The Research Of The Spline Function Method Of Any Quadrilateral Thickness Plate

The paper use the method of coordinate transformation. It transforms any quadrilateral under the natural coordinates into the rectangle under a Cartesian coordinate of. Then, calculate the rectangular plate after coordinate changed with the spline domains method and the QR method respectively. And Under the natural coordinates we can obtain the calculation results of any quadrilateral. Meanwhile, the calculation results and abaqus simulation results were compared, and the result is satisfactory. And because that the calculation of spline function their is smaller, the calculation accuracy is higher, so it has the necessity to further study. Through the analysis found that the calculation process not only can be used in the plate but also in sheet. The main content of the paper as follows:1. With the using of coordinate transformation it transforms any quadrilateral under the natural coordinates into the rectangle under a Cartesian coordinate of. This method has been verified by the finite element method. It is really an effective way which can guarantee that the convergence of the solution.2. Established a new arbitrary Angle of the triangle spline domains.3. Established based on new spline function (RBF) of any quadrilateral elastic elastic thickness plate for QR method for calculation of the new format. 4. Based on the newly established kind note domain, establish any quadrilateral thickness plate elastic kind note domain method of the calculation of the new format.5. Based on the newly established kind note domain, establish any quadrilateral thickness plate elastic-plastic kind note domain method of the calculation of the new format.The paper has the following advantages:1. The method applies to both plate and sheet. Though the analysis we can find that the method can avoid shear atresia problem effectively, and has some of the simplified role for the research, and to simplify the calculation problem of board. It makes the computer programming process simply and helps to promote the method.2. After the transformation of quadrilateral coordinate, the computation is easier to be convergence, and the precision is higher than the triangle. The four nodes of coordinate transformation could avoid grid distortion easily. the precision it has great practical significance is also enough to meet the need.3. It also simply explore the problem of the power which is helpful for the extension of spline function method’s using range.