基于B样条曲面参数方程的曲面边界元精细后处理方法研究

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

B样条曲面四边形边界元方法,是用B样条曲面拟合实际边界面,比一阶单元更接近实际边界,相应的顶点节点上的函数值也比较精确。但由于模型采用高阶单元粗略剖分,该方法单元数量相对较少,剖分后的模型较粗糙,而且模型只能以平面线性单元的形式显示,与实际模型边界差别较大。本文提出了基于B样条曲面参数方程的曲面边界元精细后处理方法。在该方法中,利用B样条曲面的参数方程把曲面单元精细显示出来。单元上新建节点的函数值可由曲面单元顶点上的函数值和面积比值法定义的形状函数插值得到。最后形成经精细显示后的B样条曲面边界元方法。算例表明,经精细显示后边界面比未处理前更接近实际边界。

： The quadrilateral BEM of B-spline surface is that actual boundary surface is fitted with B-spline curved sur- face, which is closer to actual boundary than that fitted with the first-order element. The function value of the corre- sponding vertices on the nodes is also more accurate. How- ever, 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 mod- el is only in the form of a planar linear element which is dif- ferent from the actual model boundary. In this paper, fine processing method is put forward, in which the surface ele- ments 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 sur- face element can be obtained by the shape function interpo- lation of the ratio of function value to area on the vertex of surface element. In the end, the fine display of the B-splinesurface BEM is formed. The calculated results show that the boundaries are closer to the actual boundary.