Chaotic Motion of an Elastic-Plastic Beam

Abstract

A numerical study is presented here which suggests that chaotic motion is possible from periodic excitation of an elastic-plastic beam. Poincare´ maps of the motion reveal a fractal-like structure of the attractor. The results suggest that geometric and material nonlinearities in solid mechanics problems may lead to extreme sensitivity to small changes in parameters and resulting unpredictability. These results may explain the total disagreement of nine finite element codes in the analysis of the transient response of an elastic-plastic beam, that has been reported recently by Symonds and his coworkers.