| The finite element method since its birth, with the development of computer technology, has become the most widely used numerical analysis method in engineering analysis. Due to its high effectiveness, finite element method is highly valued in the fields of science and engineering. Nowadays, it has become an important part of the computer aided design (CAD) and Computer Aided Engineering (CAE). B-spline has been widely used in the computer aided design, because of its well mathematical properties and good performance of free form of curve and surface. Developed on the basis of B-spline, the non-uniform rational B-spline (NURBS) overcomes the defect that the B-spline can not accurately express quadratic curve or surface, and becomes the standard technology to define the geometry of the CAD. B-spline finite element method is not used widely in engineering because of its poor universality. With the demand of engineering application to simulation more and more strict, voice of seamless integration of CAD and CAE is growing, forcing people to seek new finite element method. NURBS spline finite element method, constructing geometric model by NURBS basis function and using the same spline function to calculate in the subsequent finite element analysis, unites the CAD and CAE under the same framework and is likely to realize seamless integration of the CAD and CAE field. The basic theory of B spline and NURBS is studied, important properties of the basis are analyzed and the NURBS curve generation examples is given. The basic principle of NURBS spline finite element method is introduced in detail, the Poisson equation is chose to solve and calculation formula is derived by Galerkin method. Based on the basic theory, with reference to the program development process of traditional finite element method, MATLAB language is used to compile related packages, and the application of the linear elastic problems is studied to show the feasibility and effectiveness of the method. |
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