Dynamic Viscoelastic Beam Model for Finite Element Method

Abstract

A finite element formulation is presented for the viscoelastic dynamic responses of Euler‐Bernoulli beams. A time‐stepping procedure based on New‐mark's method is employed. The changes in creep strain during a time step are treated as additional fictitious body forces for the next time step. A uniaxial Norton‐type strain‐hardening material law is employed. The aims of the proposed formulation are model simplicity, efficiency of the solution procedure, and ease of application. Quasi‐static and dynamic viscoelastic responses for beams under quasi‐static and earthquake motion are obtained. The results are compared with existing alternate solutions to demonstrate the validity of the present work.