Search results for "torsion problem"

showing 3 items of 3 documents

Wulff shape characterizations in overdetermined anisotropic elliptic problems

2017

We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.

Applied Mathematics010102 general mathematicsDegenerate energy levelsMathematical analysisMathematics::Analysis of PDEsElliptic pdesComputer Science::Numerical Analysis01 natural sciencesMathematics::Numerical Analysis010101 applied mathematicsOverdetermined systemMathematics - Analysis of PDEsNonlinear Sciences::Exactly Solvable and Integrable SystemsSettore MAT/05 - Analisi MatematicaOverdetermined problems. Finsler manifold. Wulff shapes. Torsion problem. CapacityFOS: MathematicsMathematics::Differential GeometryFinsler manifold0101 mathematicsAnisotropyAnalysisAnalysis of PDEs (math.AP)Mathematics
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The Line Element-less Method Analysis of orthotropic beam for the De Saint Venant torsion problem

2010

Abstract This paper deals with the extension of a novel numerical technique, labelled line element-less method (LEM), in order to provide approximate solutions of the De Saint Venant torsion problem for orthotropic beams having simply and multiply connected cross-section. A suitable transformation of coordinates allows to take full advantage of the theory of analytic complex functions as in the isotropic case. A complex potential function analytic in all the transformed domain whose real and imaginary parts are related to the shear stress components and to the orthotropic ratio is introduced and expanded in the double-ended Laurent series involving harmonic polynomials. An element-free weak…

DiscretizationLine elementMechanical EngineeringLaurent seriesMathematical analysisIsotropyTorsion (mechanics)GeometryOrthotropic materialCondensed Matter PhysicsOrthotropic materialanalytic functiontorsion problemAlgebraic equationMechanics of MaterialsShear stressGeneral Materials ScienceSettore ICAR/08 - Scienza Delle CostruzioniCivil and Structural EngineeringMathematics
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De Saint-Venant flexure-torsion problem handled by Line Element-less Method (LEM)

2010

In this paper, the De Saint-Venant flexure-torsion problem is developed via a technique by means of a novel complex potential function analytic in all the domain whose real and imaginary parts are related to the shear stresses. The latter feature makes the complex analysis enforceable for the shear problem. Taking full advantage of the double-ended Laurent series involving harmonic polynomials, a novel element-free weak form procedure, labelled Line Element-less Method (LEM), is introduced, imposing that the square of the net flux across the border is minimized with respect to expansion coefficients. Numerical implementation of the LEM results in systems of linear algebraic equations involv…

Line elementMechanical EngineeringLaurent seriesMathematical analysisComputational MechanicsTorsion (mechanics)Geometryflexure-torsion problem Laurent seriesAlgebraic equationRobustness (computer science)Solid mechanicsShear stressSymmetric matrixSettore ICAR/08 - Scienza Delle CostruzioniMathematics
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