Quadrilateral mesh is a commonly used mathematical cover for numerical manifold method (NMM). However, the NMM based on quadrilateral isoparametric mapping has some intrinsic shortcomings, which is revealed for the first time in this study. Therefore, a new NMM is established to overcome these drawbacks by adopting a quadrilateral area coordinate system. In the proposed NMM, the stiffness matrix can be analytically determined without resorting to cumbersome Jacobian inversion and numerical integration. Moreover, a cone-complementary-based contact model is formulated in the context of the new NMM framework, which enables accurate determination of frictional and cohesive contact forces in solving dynamic contact problems. Thus, artificial penalty and open-close iteration in the original NMM can be all avoided. Several benchmark examples are simulated to demonstrate the excellent performance of the presented NMM.

四边形网格是数值流形方法 (NMM) 的常用数学覆盖。然而，基于四边形等参映射的 NMM 存在一些固有的缺点，这是本研究首次揭示的。因此，通过采用四边形区域坐标系，建立了一种新的 NMM 来克服这些缺点。在提出的 NMM 中，刚度矩阵可以通过分析确定，而无需求助于繁琐的雅可比反演和数值积分。此外，在新的 NMM 框架的上下文中制定了一个基于锥体互补的接触模型，它可以在解决动态接触问题时准确确定摩擦力和内聚力。这样，原始 NMM 中的人为惩罚和开闭迭代都可以避免。