Reduction Methods for FE Analysis in Nonlinear Structural Dynamics

The computation of the nonlinear motion of large structures with implicit time integration schemes is costly. In each time step a large system of linear equations needs to be solved several times. In finite element models often a fine discretization is necessary to represent the geometry and to yield accurate results for the stress field. But from experience it is known that only a small number of degrees of freedom is sufficient to account for the dominant parts of a dynamic motion. Similar to modal decomposition, methods were developed to reduce the number of degrees of freedoms in nonlinear problems. Even though it is not possible to decompose the motion into decoupled modes, a reduction of the number of degrees of freedom yields less computational effort in many cases. The choice of appropriate basis vectors is important. Often used are load-dependent ‘Ritz’ vectors, which should be updated during the computation to yield sufficient accuracy. Dominant modes, computed by a proper orthogonal decomposition of a previous calculation can be used for repeated analyses of the same system with different loads. Significant time savings can be achieved with reduction methods. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)