球面各向同性弹性体的平衡问题

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Equilibrium Problems of Spherically Isotropic Bodies

摘要: 本文将位移和体积力同时进行分解,把含体积力的球面各向同性三维弹性理论平衡问题,化为一个二阶微分方程和一个四阶微分方程.利用球面函数的性质和级数展开方法,得到了相应于这两个方程齐次方程的级数解,可用于解决整球体和整球壳的平衡问题.最后,给出了旋转球的特解.
- 球面各向同性 /
- 弹性 /
- 平衡 /
- 体积力
Abstract: In this paper the displacements and body-forces are resolved, respectively, and the 3-dimensional equilibrium problems of spherically isotropic bodies with body-forces are transferred into a two-order differential equation and a four-order differential equation. Based on the series expansion technique and properties of spherical functions, the series solutions are obtained for the corresponding homogeneous equations, which can be adapted to solve equilibrium problems oj whole spheres or spherical shells. The special solution for a revolving sphere is also given.
- spherical isotropism /
- elasticity /
- equilibrium /
- body forces

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[2]	胡海昌,球面各向同性体弹性力学的一般理论,物理学报,10,1(1954),57.
[3]	夏涛、何福保,横观各向同性球体轴对称弯曲的三维弹性理论解,应用力学学报,5.3(1988),55.