This paper formulates quadrilateral elements for the NURBS-enhanced finite element method (NEFEM). The objective is to extend the application of NEFEM to problems where the use of quadrilateral elements is preferred. By leveraging a mapping, between reference and physical spaces, that encapsulates the exact boundary representation of the domain, a tight integration with computer aided design (CAD) systems is achieved. The contribution of this work is an enhanced quadrilateral finite element that incorporates the exact CAD geometry purely from the boundary representation (B-rep) from CAD and without the need for a whole volume representation (V-rep) as a NURBS entity. Numerical examples involving heat transfer and linear elastic problems are used to numerically demonstrate the optimal convergence properties of the method under mesh refinement.

本文为 NURBS 增强有限元法 (NEFEM) 制定了四边形单元。目标是将 NEFEM 的应用扩展到优先使用四边形单元的问题。通过利用参考空间和物理空间之间的映射，封装域的精确边界表示，实现与计算机辅助设计 (CAD) 系统的紧密集成。这项工作的贡献是增强的四边形有限元，它结合了纯粹来自 CAD 边界表示 (B-rep) 的精确 CAD 几何形状，而不需要作为 NURBS 实体的整个体积表示 (V-rep)。涉及传热和线弹性问题的数值例子被用来数值证明该方法在网格细化下的最佳收敛特性。