Analysis of transient heat conduction in 3D anisotropic functionally graded solids, by the MLPG method

J. Sladek, V. Sladek, C. L. Tan, S. N. Atluri

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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 nonhomogeneous 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.

Original languageEnglish
Pages (from-to)161-174
Number of pages14
JournalCMES - Computer Modeling in Engineering and Sciences
Issue number3
StatePublished - Dec 4 2008



  • Heaviside step function
  • Laplace transform
  • Local weak form
  • Meshless method
  • Moving least squares interpolation

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