A Numerical Scheme for Time-Domain FE Analysis of Viscoelastic Structures with Fractional Derivative Constitutive Equations

Abstract

A numerical scheme is presented for time-domain simulations of structural dynamic problems with viscoelastic materials described by fractional derivative constitutive equations. The proposed approach combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a system of linear differential equations. The focus is given on the general formulation of the problem, the algorithm implementation into a finite element framework, and the developpement of a closed-form solution for a fractionnally damped single degree-of-freedom equation.