Model reduction methods for dynamic analyses of large structures

Abstract

User-friendly finite element pre-processors permit detailed modelling of engineering structures with complicated topologies, often resulting in a much larger number of degrees of freedom than that motivated by the expected complexity of the structural response. Dynamic analyses of these large-scale models might require a prohibitive amount of CPU time. In particular, the uncoupling of the equations of motion for linear systems with non-proportional damping by means of a complex eigenvector basis is computationally very demanding. We present general model reduction procedures, applicable to whole structures or substructures, that produce a series of reduced models each spanning appropriate subspaces (general Krylov spaces) of the solution space. Crucial steps in such procedures are the selection of basis vectors for the (sub)structures and the control of reduction errors. The set of basis vectors is generated by using a simple physical approach for successively reducing the residual error in the governing equilibrium equations. A frequency window method (shifting) is used to capture the relevant frequency content. The residuals of the equilibrium equations, computed on fully expanded level, are used as reliable measures of the reduction errors. The efficiency of the techniques is demonstrated in some numerical experiments and on a large engineering problem, using a program based on SAP IV.