Effects of Inhomogeneity and Thickness Parameters on the Elastic Response of a Pressurized Hyperbolic Annulus/Disc Made of Functionally Graded Material

Abstract

A broad parametric study is carried out to investigate the effects of both the inhomogeneity parameter, and a profile index of Stodola's hyperbolic function on the static response of such structures subjected to both the inner and outer pressures. The investigation is based on the analytical formulas lately published by the author. The effects of those parameters on the variation of the radial displacement, the radial and hoop stresses are all graphically illustrated for an annulus pressurized at its both surfaces. It is observed that, especially, the variation of the hoop stress in radial coordinate is closely sensible to variation of those parameters. For the chosen problems it was observed that one of two materials whose Young's modulus is higher than the other is better to locate at the inner surface of the disc having divergent profile to get reasonable maximum hoop stresses. However much smaller radial displacements may be obtained by using positive inhomogeneity indexes for all discs whose surfaces host a material whose Young's modulus is smaller than the other. To reach a final decision, analytical formulas such as those used in the present study together with a failure criteria such as Von Mises and Tresca become indispensable means in a design process.

Elastic Stresses of Rotating Transversely Isotropic Fiber Reinforced Composite Cylinders

“…is the elastic modulus of the matrix. Followingly, Poisson's ratios of the composite material in different directions ( () , )( , )) ) are presented (6) in which *7# and 77# are the Poisson's ratios of the fibers in l-t and t-t directions. Poisson's ratio of the isotropic matrix is indicated with " .…”

“…Stress analyses of rotating functionally graded material (fgm) disks have been broadly examined by the use of analytical and numerical methods [1][2][3][4][5]. Deformations and stresses of pressurized fgm cylinders and tubes can be found in the publications as well [6][7][8][9][10]. Similar studies are also carried out for orthotropic cylindrical structures.…”

The best grading pattern selection for the axisymmetric elastic response of pressurized inhomogeneous annular structures (sphere/cylinder/annulus) including rotation

“…Zheng et al [26] numerically investigated stresses in functionally graded rotating disks with nonuniform thickness and variable angular velocity. Yıldırım [27] investigated effects of inhomogeneity and thickness parameters on the elastic response of a pressurized hyperbolic annulus/disk made of FGM. Based on both complementary functions and transfer matrix methods, Yıldırım and Kacar [28] introduced a versatile computer package program for the elastic analysis of arbitrarily graded isotropic thick-walled annular structures, namely variable thickness disks, cylinders, and spheres under all possible boundary conditions.…”

Thermomechanical Characteristics of a Functionally Graded Mounted Uniform Disc with/without Rigid Casing

“…Yildirim (2016) proposed analytic solutions to power-law graded hyperbolic rotating discs subjected to both pressure and centrifugal loads under different boundary conditions. By exploiting Yildirim's (2016) closed-form formulas, Yildirim (2017a) conducted analytically a broad parametric study to investigate the effects of both the inhomogeneity parameter, and a profile index of Stodola's hyperbolic function on the static response of such structures subjected to both the inner and outer pressures. He observed that one of two materials in which Young's modulus is higher than the other is better to locate at the inner surface of the disc having divergent thickness profile to get reasonable maximum hoop stresses.…”