A reduction method for nonlinear structural dynamic analysis

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.