A reduction method for nonlinear structural dynamic analysis

Published in Comput. Methods Appl. Mech. Engrg. Vol. 49(3), pp. 253-279, 1985
doi: 10.1016/0045-7825(85)90125-2

Abstract

A computational algorithm for predicting the nonlinear dynamic response of a structure is presented. The nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a Rayleigh-Ritz analysis. The basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing. Only a few basis updatings are required during the whole time integration.

The truncation error introduced at every change of basis is pointed out as the cause for a divergence-type behaviour, and some means for eliminating it are discussed.

Results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations.