Direct and Inverse Multi-Scale Analyses of Functionally Graded Layered Hollow Cylinders (Discs), with Different Shaped Reinforcements, under Harmonic Pressure Loads

A multi-scale model is proposed to investigate functionally graded (exponential or power-law grading in the radial direction) hollow cylinders (discs), with fibers, particles, or disc-shaped reinforcements, subjected to harmonic loading conditions. The stress analyses are performed by dividing the cylinders (discs) into several layers each with homogeneous properties, which are functionally graded through the thickness of the structures, with varying microstructural details. Good agreement can be obtained by comparing the present stress distributions for laminated structures with each layer being homogeneous against analytical solutions used as inner and outer boundary conditions or obtained for homogeneous and continuously graded structures. Furthermore, the Mori-Tanaka model is used to generate effective properties of each layer reinforced with fibers, particles or disc-shaped inclusions. The stress distributions in the cylinders in the radial direction are effectively investigated with the influence of either the shape (decided by aspect ratio) or the volume fraction of reinforcements. Finally, the particle swarm optimization technique is combined with the present framework to provide inverse calculations for microstructural details, in the effort of finding proper inclusion volume fractions or minimizing the shear stress along radial direction, which are necessary for the design of functionally graded structures.