Search results for "Mathematica"

showing 10 items of 7971 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…

Body forceApplied MathematicsMechanical EngineeringMathematical analysisBoundary (topology)Mixed boundary conditionSingular boundary methodBoundary knot methodVolume integralMechanics of MaterialsModeling and SimulationGalerkin methodBoundary element methodMathematicsThe Journal of Strain Analysis for Engineering Design
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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…

Body forceNon-local elasticityDiscretizationField (physics)Mechanical EngineeringLinear elasticityConstitutive equationMathematical analysisCentral volume forceEquivalent mechanical modelThermodynamic consistencyContact forceLong-range interactionMechanics of MaterialsDisplacement fieldGeneral Materials ScienceBoundary value problemSettore ICAR/08 - Scienza Delle CostruzioniMathematicsJournal of Elasticity
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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…

Body forceNon-local elasticityElastic foundationsDifferential equationConstitutive equationFractional calculuElastic foundationMaterials Science(all)Long-range forcesLong-range forceModelling and SimulationGeneral Materials ScienceMathematicsApplied MathematicsMechanical EngineeringMathematical analysisFractional calculusFunction (mathematics)Condensed Matter PhysicsIntegral equationFractional calculusExponential functionMejier-G functionsGradient modelsMechanics of MaterialsModeling and SimulationDisplacement fieldGradient modelSettore ICAR/08 - Scienza Delle Costruzioni
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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.

Body forceNon-local elasticityField (physics)non-local elasticity; long-range interactions; interval field; upper bound and lower bound.Mathematical analysisModulusGeneral MedicineInterval (mathematics)Upper and lower boundsLong-range interactionLong-range interactionsInterval field; Long-range interactions; Non-local elasticity; Upper bound and lower boundDisplacement fieldRange (statistics)Interval fieldUpper bound and lower boundSettore ICAR/08 - Scienza Delle CostruzioniElastic modulusMathematics
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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…

Body forceNumerical AnalysisCauchy stress tensorApplied MathematicsNumerical analysisMathematical analysisConstitutive equationGeneral EngineeringFinite difference methodVolume elementElasticity (economics)Finite element methodMathematicsInternational Journal for Numerical Methods in Engineering
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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…

Body forceState variableNon-local elasticityNon-local state variablesConstitutive equationEuler–Lagrange equationLong-range interactionNon-local state variableMaterials Science(all)Modelling and SimulationGeneral Materials ScienceVirtual workBoundary value problemMathematicsVariational theoremsMechanical EngineeringApplied MathematicsMathematical analysisCondensed Matter PhysicsPotential energyLong-range interactionsClassical mechanicsMechanics of MaterialsModeling and SimulationNon-local elastic potential energyCalculus of variationsSettore ICAR/08 - Scienza Delle CostruzioniInternational Journal of Solids and Structures
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The development of a hybrid technique employing the boundary element method for thermoelastic stress separation

2000

: This paper presents a development of a hybrid technique employing a boundary element method for determining individual stress components in two-dimensional arbitrarily shaped domains from experimental isopachics only. The procedure consists of a numerical solution of two Poisson equations representing equilibrium for two-dimensional plane-stressed solids with zero body forces. An existing technique is employed for smoothing interior thermoelastic data and enhancing boundary information. The algorithm of stress separation has been implemented with the help of commercial codes. The whole procedure has been tested through a complete post-processing example of thermoelastic stress analysis da…

Body forceStress (mechanics)Thermoelastic dampingMechanics of MaterialsMechanical EngineeringNumerical analysisMathematical analysisBoundary (topology)GeometryPoisson's equationBoundary element methodSmoothingMathematics
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One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis

2013

The analysis of one-dimensional non-local elastic solids with uncertain Young's modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic response.

Body forcedecompositionRandom fieldNon-local elasticityStochastic processMechanical EngineeringMathematical analysisKarhunen-Loeve decompositionModulusInterval (mathematics)Karhunen–LoèveComputer Science ApplicationsInterval arithmeticResponse statisticsNon-local elasticity; Interval field; Random field; Karhunen–Loève; decomposition; Upper bound and lower bound; Response statisticsModeling and SimulationDisplacement fieldRandom fieldGeneral Materials ScienceInterval fieldUpper bound and lower boundSettore ICAR/08 - Scienza Delle CostruzioniElastic modulusCivil and Structural EngineeringMathematics
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The Complex System Theory for the Analysis of Inter-Firm Networks: A Literature Overview and Theoretic Framework

2011

In this paper we discuss the body of knowledge known as complex system theory and its relevance to the analysis of inter-firm networks. We start by addressing the development of systems thinking. Through a literature overview, we point out the main elements for the development of systemic thought from its beginning, through its application in business sciences, to the birth of Complex Systems Theory (CST). With these initial annotations we provide an introduction to the concepts of the complex systems theory. We will underscore those aspects of CST that can be useful to analyze inter-firm networks, in order to highlight the evolutionary dynamics of the networks and to clarify the logical li…

Body of knowledgeStructure (mathematical logic)Inter-firm networks Complex System TheoryManagement scienceComputer scienceComplex systemBusiness system planningMulti-level logicSystems thinkingCognitionRelevance (information retrieval)Evolutionary dynamicsSettore SECS-P/08 - Economia E Gestione Delle Imprese
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Structure of Dioxygen Binding Xerogels Incorporating Cyclams Complexed with CuCl2 Salts

2005

X-ray absorption/emission spectroscopies were combined in order to elucidate how hybrid xerogels complexed with CuCl2 could bind reversibly O2. Difference EXAFS analyses at the Cu K-edge revealed the existence of binuclear structures with long Cu...Cu distances, i.e. RCu–Cu ≈ 3.98 A and 3.87 A for the oxygenated and oxygen-free xerogels. In oxygenated xerogels, dioxygen would bridge two Cu atoms in a μ-η1 : η1 peroxo-like conformation. The Cu-O signal found at short distance (RCu−O1 = 1.85 ± 0.01 A) is fully consistent with 40% of O2 molecules being chemisorbed per Cu site. In oxygen-free xerogels, Cl K-edge EXAFS revealed the presence of CuI sites with short Cl-Cu bond lengths (RCl−Cu = 2.…

Bond lengthCrystallographyExtended X-ray absorption fine structureChemistryChemical shiftMoleculeAbsorption (chemistry)Condensed Matter PhysicsResonance (chemistry)Mathematical PhysicsAtomic and Molecular Physics and OpticsXANESSpectral linePhysica Scripta
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