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论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.
The paper attempts to generalize the traditional non-coordinated finite element method to the field of geometric equivalent finite element, and establishes a non-coordinated geometric analysis method based on exact geometry to expand the application range of geometric analysis so that the geometric analysis technology can really achieve CAD And FEA, so as to realize the goal of no mesh division.We define the non-coordination NURBS geometry (similar to non-coordination elements), and give the sufficient conditions for the geometric weak continuity between NURBS surfaces, and then define the non-coordination , Which are summarized as the problem of constrained stationed values and solved by Lagrange method.The two examples show the effectiveness of this method.The main work in the future is to prove that this method is applicable in different geometrical continuity Convergence under the conditions and its application to a wider area.