Static reanalysis of structures with added degrees of freedom

Abstract

This paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate-gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd.