Search results for " mechanics."
showing 10 items of 5002 documents
Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation
2013
The solution of curved Timoshenko beams with or without generalized two-parameter elastic foundation is presented. Beam can be subjected to any kind of loads and imposed external actions, distributed or concentrated along the beam. It can have external and internal restraints and any kind of internal kinematical or mechanical discontinuity. Moreover, the beam may have any spatial curved geometry, by dividing the entire structure into segments of constant curvature and constant elastic properties, each segment resting or not on elastic foundation. The foundation has six parameters like a generalized Winkler soil with the addition of other two parameters involving the link between settlements…
Unified theory for analysis of curved thin-walled girders with open and closed cross section through HSA method
2016
Abstract The behaviour of thin-walled structures is deeply influenced by non-uniform torsion and cross section distortion. In this paper the extension of the Hamiltonian Structural Analysis (HSA) Method to thin-walled straight and curved beams is presented. The proposed method solves the structural elastic problem of thin-walled beams through the definition of a Hamiltonian system composed of 1st order differential equations. The method allows engineers to solve the elastic problem by introducing the degrees of freedom and the corresponding compatibility equations, founding equilibrium equations in the variational form. The methodology is explained in the framework of the so-called Generali…
From the Euler–Bernoulli beam to the Timoshenko one through a sequence of Reddy-type shear deformable beam models of increasing order
2015
Abstract A sequence of elastic Reddy-type shear deformable beams of increasing (odd) order is envisioned, which starts with the Euler–Bernoulli beam (first order) and terminates with the Timoshenko beam (infinite order). The kinematics of the generic beam, including the warping mode of the cross sections, is specified in terms of three deformation variables (two curvatures, one shear angle), work-conjugate of as many stress resultants (two bending moments, one shear force). The principle of virtual power is used to determine the (static) equilibrium equations and the boundary conditions. The equations relating the bending moments and shear force to the curvatures and shear angle are also re…
Finite element method for a nonlocal Timoshenko beam model
2014
A finite element method is presented for a nonlocal Timoshenko beam model recently proposed by the authors. The model relies on the key idea that nonlocal effects consist of long-range volume forces and moments exchanged by non-adjacent beam segments, which contribute to the equilibrium of a beam segment along with the classical local stress resultants. The long-range volume forces/moments are linearly depending on the product of the volumes of the interacting beam segments, and their relative motion measured in terms of the pure beam deformation modes, through appropriate attenuation functions governing the spatial decay of nonlocal effects. In this paper, the beam model is reformulated wi…
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 …
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…
A new displacement-based framework for non-local Timoshenko beams
2015
In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of non-adjacent beam segments, and separately accounting for pure axial, pure bending and pure sh…
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…
Dehydration of Fructose to 5-HMF over Acidic TiO2 Catalysts
2020
Different solid sulfonic titania-based catalysts were investigated for the hydrothermal dehydration of fructose to 5-hydroxymethylfurfural (5-HMF). The catalytic behavior of the materials was evaluated in terms of fructose conversion and selectivity to 5-HMF. The surface and structural properties of the catalysts were investigated by means of X-ray diffraction (XRD), N2 adsorption isotherms, thermo-gravimetric analysis (TGA), X-ray photoelectron spectroscopy (XPS) and acid capacity measurements. Special attention was focused on the reaction conditions, both in terms of 5-HMF selectivity and the sustainability of the process, choosing water as the solvent. Among the various process condition…