UPDATING OF A NONLINEAR FINITE ELEMENT MODEL USING DISCRETE-TIME VOLTERRA SERIES

Abstract

IN THIS STUDY, THE DISCRETE-TIME VOLTERRA SERIES ARE USED TO UPDATE PARAMETERS IN A NONLINEAR FINITE ELEMENT MODEL. THE MAIN IDEA OF THE VOLTERRA SERIES IS TO DESCRIBE THE DISCRETE-TIME OUTPUT OF A NONLINEAR SYSTEM USING MULTIDIMENSIONAL CONVOLUTIONS BETWEEN THE VOLTERRA KERNELS REPRESENTED IN A KAUTZ ORTHOGONAL BASIS AND THE EXCITATIONS. A METRIC BASED ON THE RESIDUE BETWEEN THE EXPERIMENTAL AND THE NUMERICAL VOLTERRA KERNELS IS USED TO IDENTIFY THE PARAMETERS OF THE NUMERICAL MODEL. FIRST, THE IDENTIFICATION OF THE LINEAR PARAMETERS IS PERFORMED USING A METRIC BASED ONLY ON THE FIRST ORDER VOLTERRA KERNELS. THEN THE NONLINEAR PARAMETERS ARE IDENTIFIED THROUGH A METRIC BASED ON THE HIGHER-ORDER KERNELS. THE ORIGINALITY OF THIS NONLINEAR UPDATING METHOD STEMS FROM THE DECOUPLING OF LINEAR AND NONLINEAR PARAMETERS AND THE USE OF GLOBAL NONLINEAR MODEL. IN ORDER TO PUT IN LIGHT THE APPLICABILITY OF THIS TECHNIQUE, THIS WORK FOCUS ON THE IDENTIFICATION OF THE PARAMETERS IN A NONLINEAR FINITE ELEMENT MODEL OF A BEAM THAT WAS PRELOADED BY COMPRESSION MECHANISM. THIS WORK SHOWS THAT THE UPDATED NUMERICAL MODEL WAS ABLE TO REPRESENT THE BEHAVIOUR OBSERVED IN THE EXPERIMENTAL MEASUREMENTS.