Nonlinear transient transfinite element thermal analysis of thick-walled FGM cylinders with temperature-dependent material properties

An algorithm for investigation of nonlinear systems by the transfinite element method is presented. Basically, the transformation techniques have been developed for linear systems. Nonlinear transient heat transfer of a thick FGM cylinder with temperature-dependent material properties is investigated in the present paper to clarify the proposed algorithm. 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 element procedure to solve the resulted highly nonlinear 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 iterative time integration or analytical method. Furthermore, results reveal the significant effect of the temperature-dependency of the material properties. The present solution algorithm prevents numerical oscillations and damping, and accumulated time integration errors. The present technique may be used to obtain relatively accurate and stable results in a less computational time.