中文摘要：

当为 isogeometric 分析的几何建模和数字模拟工具，概括 B 花键被采用了(IGA 为短) 。然而，在 IGA 使用的以前的模型例如三角法的概括 B 花键或夸张概括 B 花键，不是 conics 和多项式的统一数学表示参量的弄弯 / 出现。在这份报纸，在空间构造概括不一致的 B 花键的一条统一途径跨越了由 {(t) ，(t) ，(t) ，(t) ， 1， t，攠楶敤吗？

英文摘要：

Abstract Generalized B-splines have been employed as geometric modeling and numerical simu- lation tools for isogeometric analysis （IGA for short）. However, the previous models used in IGA, such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper, a unified approach to construct the generalized non-uniform B-splines over the space spanned by {α（t）,β（t）,ξ（t）, η（t）, 1, t,……. , tn-4} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometrie heat conduction problems are presented to show the effectiveness of the proposed methods.