On the best volume fraction distributions for functionally graded cylinders, spheres and disks – A pseudospectral approach

Abstract

The paper is devoted to the optimization of axisymmetric structures made of functionally graded materials and subject to mechanical and thermal loads. The novelty of the results is that the volume fraction distribution is not limited to a power-law variation, as in most of the works available in the literature, but can be any (piecewise continuous) function. This approach leads to an intrinsic tailoring approach, in the sense it occurs without prefixing the spatial distribution of effective mechanical properties a priori, and therefore exploiting at best the inhomogeneity of functionally graded material. After recalling the governing equations and showing some recent results concerning candidate solutions for the optimal volume fraction distribution in some particular cases, several instances of the optimization problems aiming at minimizing occurring maximum stresses are formulated. We show that all these formulations can be treated within the same numerical approach based on the so-called pseudospectral methods. In the last part of the paper we describe how these methods have been effectively applied to the considered problems and we discuss the yielded solutions comparing them, where possible, with power-law solutions.