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.
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 of whole spheres or spherical shells. The special solution for a revolving sphere is also given.
出处
《应用数学和力学》
EI
CSCD
北大核心
1991年第2期141-148,共8页
Applied Mathematics and Mechanics
关键词
球面各向同性
弹性
平衡
体积力
spherical isotropism, elasticity, equilibrium, body forces
