A differential transformation boundary element method for solving transient heat conduction problems in functionally graded materials

ABSTRACT

This paper presents a new method that is formed by the differential transformation method (DTM) and the radial integral boundary element method to solve transient heat conduction problems of functionally graded materials. The original governing equation is accurately transformed into a time-independent and recursive form equation on some time intervals by the DTM. Based on the fundamental solution of steady potential problems, the boundary integral equation is derived, where domain integrals are transformed into boundary integrals by the radial integral method. A self-adaptive convergence criterion is used to improve the accuracy of the results. Finally, the unknown variables are solved by the recursive process in any time interval. Numerical examples show that for two- or three-dimensional problems highly accurate and stable results can be obtained by using the present method.

Acknowledgments

The research is supported by the National Natural Science Foundation of China (No. 11502063), the Natural Science Foundation of Anhui Province (No. 1608085QA07), and the Fundamental Research Funds for the Central Universities of China (Nos. JZ2015HGBZ0107, JZ2015HGQC0214).