Search results for " Fractional viscoelasticity"
showing 4 items of 4 documents
On the dynamics of non-local fractional viscoelastic beams under stochastic agencies
2018
Abstract Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white no…
Stochastic Analysis of a Nonlocal Fractional Viscoelastic Bar Forced by Gaussian White Noise
2017
Recently, a displacement-based nonlocal bar model has been developed. The model is based on the assumption that nonlocal forces can be modeled as viscoelastic (VE) long-range interactions mutually exerted by nonadjacent bar segments due to their relative motion; the classical local stress resultants are also present in the model. A finite element (FE) formulation with closed-form expressions of the elastic and viscoelastic matrices has also been obtained. Specifically, Caputo's fractional derivative has been used in order to model viscoelastic long-range interaction. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non…
Stochastic analysis of a non-local fractional viscoelastic beam forced by Gaussian white noise
2017
Recently, a displacement-based non-local beam model has been developed and the relative finite element (FE) formulation with closed-form expressions of the elastic and fractional viscoelastic matrices has also been obtained. The static and quasi-static response has been already investigated. This work investigates the stochastic response of the non-local fractional viscoelastic beam, forced by a Gaussian white noise. In this context, by taking into account the mass of the beam, the system of coupled fractional differential equations ruling the beam motion can be decoupled with the method of the fractional order state variable expansion and statistics of the motion of the beam can be readily…
The finite element implementation of 3D fractional viscoelastic constitutive models
2018
Abstract The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1]. Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long “fading memory”. From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. …