Interfacing nonmatching FEM meshes: the zero moment rule

Abstract

This is a tutorial paper that outlines, through a benchmark example, an efiective method for coupling nonmatched flnite element meshes. Coupling is done through a displacement frame interposed between the interface meshes. That frame is treated with a FEM discretization and \glued" to the meshes through localized Lagrange multipliers collocated at mesh-interface nodes. The approach can be used to couple meshes of arbitrary geometry, discretization type (e.g., FEM and BEM) and even meshes of difierent physics (e.g., structure and ∞uids). The example, however, focuses on a simplifled 2D case that can be explained within space constraints. The requirement for preservation of constant stress states leads to an easily visualized condition, called the zero-moment rule or ZMR, that can be used to locate frame nodes on frame geometry. The ZMR provides all possible consistent frame-node conflgurations. Generalizations of the 2D ZMR rule to 3D problems involve partitioning of the frame and are not reported here. Thus the ZMR is necessary but not su-cient. The constant stress consistency condition may be interpreted, according to the reader's taste, as either an interface patch test, a vanishing of the flrst variation of the interface potential under admissible kinematic modes, or a requirement for energy conservation across the interface.

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