On the tailoring of radially FGM hollow spheres, cylinders and disks

Homogeneous and isotropic thick spheres, cylinders, and thin disks subjected to constant internal and/or external pressures are not easily designed in an economical way due to the localized occurrence of maximum equivalent stress. It has been analytically shown that using a radial functionally graded material (FGM) can enhance the design process by ensuring that the maximum shear stress or the circumferential stress component remains constant along the radius of the body. This problem is an inverse one. An isotropic FGM in linear static analysis can be defined by two elastic constants: Young's modulus E(r) and Poisson's ratio ν(r). In this study, focusing on mechanical loading, the conditions for the existence of a solution for E(r) in the inverse problem are derived, assuming a constant Poisson's ratio and using two commonly applied stress criteria in design. Additionally, the advantages of employing FGMs over homogeneous materials are demonstrated by comparing the maximum equivalent stresses in both cases.