Three boundary meshless methods for heat conduction analysis in nonlinear FGMs with Kirchhoff and Laplace transformation
Date
2012
Authors
Fu, Zhuo-Jia
Chen, Wen
Qin, Qing Hua
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Publisher
Global Science Press
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, easyto-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.
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Keywords: Boundary knot method; Collocation trefftz method; Kirchhoff transformation; Laplace transformation; Meshless method; Method of fundamental solution
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Source
Advances in Applied Mathematics and Mechanics
Type
Journal article
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2037-12-31
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