Torsion of linearly elastic isotropic beams, with both cross-sectional and axial inhomogeneities, is analyzed. Twist (rate of torsional rotation along the beam axis) and warping of cross-sections are not uniform if arbitrary axial variations of elastic properties are considered. Composite beams undergoing nonuniform torsion are commonly investigated by finite and boundary element methods. New closed-form solutions are found in the present paper, by detecting axial distributions of longitudinal and shear moduli inducing an axially uniform warping field. The warping is evaluated by Saint-Venant beam theory, while twist and axial distribution of shear moduli are inversely proportional. Coordinate-free expressions of displacement, normal and shear stress fields are given for simply and multiply connected cross-sections. Exact solutions are obtained for elliptic and equilateral triangle beams, by assuming exponentially graded longitudinal and shear moduli. New benchmarks for numerical analyses are thus also provided.

Some closed-form solutions of functionally graded beams undergoing nonuniform torsion / Barretta, Raffaele; Feo, Luciano; Luciano, Raimondo. - In: COMPOSITE STRUCTURES. - ISSN 0263-8223. - 123:(2015), pp. 132-136. [10.1016/j.compstruct.2014.12.027]

Some closed-form solutions of functionally graded beams undergoing nonuniform torsion

BARRETTA, RAFFAELE;
2015

Abstract

Torsion of linearly elastic isotropic beams, with both cross-sectional and axial inhomogeneities, is analyzed. Twist (rate of torsional rotation along the beam axis) and warping of cross-sections are not uniform if arbitrary axial variations of elastic properties are considered. Composite beams undergoing nonuniform torsion are commonly investigated by finite and boundary element methods. New closed-form solutions are found in the present paper, by detecting axial distributions of longitudinal and shear moduli inducing an axially uniform warping field. The warping is evaluated by Saint-Venant beam theory, while twist and axial distribution of shear moduli are inversely proportional. Coordinate-free expressions of displacement, normal and shear stress fields are given for simply and multiply connected cross-sections. Exact solutions are obtained for elliptic and equilateral triangle beams, by assuming exponentially graded longitudinal and shear moduli. New benchmarks for numerical analyses are thus also provided.
2015
Some closed-form solutions of functionally graded beams undergoing nonuniform torsion / Barretta, Raffaele; Feo, Luciano; Luciano, Raimondo. - In: COMPOSITE STRUCTURES. - ISSN 0263-8223. - 123:(2015), pp. 132-136. [10.1016/j.compstruct.2014.12.027]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/613421
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