Dynamic analysis of viscoelastic structures using incremental finite element method

Abstract

This paper presents an efficient and accurate incremental finite element procedure, without involving any integral transformations, to deal with practical viscoelastic structures with complicated geometries subjected to dynamic loadings. The numerical error induced from the approximate inversion technique used is thus avoided. Based on the Hamilton's variational principle, an incremental functional is derived for each time increment and the inertia terms are retained in the analysis to estimate the transient viscoelastic behaviours. To model the specific stress-strain-time constitutive behaviours of viscoelastic materials, the Norton type time hardening rule is employed. In the present computation procedure, the change of creep strains is regarded as increments of fictitious body forces at the nodal points for the next time increment. To evaluate the accuracy and the versatility of the solution technique developed in this work, several examples are given.