用样条有限点法求解任意四边形薄板的弯曲问题

The Calculation of Arbitrary Quadrilateral Thin Plates by Spline Finite Nodes Method

通过坐标变换，将xoy平面上的任意四边形区域化为ξoη平面上的正方形区域，并在一个方向取梁的振型函数，另一方向取样条函数为位移试函数，应用变分原理，推出了求解具有简支或固定边界条件的任意四边形薄板弯曲问题的基本公式，从而得到了一种计算非规则区域薄板的途径。算例证明该法简捷，精度高，可以在微机上运行。

By taking coordinates transformation method, in this paper, the arbitrary quadrilateral domain of a Plate is transformed into a squarte one from the xoy plane to the Eon plane. And using spline functions as displacement trying functions, the basic formulas of the spline finite nodes method for analysing the bending problems of arbitrary quadrilateral thin plates are derived. The present method can be used for analysing a series of thin plates with .non regular boundary conditions.