矩形板耦合热冲击问题的摄动解

Singular Perturbation Solution of Coupled Thermal Shock on Rectangular Plates

本文通过对薄板耦合热弯曲问题的完备方程的无量纲化,引出了关于薄板的无量纲热弹性耦合系数,并以此系数为摄动参数,运用奇异摄动方法,导出了其摄动方程,得到了关于矩形薄板耦合热冲击问题的一致有效的渐近解。然后,在对该解讨论及计算的基础上,获得了一些关于该类问题的规律性的结论。

In this paper, the authors discovered a coupling coefficient in non-dimensional form from the governing differential epuation of coupled thermal bending of thin plate also in dimensionless form. Taking this coefficient as the parameter of perturbation, the authors derived the perturbation equation of the thin plates subjected to coupied thermal shock by the singular perturbation method. An uniformly valid asymptotical solution for rectangular plates subjected to coupled thermal shock is thus obtained. Finally, on the basis of the solution followed by a discussion, a conclusion of regularity of this kind problem is obtained.