@Article{cmes.2008.032.161,
AUTHOR = {J.  Sladek, V.  Sladek, C.L.  Tan, S.N.  Atluri},
TITLE = {Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {32},
YEAR = {2008},
NUMBER = {3},
PAGES = {161--174},
URL = {http://www.techscience.com/CMES/v32n3/25183},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2008.032.161}
}