The study of two dimensional B-Spline finite element method on irregular boundary shape and the application on plate analysis

• Main Authors: Hong-jhe Liao, 廖宏哲
• Other Authors: Shi-Pin Ho
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/90342187757862642489

碩士 === 國立成功大學 === 機械工程學系碩博士班 === 95 === B-Spline finite element method is a numerical method which using B-Spline basis functions instead of finite element method basis function. The state variables of the B-Spline functions have Ck-2 continuity, where k is the order of the polynomials in B-Spline functions plus one. In order to enable the basis functions have Ck-2 continuity at boundaries between every cell, we should make the size of each cell the same. The cell is the square subdomain used for integration. The computational geometry theory used in this study is the Binary space partition. This method will spilt the polygon and we can use this property to proceed Boolean operation of geometric polygon. The cell mesh of the geometric polygon in the analysis is the results of a series of intersection test to the irregular geometric polygon. The program will deal with the boundaries between the polygon and intersected cell, and spilt the geometric solids included in the cell. We analyze the regular and the irregular shape plates in the two dimensional problems. In these plate examples, we find that the accuracy of the displacements and the stresses of B-Spline finite element method are almost the same as in the finite element method, but the degree of freedom in B-Spline finite element method is much less than finite element method.