Krylov Subspace Accelerated Newton Algorithm: Application to Dynamic Progressive Collapse Simulation of Frames

Abstract

An accelerated Newton algorithm based on Krylov subspaces is applied to solving nonlinear equations of structural equilibrium. The algorithm uses a low-rank least-squares analysis to advance the search for equilibrium at the degrees of freedom (DOFs) where the largest changes in structural state occur; then it corrects for smaller changes at the remaining DOFs using a modified Newton computation. The algorithm is suited to simulating the dynamic progressive collapse analysis of frames where yielding and local collapse mechanisms form at a small number of DOFs while the state of the remaining structural components is relatively linear. In addition, the algorithm is able to resolve erroneous search directions that arise from approximation errors in the tangent stiffness matrix. Numerical examples indicate that the Krylov subspace algorithm has a larger radius of convergence and requires fewer matrix factorizations than Newton-Raphson in the dynamic progressive collapse simulation of reinforced concrete and steel frames.