Search results for "Applied Mathematics"
showing 10 items of 4379 documents
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…
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…
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…
Mechanically-based approach to non-local elasticity: Variational principles
2010
Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…
Analysis of Spatially and Temporally Overlapping Events with Application to Image Sequences
2006
Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonisotropic 3D Boolean model, for performing this analysis: the temporal Boolean model. Some probabilistic properties are derived and a methodology for parameter estimation from time-lapse image sequences is proposed using an explicit treatment of the temporal dimension. We estimate the mean number of germs per unit area and time, the mean grain size and the duration distribution. A wide simulation study in order to assess the proposed estimators showed promising resul…
Managing Human Factors to Reduce Organisational Risk in Industry
2018
[EN] Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making (MCDM)-based approach to support organizational risk assessment in industrial environments. The decision-making trial and evaluation laboratory (DEMATEL) method is proposed as a mathematical framework to evaluate mutual relationships within a set of human factors involved in industrial processes, with the aim of highlighting priorities of intervention. A case study relat…
Uniqueness of diffusion on domains with rough boundaries
2016
Let $\Omega$ be a domain in $\mathbf R^d$ and $h(\varphi)=\sum^d_{k,l=1}(\partial_k\varphi, c_{kl}\partial_l\varphi)$ a quadratic form on $L_2(\Omega)$ with domain $C_c^\infty(\Omega)$ where the $c_{kl}$ are real symmetric $L_\infty(\Omega)$-functions with $C(x)=(c_{kl}(x))>0$ for almost all $x\in \Omega$. Further assume there are $a, \delta>0$ such that $a^{-1}d_\Gamma^{\delta}\,I\le C\le a\,d_\Gamma^{\delta}\,I$ for $d_\Gamma\le 1$ where $d_\Gamma$ is the Euclidean distance to the boundary $\Gamma$ of $\Omega$. We assume that $\Gamma$ is Ahlfors $s$-regular and if $s$, the Hausdorff dimension of $\Gamma$, is larger or equal to $d-1$ we also assume a mild uniformity property for $\Omega$ i…
Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions
2016
Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…
Stress gradient versus strain gradient constitutive models within elasticity
2014
Abstract A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Helling…