An inverse-free interface patch test for nonmatching FEM meshes

摘要

This paper considers methods for coupling of non-matching FEM meshes by dual schemes based on Lagrange multipliers. Nonmatching meshes are those where nodes and/or degrees of freedom do not match at an interface between two FEM models. One particular scheme is studied in some detail: concentrated Lagrange multipliers collocated at the boundary nodes and linked by an intermediate displacement-assumed frame. The key advantage of this configuration is that it does not require detailed knowledge of boundary displacement interpolation on either side of the interface. This increases software modularity since interfacing modules do not need to know the type of elements being coupled. A new inverse-free interface patch test (IFIPT) is developed to test the consistency of the frame in transmitting arbitrary constant stress states exactly. This form of the patch is of interest in symbolic manipulation because it does not require matrix inversion. In the case of displacement-frame-connected submeshes, the IFIPT is used to define the location of the frame nodes. An algebraic criterion that provides the frame node locations as the roots of a polynomial equation is presented. This criterion has been used in contact problems, in which frame node locations are adjusted during the response computations.