小于内压时，球壳处于膨胀状态．同时讨论了球壳的内外半径比例对球壳变形的影响．

Radially Symmetric Deformation of a Class of Compressible Hyper- elastic Spherical Shells

For a radially symmetric deformation problem of a spherical shell composed of a class of isotropic compressible hyper - elastic materials, the mathematical model is described as a boundary - value problem of a second -order nonlinear ordinary differential equation. Analytic solutions of parametric type are obtained and numerical simulations are also given. The mechanism of static finite deformation of the spherical shell is analyzed as the inner surface and the outer surface are respectively subjected to pressures, namely, the spherical shell is at a compression state as the outer pressure is greater than the inner pressure, however, the spherical shell is at an expansion state as the outer pressure is less than the inner pressure. The effect of the ratio between the inner surface and the outer surface on deformation of the spherical shell is also discussed.