Search results for "NONLOCAL ELASTICITY"

Wave propagation in 1D elastic solids in presence of long-range central interactions

2011

Abstract In this paper wave propagation in non-local elastic solids is examined in the framework of the mechanically based non-local elasticity theory established by the author in previous papers. It is shown that such a model coincides with the well-known Kroner–Eringen integral model of non-local elasticity in unbounded domains. The appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the Cauchy stress. In fact, the long-range forces between different volume elements are modelled, in the body domain, as central body forces applied to the interacting elements. It is …

Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay

2010

Abstract An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. …

Nonlocal analytical solution for multilayered composite shells

2021

Abstract In this work, an advanced nonlocal analytical formulation for the static analysis of composite shell structures is proposed. The governing equations are derived from the Principle of Virtual Displacement (PVD) [1] and are solved by the use of the Navier solution [2]. Layer-Wise models related to linear up to fourth order variations of the unknown variables in the thickness direction are treated. The modelization of multilayered structure materials takes into account the composite material properties and the nonlocal behavior based on the work of Eringen [3]. In order to take into account the nonlocality of the material, the Eringen’s stress-gradient model is employed [4]. The novel…

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

2021

AbstractIn this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the prop…

Mixed finite elements for nonlocal elastic multilayered composite plate refined theories

2020

Abstract A novel mixed finite element formulation for the layerwise analysis of nonlocal multilayered composite plates is presented. The finite elements are formulated starting from the weak form of a set of governing equations for the laminate layers that were deduced via the Reissner Mixed Variational Theorem. The primary variables, namely displacements and out-of-plane stresses, are expressed at layer level as through-the-thickness expansions of suitable selected functions with coefficients approximated by the finite element scheme. The through-the-thickness expansion order is considered as a free parameter. This way, finite elements for different refined higher order plate theories can …

Refined layer-wise models for nonlocal analysis of magneto-electro-elastic plates

Size-dependent theories of continuum mechanics are an important tool for structural and material modeling in engineering applications, with particular regard to those involving micro- and nano-scales. Among various approaches proposed in the literature to account for the effect of the microstructure via continuum models, the Eringen’s nonlocal elasticity model incorporates important features of material behavior via a differential stress-strain relationship involving a scale coefficient, or characteristic length, depending on the material microstructure [1]. In the framework of Eringen’s nonlocal elasticity, plate theories have been reformulated for homogeneous and multilayered configuratio…

Mixed Finite Elements for multilayered smart plates nonlocal analysis

2022

A mixed finite element formulation for the Eringen’s nonlocal analysis of smart, magneto-electro-elastic, multilayered plates is presented. Finite elements for different refined higher order plate layerwise theories are systematically developed. They ensure interface continuity and allow associating different values of the nonlocal parameter to the laminate layers. Standard 9-node and 16-node isoparametric, quadrilateral finite elements have been implemented and tested, showing the characteristics and limitations of the proposed approach.

A theoretical link between gradient and nonlocal elasticity models, including higher order boundary conditions

2013

The paper presents a recently developed rational derivation of the strain gradient elasticity model from the nonlocal (or integral) model. This kind of derivations are generally recovered just by an expansion into a Taylor series of the nonlocal strain field up to a certain order, and then operating the integration (or averaging) over the spatial interaction domain. The latter procedure is fully consistent when the analysis is performed over an unbounded domain, but when a classical bounded domain is analyzed it lacks in reproducing the so-called higher-order boundary conditions. In the present contributions the complete derivation is achieved employing an extended version of the Principle …

Mechanically Based Nonlocal Euler-Bernoulli Beam Model

2014

AbstractThis paper presents a nonlocal Euler-Bernoulli beam model. It is assumed that the equilibrium of a beam segment is attained because of the classical local stress resultants, along with long-range volume forces and moments exchanged by the beam segment with all the nonadjacent beam segments. Elastic long-range volume forces/moments are considered, built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the nonlocal effects are introduced. The motion equations are derived in an integro-differential …