Open Access

ARTICLE

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

1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia.
2 Department of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada K1S 5B6.
3 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. https://doi.org/10.3970/cmes.2008.032.161

Abstract

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.

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Keywords

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