Algebraic elimination of slide surface constraints in implicit structural analysis

Slide surface and contact boundary conditions can be implemented via Lagrange multipliers in the algebraic equations in implicit structural analysis. This indefinite set of equations is difficult to solve by iterative methods and is often too large to be solved by direct methods. When there are m constraints and there exists a set of in variables where each variable is only involved in a single constraint, we advocate a direct elimination technique which leaves a sparse, positive definite system to solve by iterative methods. We prove that the amount of 'fill-in' created by this process is independent of the size of the slide surfaces. In addition, the eigenvalues of the reduced matrix do not differ significantly from the eigenvalues of the unconstrained matrix. This method can be extended to the case where constrained surfaces intersect and leads to a graph theoretic approach for determining which variables can be eliminated efficiently for constraints with more general structure. Published in 2003 by John Wiley Sons, Ltd.