Search results for "Virtual work principle"

showing 2 items of 2 documents

Fractional visco-elastic Euler–Bernoulli beam

2013

Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…

Constitutive equationVirtual work principleCurvatureFractional calculuViscoelasticityQuasi-static problemsVisco-elastic beamMaterials Science(all)Euler-Bernoulli beamModelling and SimulationGeneral Materials ScienceVirtual workBoundary value problemMathematicsApplied MathematicsMechanical EngineeringMathematical analysisFractional calculusCondensed Matter PhysicsFractional calculusClassical mechanicsMechanics of MaterialsQuasi-static problemModeling and SimulationEuler–Bernoulli beamBending momentCylinder stressSettore ICAR/08 - Scienza Delle CostruzioniInternational Journal of Solids and Structures
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The role of virtual work in Levi-Civita's parallel transport

2015

International audience; According to current history of science, Levi-Civita introduced parallel transport solely to give a geometrical interpretation to the covariant derivative of absolute differential calculus. Levi-Civita, however, searched a simple computation of the curvature of a Riemannian manifold, basing on notions of the Italian school of mathematical physics of his time: holonomic constraints, virtual displacements and work, which so have a remarkable, if not dominant, role in the origin of parallel transport.

[SHS.HISPHILSO]Humanities and Social Sciences/History Philosophy and Sociology of Sciences[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Virtual Works[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO]Levi-CivitaMathematics::Differential GeometryParallel Transportlevi-civita; parallel transport[MATH]Mathematics [math]Virtual Work PrincipleLévi-Civita[SHS]Humanities and Social Sciences
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