Research on Fine Processing for Curved Surface BEM Based on Parametric Equation of the B-spline Surface

The quadrilateral BEM of B-spline surface is that actual boundary surface is fitted with B-spline curved surface, which is closer to actual boundary than that fitted with the first-order element. The function value of the corresponding vertices on the nodes is also more accurate. However, due to the model is enmeshed into high-order element roughly, the number of element is relatively few, and the enmeshed model is rough. The boundary surface of the model is only in the form of a planar linear element which is different from the actual model boundary. In this paper, fine processing method is put forward, in which the surface elements can be finely showed with the parametric equations of B-spline curved surface. By the function value on vertex of the surface element and the shape function defined by the area ratio method, function value on new nodes of the surface element can be obtained by the shape function interpolation of the ratio of function value to area on the vertex of surface element. In the end, the fine display of the B-spline surface BEM is formed. The calculated results show that the boundaries are closer to the actual boundary.