Exact elasticity solutions to rotating pressurized axisymmetric vessels made of functionally graded materials (FGM)

Abstract

In this study the plane elasticity equations of pressurized and rotating structures, generalized analytical closed-form solutions are presented for hollow cylinders, spheres and thin disks. Three well known material pairs are graded in radial direction by using the power rule for various boundary and load conditions. Stress and displacement solutions are obtained. The effect of a constant rotational velocity is also investigated separately in absence of the internal and external pressures. Crucial results are also presented in tabular form. Keywords: Functionally graded material / elastic analysis / power rule / pressurized vessel / stress and displacement In dieser Studie werden die ebenen Elastizitätsgleichungen von unter Druck stehenden dickwandigen rotierenden zylindrischen und kugelförmigen Gefäßen und dünnen Scheiben analytisch gelöst. Der funktional gradierte Werkstoff wird in radialer Richtung gradiert und die Einstufung variiert gemäß der Machtregel. Geschlossene Lösungen, sowohl der Radial-, als auch der Umfangsspannungen und der Radialverschiebungen, werden in der für Wissenschaftler, Designer und Ingenieure am besten geeigneten Form erhalten. Unter Berücksichtigung von drei verschiedenen Metall-Keramik-Paaren und zwei verschiedenen Randbedingungen werden die Ergebnisse der Lösungen in geschlossener Form für die rotierende Struktur grafisch dargestellt, während, sowohl der innere, als auch der äußere Druck, gleichzeitig angewendet werden. Der Effekt einer konstanten Rotationsgeschwindigkeit wird auch ohne internen und externen Druck getrennt untersucht. Entscheidende Ergebnisse werden in tabellarischer Form dargestellt.

Comprehensive elastic analysis of functionally graded variable thickness pressurized disk

“…The term Y n (Ωr 𝛽∕2 ) is the Bessel function of the second kind. Once again, the order and the argument are obtained with Equation (15). So, the radial stress is…”

“…In the scientific literature, there are studies that consider graded cylinders subjected to not only pressure loads but also thermal [8,11] or magnetic fields [12]. Investigations concerning functionally graded pressure vessels under different loading conditions are also present, which are cylindrical [13][14][15] and spherical [16][17][18][19][20]. Regarding the references mentioned in the previous sentence, it is to be mentioned that some studies only took mechanical loads into account [13,15,16].…”

“…Investigations concerning functionally graded pressure vessels under different loading conditions are also present, which are cylindrical [13][14][15] and spherical [16][17][18][19][20]. Regarding the references mentioned in the previous sentence, it is to be mentioned that some studies only took mechanical loads into account [13,15,16]. On the other hand, some investigations have considered both thermal and mechanical loading conditions in pressure vessels [14,[17][18][19][20].…”

“…Additionally, unlike the common assumption in related researches, which is the constant Poisson's ratio consideration, we have taken it as a variable. In examinations that consider power‐law as a grading rule [3, 5, 14–15, 17, 19, 23, 26–30, 42], none of them have taken Poisson's ratio as a variable. Moreover, at the current state of the literature most disk investigations often focus on the elastic state stresses not the elastic limits.…”

Numerical Simulation of Stresses in Functionally Graded HCS-MgO Cylinder Using Iterative Technique and Finite Element Method

“…An axisymmetric elastic stress analysis is performed for a functionally graded spinning disk where thickness and material properties of the rotary disk vary along the power law function, and the numerical solution is obtained by applying the finite difference method under clamped-clamped, clamped-free, and free-free boundary conditions [13]. Kacar [14] has derived an elastic analytical solution for an FGM disk, cylinder and sphere, where material changes by power law in the radial direction. Using the energy principle and Lagrange equations, a dynamic model of structure is investigated assuming combined dynamic properties to obtain an optimum design [15].…”