Journal of Theoretical
and Applied Mechanics

55, 1, pp. 343-351, Warsaw 2017
DOI: 10.15632/jtam-pl.55.1.343

A novel approach to thermal and mechanical stresses in a FGM cylinder with exponentially-varying properties

Kerimcan Celebi, Durmuş Yarimpabuç, Ibrahim Keles
A novel approach is employed to a general solution for one-dimensional steady-state thermal
and mechanical stresses in a hollow thick cylinder made of a functionally graded material
(FGM). The temperature distribution is assumed to be a function of radius, with general
thermal and mechanical boundary conditions on the inside and outside surfaces of the cylin-
der. The material properties, except Poisson’s ratio, are assumed to be exponentially-varying
through the thickness. Forcing functions applied to the inner boundary are internal pressures
which may be in form of steps. These conditions result in governing differential equations
with variable coefficients. Analytical solutions to such equations cannot be obtained except
for certain simple grading functions and pressures. Numerical approaches must be adopted
to solve the problem in hand. The novelty of the present study lies in the fact that the
Complementary Functions Method (CFM) is employed in the analysis. The Complementary
Functions method (CFM) will be infused into the analysis to convert the problem into an
initial-value problem which can be solved accurately. Benchmark solutions available in the
literature are used to validate the results and to observe the convergence of the numerical
solutions. The solution procedure is well-structured, simple and efficient and it can be re-
adily applied to cylinders. It is also well suited for problems in which mechanical properties
are graded.
Keywords: thermal stresses, functionally-graded materials, thick cylinder, Complementary Functions Method Complementary Functions Method.