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Three Boundary Meshless Methods for Heat Conduction Analysis in Nonlinear FGMs with Kirchhoff and Laplace Transformation

Published online by Cambridge University Press:  03 June 2015

Zhuo-Jia Fu ,
Wen Chen  and
Qing-Hua Qin
Zhuo-Jia Fu*
Affiliation:
Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Nanjing, Jiangsu, P. R. China Research School of Engineering, Building 32, Australian National University, Canberra, ACT 0200, Australia
Wen Chen*
Affiliation:
Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Nanjing, Jiangsu, P. R. China
Qing-Hua Qin*
Affiliation:
Research School of Engineering, Building 32, Australian National University, Canberra, ACT 0200, Australia
*
URL:http://em.hhu.edu.cn/chenwen/english.html, Email: paul212063@hhu.edu.cn
Corresponding author: Email: chenwen@hhu.edu.cn
Email: qinghua.qin@anu.edu.au
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Abstract

This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials (FGMs). The three methods are, respectively, the method of fundamental solution (MFS), the boundary knot method (BKM), and the collocation Trefftz method (CTM) in conjunction with Kirchhoff transformation and various variable transformations. In the analysis, Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions. The proposed MFS, BKM and CTM are mathematically simple, easy-to-programming, meshless, highly accurate and integration-free. Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered, and the results are compared with those from meshless local boundary integral equation method (LBIEM) and analytical solutions to demonstrate the efficiency of the present schemes.

Keywords

35k5541A3044A1065M7080M25Method of fundamental solutionboundary knot methodcollocation Trefftz methodKirchhoff transformationLaplace transformationmeshless method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 5 , October 2012 , pp. 519 - 542
Copyright
Copyright © Global-Science Press 2012

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