Search results for "Body force"
showing 10 items of 28 documents
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 …
Stress fields by the symmetric Galerkin boundary element method
2004
The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals. The aim of the paper is to show the tension state in Ω∞ as a response to all the actions acting in Ω when this analysis concerns the crossing of the discretized boundary, thu…
Iterative momentum relaxation for fast lattice-boltzmann simulations
1999
Lattice-Boltzmann simulations are often used for studying steady-state hydrodynamics. In these simulations, however, the complete time evolution starting from some initial condition is redundantly computed due to the transient nature of the scheme. In this article we present a refinement of body-force driven lattice-Boltzmann simulations that may reduce the simulation time significantly. This new technique is based on an iterative adjustment of the local body-force and is validated on a realistic test case, namely fluid flow in a static mixer reactor.
Modelling and Simulation of Gas–liquid Hydrodynamics in a Rectangular Air-lift Reactor
2013
Abstract Computational Fluid Dynamics is a quite well established tool for carrying out realistic simulations of process apparatuses. However, as a difference from single phase systems, for multiphase systems the development of CFD models is still in progress. Among the two-phase systems, gas–liquid systems are characterised by an additional complexity level, related to the fact that bubble sizes are not known in advance, being rather the result of formation and breakage-coalescence dynamics and therefore of complex phenomena related to flow dynamics and interfacial effects. In the present work, Euler–Euler Reynolds-averaged flow simulations of an air-lift reactor are reported. All bubbles …
Variational Aspects of the Physically-Based Approach to 3D Non-Local Continuum Mechanics
2010
This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…
Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory
2009
In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself…
A generalized model of elastic foundation based on long-range interactions: Integral and fractional model
2009
The common models of elastic foundations are provided by supposing that they are composed by elastic columns with some interactions between them, such as contact forces that yield a differential equation involving gradients of the displacement field. In this paper, a new model of elastic foundation is proposed introducing into the constitutive equation of the foundation body forces depending on the relative vertical displacements and on a distance-decaying function ruling the amount of interactions. Different choices of the distance-decaying function correspond to different kind of interactions and foundation behavior. The use of an exponential distance-decaying function yields an integro-d…
Long-range interactions in 1D heterogeneous solids with uncertainty
2013
Abstract In this paper, the authors aim to analyze the response of a one-dimensional non-local elastic solid with uncertain Young's modulus. The non-local effects are represented as long-range central body forces between non-adjacent volume elements. Following a non-probabilistic approach, the fluctuating elastic modulus of the material is modeled as an interval field. The analysis is conducted resorting to a novel formulation that confines the overestimation effect involved in interval models. Approximate closed-form expressions are derived for the bounds of the interval displacement field.
The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions
2010
Abstract This paper presents the generalization to a three-dimensional (3D) case of a mechanically-based approach to non-local elasticity theory, recently proposed by the authors in a one-dimensional (1D) case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range forces exerted by non-adjacent elements. Specifically, the long-range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements, measured along the line connecting the centroids. Further, the long-range forces are assumed to be proportional to a proper, material-dependent, dis…
The finite element method for the mechanically based model of non-local continuum
2011
SUMMARY In this paper the finite element method (FEM) for the mechanically based non-local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter-distance and proportional to the product of the interacting volume elements. The constitutive relations of the long-range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance-decaying function, which accounts for the decrement of the long-range interac…