Search results for "Mathematical analysis"

showing 10 items of 2409 documents

A new method for generating fully isotropic laminates

2002

In this paper the authors propose some new kinds of isotropic laminates, made with identical anisotropic layers. In particular, these laminates satisfy some conditions which generalise the well-known Werren and Norris rules, in order to obtain fully isotropy, that is, isotropy of the three tensors A, B and D. To this purpose, the authors utilise some results found in a preceding research, namely the so-called quasi-trivial solutions. The way to form particular isotropic laminates that do not follow the Werren and Norris rule is also indicated. The paper ends with some numerical examples which illustrate the theoretical results found.

Materials scienceClassical mechanicsNumerical analysisMathematical analysisIsotropyCeramics and CompositesPolar coordinate systemAnisotropyCivil and Structural EngineeringComposite Structures
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A physical description of fractional-order Fourier diffusion

2014

In this paper the authors introduce a physical picture of anomalous heat transfer in rigid conductor. The analysis shows that a fractional-order Fourier transport is obtained by the analysis of the heat transport in a functionally graded conductor. The order of the fractional-type operator obtained is related to the grading of the physical properties of the conductor.

Materials scienceDifferential equationMathematics::Number TheoryOperator (physics)Mathematical analysisCondensed Matter::Mesoscopic Systems and Quantum Hall EffectConductorsymbols.namesakeFourier transformFourier numberThermal diffusion Fourier Equations Fractional-order calculus Temperature evolutionHeat transfersymbolsDiffusion (business)Settore ICAR/08 - Scienza Delle CostruzioniElectrical conductorICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014
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On the dynamics of non-local fractional viscoelastic beams under stochastic agencies

2018

Abstract Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white no…

Materials scienceDiscretization02 engineering and technologyWhite noiseIndustrial and Manufacturing Engineering0203 mechanical engineeringFractional viscoelasticityComposite materialImpulse responseNon local Timoshenko beamMechanical EngineeringMathematical analysisEquations of motionWhite noise021001 nanoscience & nanotechnologyPhysics::History of PhysicsNon local Timoshenko beam; Fractional viscoelasticity; White noise; State variable expansionFractional calculusNumerical integration020303 mechanical engineering & transportsMechanics of MaterialsStress resultantsFrequency domainCeramics and CompositesState variable expansionSettore ICAR/08 - Scienza Delle CostruzioniFractional viscoelasticity Non local Timoshenko beam State variable expansion White noise0210 nano-technologyNon local Timoshenko beam Fractional viscoelasticity White noise State variable expansionComposites Part B: Engineering
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Analytical solution for composite layered beam subjected to uniformly distributed load

2016

ABSTRACTThe article presents an analytical theory for multilayered composite beams subjected to transverse uniformly distributed loads. The formulation is based on a layerwise model characterized by third-order approximation of the axial displacements and fourth-order approximation of the transverse displacements. The layerwise kinematical model is rewritten in terms of generalized variables. The beam equilibrium equations, expressed in terms of stress resultant, allow writing the boundary value governing problem. The layerwise fields are obtained by postprocessing steps. The main advantage is to ensure the accuracy level associated to the layerwise formulations preserving the computational…

Materials scienceGeneral MathematicsComposite number02 engineering and technologyEquilibrium equationBoundary valuesComposite beamsStress (mechanics)0203 mechanical engineeringdistributed loadMathematics (all)General Materials ScienceMechanics of MaterialSettore ING-IND/04 - Costruzioni E Strutture AerospazialiKinematical modelcomposite laminateCivil and Structural Engineeringbusiness.industryMechanical EngineeringMathematical analysisStructural engineering021001 nanoscience & nanotechnologyanalytical solutionTransverse plane020303 mechanical engineering & transportsMechanics of MaterialsMaterials Science (all)Beam theory0210 nano-technologybusinessBeam (structure)
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A grain boundary formulation for crystal plasticity

2016

Abstract A three-dimensional grain-boundary formulation for small strains crystal plasticity is presented for the first time. The method is developed and implemented for both single grains and polycrystalline aggregates and it is based on the use of a suitable set of boundary integral equations for modelling the individual grains, which are represented as anisotropic elasto-plastic domains. In the boundary integral framework, crystal plasticity is modelled resorting to an initial strains approach and specific aspects, related to the integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations, are discussed and suitably addressed for the first…

Materials scienceIterative methodCrystal plasticityCrystal plasticity Polycrystalline material02 engineering and technologyB. Polycrystalline materialNOVolume integralPolycrystalline material0203 mechanical engineeringGeneral Materials SciencePolygon meshMechanics of MaterialAnisotropyMechanical EngineeringMathematical analysis021001 nanoscience & nanotechnologyStrength of materialsCrystallography020303 mechanical engineering & transportsMechanics of MaterialsEmbeddingGrain boundaryCrystalliteMaterials Science (all)0210 nano-technologyB. Crystal plasticity
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CAM with special splines for solving of diffusion-convection problems with discontinuous coefficients for layered materials exposed to fire

2019

Materials scienceMathematical analysisDiffusion convectionEngineering for Rural Development
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Magneto-Electro-Elastic Bimorph Analysis by the Boundary Element Method

2008

The influence of the magnetic configuration on the behavior of magneto-electro-elastic bimorph beams is analyzed by using a boundary element approach. The problem is formulated by using the generalized displacements and generalized tractions. The boundary integral equation formulation is obtained by extending the reciprocity theorem to magneto-electro-elastic problems; it is numerically implemented by using the boundary element method multidomain technique to address problems involving nonhomogeneous configurations. Results under different magnetic configurations are compared highlighting the characteristic features of magnetopiezoelectric behavior particularly focusing on the link between …

Materials scienceMechanical EngineeringGeneral MathematicsMathematical analysisBimorphGeometrySingular boundary methodBoundary knot methodElectromagnetic inductionMechanics of MaterialsAnalytic element methodMethod of fundamental solutionsGeneral Materials ScienceSettore ING-IND/04 - Costruzioni E Strutture AerospazialiBoundary element methodMagnetomagneto-electro-elastic bimorph beams boundary element approach magnetopiezoelectric interlaminar stressesCivil and Structural Engineering
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Analytical Refinement of Sandwich Plate Bending Problem Considering Local Effects-I

1999

Analytic expressions for local flexural characteristics and stresses of sandwich panels under loading by point forces have been found. A discrete-layer model for bending of a three-layer panel with a soft filler is proposed. Contractility of a normal in the model is deduced in terms of a difference between deflections of face layers. The accountability of transverse shear in the filler and the sheets is deduced on piecewise rotation of the normal. Equations of the model having four degrees of displacement freedom are of twelfth order. The specific features of the stress from point forces in cylindrical bending are considered using the operational Laplace method with the generalized Dirac f…

Materials scienceMechanical EngineeringMathematical analysisBoundary problemDirac delta functionGeometry02 engineering and technologyBending of platesBending021001 nanoscience & nanotechnologyStress (mechanics)symbols.namesake020303 mechanical engineering & transports0203 mechanical engineeringFlexural strengthMechanics of MaterialsPure bendingCeramics and Compositessymbols0210 nano-technologySandwich-structured compositeJournal of Sandwich Structures & Materials
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Meshless meso-modeling of masonry in the computational homogenization framework

2017

In the present study a multi-scale computational strategy for the analysis of structures made-up of masonry material is presented. The structural macroscopic behavior is obtained making use of the Computational Homogenization (CH) technique based on the solution of the Boundary Value Problem (BVP) of a detailed Unit Cell (UC) chosen at the mesoscale and representative of the heterogeneous material. The attention is focused on those materials that can be regarded as an assembly of units interfaced by adhesive/cohesive joints. Therefore, the smallest UC is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter show an elastoplastic soft…

Materials scienceMesoscale meteorology02 engineering and technologyCondensed Matter Physic01 natural sciencesHomogenization (chemistry)Meshle0203 mechanical engineeringTangent stiffness matrixMechanics of MaterialBoundary value problem0101 mathematicsMasonryMulti-scaleMesoscopic physicsbusiness.industryMechanical EngineeringMathematical analysisMasonryCondensed Matter PhysicsStrength of materialsFinite element method010101 applied mathematics020303 mechanical engineering & transportsMechanics of MaterialsMeso-modelingbusinessSettore ICAR/08 - Scienza Delle Costruzioni
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Poisson's ratio and the incompressibility relation for various strain measures with the example of a silica-filled SBR rubber in uniaxial tension tes…

2010

Abstract The controversy in the definition of Poisson's ratio (PR) as a material constant is discussed in this study. PR of an isotropic material is usually defined as the ratio, taken with the opposite sign, between its lateral and longitudinal strains under the action of longitudinal stresses. However, if deformations of the material are large, the value of PR depends on the strain measure used. Five different measures of strain are considered, and a unified relation in terms of stretch ratios is obtained for calculating the PR. It is demonstrated that only for Hencky strains is the value of PR of an incompressible material constant and equal to 0.5 over its entire extension range. Other …

Materials sciencePolymers and PlasticsStrain (chemistry)Organic ChemistryIsotropyMathematical analysisCauchy distributionPoisson distributionMeasure (mathematics)Poisson's ratioCondensed Matter::Materials Sciencesymbols.namesakeClassical mechanicsNatural rubbervisual_artsymbolsvisual_art.visual_art_mediumConstant (mathematics)Polymer Testing
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