TY  - EJOU
AU  - Sladek, J.  
AU  - Sladek, V.  
AU  - Tan, C.L.  
AU  - Atluri, S.N.  

TI  - Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2008
VL  - 32
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Meshless method
KW  -  local weak form
KW  -  Heaviside step function
KW  -  moving least squares interpolation
KW  -  Laplace transform

DO  - 10.3970/cmes.2008.032.161