Torsion of Cylinders With Shape Intrinsic Orthotropy

Abstract

Shape intrinsic orthotropy may be thought of as the type of elastic material symmetry possessed by the wood tissue of a tree. Each year’s new growth rings form a laminate around a central core. The axes of material symmetry lie in the directions tangent and normal to the growth rings or laminates and along the axis of the cylinder. Let Gtz denote the linear elastic orthotropic shear modulus associated with the axial and tangential directions, the tangent plane of a laminate. It is shown here that, for a certain class of elastic cylinders with shape intrinsic orthotropy, the solution to the torsion problem is the same as the solution to the torsion problem for the isotropic cylinder of the same shape if the isotropic shear modulus G were replaced by the orthotropic shear modulus Gtz .