Winkler地基上弹性薄板求解的有限差分法

Elastic Plate Resting on Winkler Foundation by Finite Difference Method

通过引入参数把 Winkler地基上弹性薄板的偏微分控制方程由四阶降为两阶 ,形成两个耦合的椭圆形方程 ,利用超松弛迭代法进行了求解。推导了简支、固支以及自由边界条件的参数表达式 ,采用五点差分格式对以上偏微分方程进行了处理 ,最后给出了算例。结果表明 ,采用参数对薄板的控制方程进行处理后可较方便地运用差分法求解 。

By introducing a parameter, the four-order governing equation of elastic plate resting on Winkler foundation is reduced to two coupling two-order elliptic equations. Three kinds of boundary conditions, i.e. simply supported edge, fixed edge and free edge, are expressed by the parameter. Five-point difference format is adopted to handle all the equations, and solution is obtained using successive over relaxation method. Finally, an example is given which is analyzed with the method put forward in this article. As is demonstrated, it is more convenient to use finite difference method when adopting parameter, and better results can be obtained.