几何精确的非协调等几何NURBS有限元

本文尝试将传统的非协调有限元技术推广到等几何有限元领域，建立了基于精确几何的非协调等几何分析方法，旨在拓展等几何分析应用范围，以便于等几何分析技术能真正实现CAD和FEA的融合，从而真正实现了无需划分网格的目的。我们定义了非协调的NURBS几何（类似非协调元），给出了NURBS曲面之间几何弱连续的充分条件，进而定义了非协调的等几何分析，将之归纳为带约束驻值问题，并用拉格朗日方法进行求解。两个算例证明这种方法的有效性。未来的工作主要是证明这种方法在不同几何连续性条件下的收敛性以及将之应用到更广的领域。

NONCONFORMING ISOGEOMETRIC ANALYSIS BASED ON NURBS WITH EXACT GEOMETRY

Inspired by the idea of the nonconforming finite element method, and intending to address the incompatible CAD geometry for isogeometric analysis, a new isogeometric method called Nonconforming Isogeometric Analysis (NIGA) is proposed in this paper. The main purpose is to apply the isogeometric analysis directly to the trimmed NURBS models for structural analysis. This can lead to an efficient method for the isogeometric analysis of both a general and complicated engineering structure.