球面各向同性弹性体热应力问题

本文讨论了球面各向同性弹性体在定常温度场情况的热应力问题.利用位移分解,导出了独立的一个二阶齐次方程和联立的一个二阶、一个三阶非齐次方程组;给出了温度能用球函数展开时非齐次方程的特解,而对应的两个联立齐次方程则化为一个四阶齐次方程.这些齐次方程的特征根均可用弹性常数显式写出,从而可得出齐次方程的通解.文中结果可方便地用于求解球体和球壳热应力问题,极限情况则给出各向同性球和球壳的解.

Thermal Stress Problem of Spherically Isotropic Bodies

In this paper,the thermal stress problem of spherically isotropic medium in a steady temperature field is discussed.Based on the displacement resolution technique proposed in Ref.2],the problem is governed by an independent two-order homogeneous equation and a set of simultaneously inho- mogeneous equations with a two-order equation and a three-order equation when the temperature can be expanded by spherical functions,the special solutions for inhomogeneous equations are given and the corresponding simu- ltaneously homogeneous equations are changed into a four-order homogeneous equation.The characteristic roots of these homogeneous equations can be expr- essed by elastic constants explicitly,so their general solutions are available. The formulation in the present paper can be conveniently used to solve thermal stress problems of spherically isotropic spheres and spherical-shells.In limit cases,it gives solutions for isotropic bodies.