Abstract
An analytical solution is given to the problem of non-uniform torsion of an elliptical cylinder made of functionally graded anisotropic linear elastic material. The material moduli of the considered anisotropic non-homogeneous elastic bar are smooth functions of the axial coordinate. The contour of the elliptical cross section depends on the elastic constants. This dependence provides the zero warping property of the considered elliptical cross section. The obtained stress field is independent of the axial coordinate as in the case of Saint-Venant’s torsion problem, but the rate of twist depends on the axial coordinate.
Highlights
Graded materials (FGMs) are a new generation of engineered materials that have emerged from the need to optimize material performance [1,6,15]
Analytical solutions to the problem of non-uniform torsion of a circular cylinder made of functionally graded material with the material moduli smooth functions of the axial coordinate only have been presented by Batra [2]
By use of an assumed form of the displacement field, an analytical solution is given to the problem of nonuniform torsion of an elliptical cylinder made of functionally graded linearly elastic anisotropic material
Summary
Graded materials (FGMs) are a new generation of engineered materials that have emerged from the need to optimize material performance [1,6,15]. Graded linearly elastic structures can be considered as non-homogeneous elastic bodies whose material moduli are smooth functions of the position coordinates. Analytical solutions for the Saint-Venant torsion and flexure of FG bars have been given by Rooney and Ferrai, they assumed that the elastic moduli are smooth functions of the cross-sectional coordinates [12]. Analytical solutions to the problem of non-uniform torsion of a circular cylinder made of functionally graded material with the material moduli smooth functions of the axial coordinate only have been presented by Batra [2]. The aim of this paper is to give an analytical solution to the non-uniform torsion problem of an elliptical cylinder made of functionally graded anisotropic linearly elastic materials. The material moduli of the considered anisotropic non-homogeneous bar are smooth functions of the axial coordinate. The considered torsion problem is not of Saint-Venant type since the rate of twist depends on the axial coordinate
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