Mixed linear complementarity formulation of discontinuous deformation analysis

Abstract

In the classical Discontinuous Deformation Analysis (DDA) the contact conditions are enforced by what is referred to as open–close iteration. The open–close iteration involves repeatedly fixing and removing the artificial springs between blocks in contact and thus falls into the category of trial-and-error solution procedures that cannot guarantee the solution is always convergent. Meanwhile, improper stiffness parameters of the artificial springs might cause numerical problems. In order to avoid the introduction of the artificial parameters and to avoid the open–close iteration, this study reformulates DDA as a mixed linear complementarity problem (MLCP). Then, the Fisher–Burmeister Line Search Algorithm (FBLSA) is modified to solve MLCP. Some typical examples including those originally designed by the DDA inventor are reanalyzed, proving the procedure is feasible.