Search results for "Elasticity"
showing 10 items of 736 documents
Variational formulations and extra boundary conditions within stress gradient elasticity theory with extensions to beam and plate models
2016
Abstract The principle of minimum total potential energy and the primary principle of virtual power for stress gradient elasticity are presented as kinematic type constructs dual of analogous static type principles from the literature (Polizzotto, 2014; Polizzotto, 2015a). The extra gradient-induced boundary conditions are formulated as “boundary congruence conditions” on the microstructure’s deformation relative to the continuum, which ultimately require that the normal derivative of the stresses must vanish at the boundary surface. Two forms of the governing PDEs for the relevant boundary-value problem are presented and their computational aspects are discussed. The Timoshenko beam and th…
On the vibrations of a mechanically based non-local beam model
2012
The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …
Fractional visco-elastic Timoshenko beam from elastic Euler-Bernoulli beam
2014
The Euler–Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler–Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a …
Fractional visco-elastic Timoshenko beam deflection via single equation
2015
SUMMARY This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letni…
A mechanically based approach to non-local beam theories
2011
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…
Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam
2017
AbstractA mechanically-based nonlocal Timoshenko beam model, recently proposed by the authors, hinges on the assumption that nonlocal effects can be modeled as elastic long-range volume forces and moments mutually exerted by nonadjacent beam segments, which contribute to the equilibrium of any beam segment along with the classical local stress resultants. Long-range volume forces/moments linearly depend on the product of the volumes of the interacting beam segments, and on pure deformation modes of the beam, through attenuation functions governing the space decay of nonlocal effects. This paper investigates the response of this nonlocal beam model when viscoelastic long-range interactions a…
Analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem
2009
Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the def…
Timoshenko vs Euler-Bernoulli beam: fractional visco-elastic behaviour
2013
The Euler-Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of stress field or def lections of the elastic beam based on this theory. Conversely Timoshenko theory is not so much used by engineers. However in such cases Euler-Bernoulli theory that n eglects the effect of transversal shear deformation leads to unacceptable results. For inst ance when dealing with the visco-elastic behaviour the shear deformations play a fundamental role. Recent studies [1]-[2] on the response evaluation of visco-elastic Euler-Bernoulli beam under quasi-static and dynamic loads, have been stressed that for better capturing the visco-elastic behavio…
A Teaching Experience: Aeroelasticity and the Finite Element Method
2015
[EN] The aeroelastic modelling of aircraft structures is a fundamental area for the students of Aerospace Engineering Degree. This subject has a strongly multidisciplinary character and involves other several subjects like mechanics, vibrations, aerodynamics, structural analysis. Consequently, the students find stimulating the challenge of merging their knowledge at different areas. In this paper, a teaching experience on the solution of the aeroelastic problem of a 3D-wing through six different computer tasks is presented. The main objective is to attempt a relatively complex problem using a simple version of the Finite Element Method with only four degrees of freedom. The students begin c…
Fractional viscoelastic beam under torsion
2017
Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.