Finite Element Analysis Using Uniform B-Spline Basis

Abstract

Implicit boundary finite element method uses structured grids for analysis instead of a conforming finite element mesh. The geometry of the structure is represented independently using curve / surface equations. These equations are used to apply boundary conditions even though there may not be nodes available on the boundary. In this paper, this method is applied for analysis using uniform B-spline basis defined over structured grids. Solutions can be constructed that are C1 or C2 continuous throughout the analysis domain using B-spline basis functions. Therefore, the computed stress and strain are continuous in the analysis domain thus eliminating the need for smoothing stress/strain results. Compared to conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B-spline elements. The results are compared with analytical solutions as well as traditional finite element solutions. Convergence studies for several examples show that B-spline elements provide accurate solutions with fewer elements and nodes as compared to traditional finite element method (FEM).