International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.4, No.2, Jun. 2018, Pub. Date: Jun. 6, 2018
Numerical Elasticity Solution for Continuously Tapered and Arbitrarily Functionally Graded (FG) Rotating Disks via the Transfer Matrix Approach
Pages: 48-73 Views: 350 Downloads: 176
Authors
[01] Vebil Yıldırım, Mechanical Engineering Department, University of Çukurova, Adana, Turkey.
Abstract
The main purpose of the present study is to introduce the transfer matrix method, which is an efficacious and accurate analytical/numerical method developed based on the initial value problem (IVP), to numerically study the elastostatic response of variable-thickness rotating thin disks made of an isotropic but non-homogeneous material which is composed of a metal and a ceramic constituents under mechanical pressure and centrifugal forces. The governing equation called Navier equation of such disks having any arbitrary thickness profile is a second order non-homogeneous differential equation with variable coefficients. It is possible to achieve an analytical solution of Navier equation by using some certain material grading rules and certain disk profiles. Those certain conditions are out of the scope of the present study. The present study deals with the numerical solution of Navier equation developed for both arbitrarily functionally graded metal-ceramic pairs and arbitrarily continuously varying disk profiles. To this end, several conventional material grading rules such as a simple power rule (P-FGM), an exponential function (E-FGM), a linear function (L-FGM), a Voigt mixture rule with power of volume fractions of constituents (V-FGM), a Mori-Tanaka scheme (MT-FGM), and a sigmoid function (S-FGM) are all considered with several parabolically/linearly/hyperbolically tapered disk profiles including uniform ones. Three boundary conditions namely free-free, fixed-free, and fixed-fixed are examined. Some numerical results are also presented to serve benchmark solutions for future advanced studies for an aluminum/aluminum oxide (Al/Al2O3) FG material.
Keywords
Transfer Matrix Approach, Complementary Functions Method, Initial Value Problem, Numerical Analysis, Axisymmetric Elasticity Solution, Rotating Variable-thickness Disk, Functionally Graded, Inhomogeneous Material
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