Analysis and material tailoring of functionally graded linearly elastic orthotropic incompressible material cylinders under combined loads

We analytically analyze static deformations of linearly elastic, incompressible and orthotropic circular cylinders with material moduli only varying in the radial direction and undergoing combined radial expansion, extension and twisting deformations. Closed-form expressions for displacements and stresses are derived for four radial variations of the elastic moduli including one given by ∑s=−SSas(rrou)s where as is a constant, r is the radial coordinate of a point, rou is cylinder’s outer radius, and S is an integer. Furthermore, we study the inverse (or material tailoring) problem in which the radial variation of the moduli is found to achieve constant value of the strain energy density. Fabrication techniques for an FGM include additive manufacturing, electron beam deposition, fused filament fabrication, and vulcanization of rubber layers of continuously varying chain densities. The findings reported herein will help optimally design FGM cylinders loaded under combined loads. Furthermore, the analytical solutions will serve as benchmarks for verifying numerical algorithms.