Torsional properties of an ovaline cross section

Abstract

Torsional properties of a solid, linearly elastic, and isotropic bar with the cross section in the shape of an ovaline were investigated. An ovaline is a variant of an ellipse defined by the parametric equations: x = a(1 + αcos²λ)cosλ, and y = b(1 + βsin²λ)sinλ. Only ovalines with a smooth, aerodynamic type of cross section under St. Venant torsion were considered. The torsional properties of interest included the maximum shear stress component, the maximum shear stress magnitude and the torsional stiffness. The results from twenty-eight finite element models were correlated to several candidate solutions for each of the torsional properties based on variances of the classical elliptical solution. Correction factors are provided where appropriate. The recommended methods of solution provide highly accurate results for the class of ovalines considered in a fraction of the time required to obtain results via the finite element method.