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A meshless procedure for transient heat conduction in functionally graded materials
Author(s) -
Mierzwiczak Magdalena
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310219
Subject(s) - taylor series , boundary value problem , homotopy analysis method , mathematics , nonlinear system , singular boundary method , mathematical analysis , regularized meshless method , thermal conduction , series (stratigraphy) , method of fundamental solutions , interpolation (computer graphics) , partial differential equation , finite difference method , finite difference , homotopy , finite element method , physics , thermodynamics , boundary element method , classical mechanics , paleontology , quantum mechanics , biology , pure mathematics , motion (physics)
A meshless numerical procedure is developed for analyzing the transient heat conduction problem in non‐homogeneous functionally graded materials. In the proposed method the time derivative of temperature is approximate by the finite difference. At each time step the original nonlinear boundary value problem is transform into a hierarchy of non‐homogeneous linear problem by used the homotopy analysis method. In this method a sought solution is presented by using a finite expansion in Taylor series, which consecutive elements are solutions of series linear value problems defining differential deformations. Each of linear boundary value problems with the corresponding boundary conditions is solved by using the method of fundamental solutions and radial basis functions which are used for interpolation of the inhomogeneous term. The accuracy of the obtained approximate solution is controlled by the number of components of the Taylor series, while the convergence of the process is monitored by an additional parameter of the method. Numerical experiments demonstrate the efficiency and accuracy of the present scheme in the solution of the heat conduction problem in nonlinear functionally graded materials. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)