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Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method

J. Sladek1, V. Sladek1, C.L. Tan2, S.N. Atluri3

Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia.
Department of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada K1S 5B6.
Center of Aerospace Research & Education, University of California at Irvine, Irvine, CA 92697-3975, USA.

Computer Modeling in Engineering & Sciences 2008, 32(3), 161-174.


A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which a local integral equation is applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. Several example problems with Dirichlet, mixed, and/or convection boundary conditions, are presented to demonstrate the veracity and effectiveness of the numerical approach.


Cite This Article

Sladek, J., Sladek, V., Tan, C., Atluri, S. (2008). Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method. CMES-Computer Modeling in Engineering & Sciences, 32(3), 161–174.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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