Coupling Non-Conforming Discrete Models with Lower-Dimensional Entities
Danczyk, J. and Suresh, K.
Research Notes, 19th International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 3-6 2010
19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010
University of Wisconsin - Madison1513 University Ave. Madison, WI 53706.
In structural mechanics, large scale simulations often exceed the capabilities of a single computer. The underlying
spatial domain is therefore partitioned into multiple sub-domains for parallel computation [1, 2]. This partitioning of
the spatial domain can be across components of an assembly or an arbitrary interface within a single part. In both cases,
the two sides are numerically ëweldedí during the analysis.
While the interface geometry, typically defined via computer-aided design (CAD) models, is unique, the
discretization, or meshing, procedure will produce a discrete model/mesh that does not necessarily: 1. conform to the
CAD model, or 2. conform to the adjoining discrete model. This is typically the case when the interface is a curved
surface. Thus the four possible outcomes are:
1. Meshes conform to CAD and to each other. This case is easily handled since both the CAD models and mesh models conform.
2. Meshes donít conform to CAD but conform to each other. Again, this case is easy to handle as the meshes conform.
3. Meshes conform to CAD but not to each other. This is illustrated in Figure 1a, and is the classic case of "non-conforming" or "non-matching" grids that is typically addressed by the Mortar Element Method [3-6] (MEM) amongst others [7-12].
4. Meshes donít conform to CAD and donít conform to each other. This is illustrated by Figure 1b, and is of primary concern in this paper.
While case (4) above has previously been addressed via a suitable modification of MEM  we propose here an
alternate, and perhaps simpler, technique to couple, or glue, the physics back together through a lower-dimensional
entity at the interface. For example, in 2D plane stress, a beam is used between the two sides of the interface. While
 demonstrates beam to solid coupling we differ in that here the beam is oriented tangent to the surface instead of
normal. This lower-dimensional entity "fills in the gaps" between the discrete models, acting as a mechanism to transfer information between the two meshes.
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