广义康托洛维奇法解任意四边形板的弯曲问题

本文从变分原理和双线性坐标变换出发,采用基于三次B样条函数的广义康托洛维奇法得到了带有各种边界条件任意四边形板弯曲的近似解答。样条函数广义康托洛维奇法是一种数值型的康托洛维奇法,因而它既能化二维问题为一维同题,同时又具有样条函数法收敛快、精度高、处理边界条件方便等优点。推导出的计算格式适用于各种边界条件,使梯形板、平行四边形板和矩形板的弯曲问题为本文的特殊情况。本文方法与通常有限元法相比,具有计算量小、精度高等显著特点,且通用性强,是一种很有前途的计算方法。

SOLVING THE BENDING PROBLEM OF ARBITRARY QUADRILATERAL PLATES BY GENERALIZED KANTOROVICH METHOD

In this paper, a generalized Kantorovich method based on cubic B-spline is presented for obtaining an approximate solution for the bending problem of arbitrary quadrilateral plates with various types of boundary conditions by the variational method and bilnear coordinate transformation. The spline generalized kantorovich method is a type of numerical kantorovich method, it not only can transfer two-dimension problems into one-dimension problems, also has the advantages the spline method possesses of, such as high precision, rapid convergence and suitability for various types of boundary conditions. Derived is a computional scheme well suited for various types of boundary conditions. The solutions of bending problem of the trapezoidal, parallelogram and rectangular plates are given as its particular cases. In comparison with the usual finite method, the main features of the present method are higher accuracy and more economy in computing storage and time requirements. This method has its generality and a good future.