Torsional deformations and material tailoring of orthotropic bi-directional FGM hollow truncated conical cylinders with curved lateral surfaces

Abstract

Converging and diverging nozzles and skyscrapers are examples of hollow structures with curved bounding surfaces. We study torsional deformations of such structures, namely, truncated conical cylinders with curved inner and outer bounding surfaces and made of linearly elastic and orthotropic functionally graded materials (FGMs). Simplifying assumptions include a plane section remains plane, deformations are axisymmetric about the cylinder axis, and a power-law relation between the radial and the axial coordinates describes the curved mantle. For four spatial variations of the two shear moduli, we analytically solve governing equations for the two non-zero shear stresses and the tangential displacement. For a general variation of the shear moduli we employ the weighted residuals approach to find an approximate solution and establish its convergence and accuracy. We also analyze the material tailoring problem to attain a desired shear stress distribution on a cross-section. We include numerical examples to illustrate spatial distributions of shear stresses for prescribed shear moduli variations, and of the shear moduli for achieving desired shear stress distributions. The analytical solutions provided herein should serve as benchmarks to verify numerical solutions of similar problems.