变厚度板弯曲的边界元分析法

由于变厚度板弯曲问题的控制分方程复杂，直接求解其基本解推导边界积分方程建立边界元分析法较为困难，本文通过引入等效荷载，等效刚度，将此问题的控制微分方程化成与普通薄板弯曲问题基本方程相同的形式，利用求解通板弯曲问题的边界元迭代求解，建立了分析变厚度板弯曲问题的蛤法，算例表明本方法理正确，精度良好。

BOUNDARY ELEMENT ANALYSIS FOR THE BENDING OF PLATES WITH VARIABLE THICKNESS

As the governing differential equation for the bending of a plate with variable thickness is rather complicated, it is difficult to set up boundary integral equation to obtain the fundamental solution from the governing equation. In this paper, the author suggests a boundary element method to solve the above-stated plate bending problem. This is to introduce equivalent load and equivalent bending rigidity into the governing differential equation to transform it becoming the governing differential equation of plate with uniform thickness which may be solved easily by the boundary element technique. By numerical calculation, it may be seen that the suggested method is accurate and efficient.