Meccanica (2010) 45: 305–318 DOI 10.1007/s11012-009-9249-4 Nonlinear transient transfinite element thermal analysis of thick-walled FGM cylinders with temperature-dependent material properties M. Azadi · M. Shariyat Received: 25 November 2008 / Accepted: 25 September 2009 / Published online: 6 October 2009 © Springer Science+Business Media B.V. 2009 Abstract An algorithm for investigation of nonlin- ear systems by the transfinite element method is pre- sented. Basically, the transformation techniques have been developed for linear systems. Nonlinear tran- sient heat transfer of a thick FGM cylinder with temperature-dependent material properties is investi- gated in the present paper to clarify the proposed al- gorithm. Two main novelties of the present research are: (1) incorporating the temperature-dependency of the material properties in the thermal analysis which lead to highly non-linear governing equations and (2) proposing an updating numerical transfinite ele- ment procedure to solve the resulted highly nonlin- ear governing equations. To reduce the effect of the artificial local heat source generation at the mutual boundaries of the elements, second order elements are used. Influences of various boundary conditions, geometric parameters, and volume fraction indices on the temperature distribution are investigated. Results of the proposed transfinite element technique show a good agreement with those obtained using the it- erative time integration or analytical method. Fur- thermore, results reveal the significant effect of the temperature-dependency of the material properties. The present solution algorithm prevents numerical os- M. Azadi ( ) · M. Shariyat Faculty of Mechanical Engineering, Sharif University of Technology, Tehran, Iran e-mail: m.azadi.1983@gmail.com cillations and damping, and accumulated time inte- gration errors. The present technique may be used to obtain relatively accurate and stable results in a less computational time. Keywords Transfinite element · Nonlinear transient heat transfer · Temperature-dependency · Thick-walled cylinder · Numerical Laplace inversion · FGM 1 Introduction FGM components are generally constructed to sus- tain elevated temperatures and severe temperature gra- dients. Low thermal conductivity, low coefficient of thermal expansion and core ductility have enabled the FGM materials to withstand higher temperature gradients for a given heat flux. Examples of struc- tures undergo extremely high temperature gradients are plasma facing materials, propulsion system of planes, cutting tools, engine exhaust liners, incinera- tor linings, thermal barrier coatings of turbine blades, thermal resistant tiles, and directional heat flux mate- rials. Continuously varying the volume fraction of the mixture in FGM materials eliminates interface prob- lems, mitigates thermal stress concentrations, and causes a more smooth stress distribution. Extensive thermal stress studies made by Noda [1] and Tani- gawa [2] reveal that the weakness of fiber reinforced