一种面片删减的等几何分析新方法

A new isogeometric analysis method using patch removal

等几何分析(IGA-Isogeometric Analysis)方法采用NURBS基函数和NURBS控制点代替等参有限元分析方法中的形函数和节点,实现了CAD与CAE模型的有机融合.然而由于单个完整NURBS面片的拓扑局限性,等几何分析方法还不便应用于带孔等复杂结构.本文提出了一种面片删减的等几何分析新方法,通过在一个基础面片中删除子面片来直接获得带孔结构的几何模型,并采用简化的T样条局部细化方法和高效的控制点调整策略,以提高计算效率和分析精度.针对平面复杂带孔结构包含的外形复杂和孔形复杂两种情况,通过相应的数值算例验证了新方法的有效性.

Isogeometric analysis （IGA） method is an integration of CAD and CAE models as it substitutes shape functions and nodal points in isoparametric FEM with NURBS basis functions and control points. However, due to the topological limitations of a single intact NURBS patch, it is inconvenient for IGA method to be applied in complex topology like the structure with holes. Thus, this paper presents a new IGA method using patch removal. This method can directly obtain the geometric model of the holed structure by removing sub-patches from the base patch. Furthermore, it can also improve the computational efficiency and analytical precision through the application of simplified T-splines local refinements and efficient adjustive strategies of control points. The validity of this new method has been proved by means of numerical examples of holed structures with complicated exterior or/and interior shapes.