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A Novel Energy-Based Approach for Merging Finite Elements

Or Yogev, Andrew A. Shapiro, and Erik K. Antonsson

International Journal for Numerical Methods in Engineering,
Published Online 2010.

Abstract

A novel approach for merging two intersecting finite elements is presented and demonstrated. The solution mimics concepts from biology and uses principles rooted in continuum mechanics.

The problem of attaching (or merging) two coincident finite elements is common when using the plastering technique as part of the advancing front method. This problem is particularly challenging for 3-D meshes of non-convex shapes. Some automatic meshing methods require portions of the partially formed mesh to coincide and merge. This problem is generally solved with heuristic rules, which lack generality, and may have difficulties with unforeseen situations. The problem of merging two overlapping polyhedra may also appear in other applications such as computer graphics and CAD software.

A new approach to address the problem of merging is presented here. This solution does not utilize heuristic rules, but rather uses an approach based on minimization of strain energy. A fully automatic merging routine has been created that can address, in an optimum way, any situation of two nearby or overlapping elements that are to be merged. This approach, with minor adjustments, is suitable for most types of 3-D elements.