渗透球壳流固耦合问题的位移及内力解

Analysis of the deformation and internal forces about the fluid-solid interaction problem on the permeable spherical shell

在弹性薄壳的线性(非线性)理论和流体力学基本方程的基础上,在小雷诺数的情况下应用相容欧拉—拉格朗日法建立了渗透球壳在流体中流固耦合的基本方程及关系式,并通过摄动法求解了渗透球壳在粘性流体中的流函数从而进一步解出其位移及内力解。通过具体算例,给出了壳的位移变形及内力图,并对有关参数进行讨论,绘出相关曲线。得出渗透系数k和流速越大的情况下,壳体位移也就越大,相应的内力也变大;球壳在三个角度处位移为零。文章能为过滤器问题提供指导。

Based on the nonlinear theory of thin elastic shells and fundamental equations of the fluid mechanics,the basic fluid-solid interaction relation formulas for a penetrative shell in fluid are given by assuming that the deformation of the shell effect on the action of the fluid field can be ignored.The united Euler-Lagrange method is set forth and used to form the equations for the small bending of a penetrative sphere shell, and the stream function can be found by the perturbation technique. As an example, the deformation and the distribution of internal forces of the shell are worked out, the effects of the variety of parameters concerned on the shell are discussed. As a conclusion, internal forces and the deformation of the shell will increase with k and the velocity of the liquid,there are three angles whose deformations is zero. This paper can supply help to the problem of filter.