自引力旋转球壳的弹性力学解

The elastic mechanical solution of a self-gravitational rotating spherical shell

考虑旋转对自引力球壳的影响,借助MATHEMATICA符号计算软件求解了Navier方程,得到了自引力旋转球壳的弹性力学解析解,给出了应变和应力张量的解析表达式,并分析了应变和应力张量的性质,得到了在球壳或球体内主应力最大的位置,即在极角θ≈49°和θ≈131°处,或在纬度41°S和41°N处。

For a large number of spherical objects existing in nature and engineering,in this paper,we consider rotation effect on the gravitational spherical shell.Using the powerful symbolic computation software MATHEMATICA,the Navier equation is solved analytically.The analytical solutions of elastic mechanics for a gravity rotating spherical shell are finally obtained and the analytic expressions of strain and stress tensors are given.The properties of the stress and strain tensors are analyzed.The results show that maximum stress and strain take place at θ ≈ 49° and θ ≈ 131° in the spherical coordinate,or at north latitude 41° and south latitude 41°.Our results include the elastic mechanics solution of gravity ball and spherical shell.Finally,some special cases are also discussed.