基于NURBS的复杂域边界单元改进方法

提出了基于非均匀有理B样条(NURBS)理论的边界单元改进方法。该方法以原分网后的节点和单元数据为依据,按照平均取值的原则获取边界单元边界边上的控制点,根据这些控制点利用NURBS理论表示边界边,并可通过不断调节权因子,使分网后的边界更加接近真实边界。最后以VC++为平台,通过算例验证了该改进方法的有效性,并推导了改进后边界单元的形函数。

An Improvement on Boundary Elements of Complicated Domain Based on NURBS

In this paper, an improved meshing approach is proposed to improve the precision of boundary elements of the complicated domains. According to the approach, a complicated domain is meshed by the free-meshing strategy firstly, and the information of elements and nodes is generated automatically. Based on the elements and nodes information, the control points can be determined, which are used to represent the edge of boundary element by Non-Uniform Rational B-Spline (NURBS) curves. The element edges represented by NURBS can be more closed to the actual boundary by adjusting the power factors appropriately. Then, the shape functions of the improved boundary elements are deduced. Finally, an example validates the improvement is effective, and demonstrates the effect of power factors on NURBS curves.