Comprehensive elastic analysis of functionally graded variable thickness pressurized disk

Abstract

This study analytically examines internally pressurized power‐law functionally graded variable thickness disk. The power‐law consideration is applied to the Young's modulus and the Poisson's ratio of the graded material as well as the radial thickness profile variation of the disk. Under this scheme, the solution yields to different Bessel functions including the first, second, and modified types. Stress and displacement fields are investigated at the elastic limits by operating with these functions. The limits are calculated with the well‐known von Mises criteria. Following the analytical modeling, numerical examples are built. Therein the examples, some noteworthy nuances have been achieved. It has been observed that unlike the usual prediction in the literature, constant Poisson's ratio, the effect of variable Poisson's ratio on stresses and displacements is still evident, although not as much as variable Young's modulus and disk geometry. We suggest assigning it as a variable in similar applications to be more precise. Additionally, according to the von Mises criterion, yielding may begin at the inner radius, the outer radius, or both at the same time. Parameters in the simultaneous flow initiation state are critical. These parameters allow the disk to reach the highest elastic limit pressure.