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

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. (C) 2014 Elsevier Ltd. All rights reserved.