Quadrilateral-area-coordinate-based numerical manifold method accommodating static and dynamic analysis

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 conecomplementary-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.

Automated summary

This study reveals the intrinsic shortcomings of NMM based on quadrilateral isoparametric mapping for the first time, leading to the establishment of a new NMM using a quadrilateral area coordinate system to overcome these drawbacks. The proposed method allows for analytically determining the stiffness matrix without the need for cumbersome Jacobian inversion and numerical integration, while also formulating a conecomplementary-based contact model to accurately determine frictional and cohesive contact forces. This new NMM framework eliminates the need for artificial penalty and open-close iteration, showing excellent performance in several benchmark examples.