Abstract
This paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.
Highlights
The Saint-Venant torsion of anisotropic linearly elastic bars has been the subject of several works from both theoretical and numerical viewpoints
In paper [3], by the use of principle of minimum of potential energy and principle of minimum of complementary energy, approximate analytical solutions are derived for the torsion function and for the Prandtl’s stress function of the uniform torsion of cylindrically orthotropic solid elliptical cross section
The considered cylindrically orthotropic homogeneous elastic annular wedgeshaped bar strengthened on its curved boundary parts by thin isotropic elastic shells
Summary
The Saint-Venant torsion of anisotropic linearly elastic bars has been the subject of several works from both theoretical and numerical viewpoints. The torsion problem of cylindrically anisotropic and orthotropic bars is studied in books by Lekhnitskii [5,6], Rand and Rovenski [9] and papers by Soós [14] and Ecsedi et al [4]. In paper [3], by the use of principle of minimum of potential energy and principle of minimum of complementary energy, approximate analytical solutions are derived for the torsion function and for the Prandtl’s stress function of the uniform torsion of cylindrically orthotropic solid elliptical cross section. Present paper deals with the Saint-Venant torsion of cylindrically orthotropic bar whose cross section is a sector of hollow circle. An analytical solution is formulated to solve the Saint-Venant’s torsion problem for the cylindrically orthotropic bar which is reinforced by thin isotropic elastic shells on its curved boundary surfaces. The developed solution gives the Prandtl’s stress function, torsion function and the torsional rigidity of the compound cross section which consists of one solid cross section and two open thin walled cross section
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