TY - JOUR
T1 - Three Boundary Meshless Methods for Heat Conduction Analysis in Nonlinear FGMs with Kirchhoff and Laplace Transformation
AU - Fu , Zhuo-Jia
AU - Chen , Wen
AU - Qin , Qing-Hua
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 519
EP - 542
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m1170
UR - https://global-sci.org/intro/article_detail/aamm/134.html
KW - Method of fundamental solution, boundary knot method, collocation Trefftz
method, Kirchhoff transformation, Laplace transformation, meshless method.
AB - <p style="text-align: justify;">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.</p>