Finite element analysis using B-Spline Basis
Associate Professor Ashok V. Kumar Department of Mechanical and Aerospace Engineering University of Florida, Gainesville, FL 32611
In order to use Uniform B-Splines as basis functions for finite element analysis it is convenient to use a structured grid for the analysis. The grid may not conform to the geometry of domain of analysis therefore the geometry is independently represented using implicit equations of the surface. To ensure that Dirichlet boundary conditions are satisfied, implicit boundary method is used where solution structures for test and trial functions are constructed using approximate step functions such that the boundary conditions are satisfied even if there are no nodes on the boundary. Solution structures that are or continuous through out the analysis domain can be constructed using B-spline basis functions. It is easier to generate structured grids that overlap the geometry (compared to conforming mesh) and the elements in the grid are regular shaped and undistorted. 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). They also provide continuous stress and strain in the analysis domain thus eliminating the need for smoothing stress/strain results..
Structured grid B-spline element model		FEM using quadratic tetrahedral elements
Plate with a hole	B-spline element model		Stress concentration
Analysis of Thick cylinder		Structured grid model using B-Spline elements