Author(s)

V. Sladek, J. Sladek & Ch. Zhang

Abstract

A reliable computational technique is developed for the solution of twodimensional (2-d) transient heat conduction problems in anisotropic media with continuously variable material coefficients. The meshless point interpolation is employed for the approximation of the spatial variation of the temperature field or its Laplace-transform. The coupling amongst the nodal values of the approximated field is given by integral equations considered on local subdomains. Three kinds of local integral equations are derived from physical principles instead of using a weak-form formulation. The accuracy and the convergence of the proposed techniques are tested by several examples and compared with exact benchmark solutions. Keywords: integral equation methods, fundamental solutions, integral balance equation, meshless interpolation, Laplace transform, time stepping technique, heat conduction, functionally graded materials (FGMs), anisotropy 1 Introduction The recent progress in the development and research of functionally graded materials (FGMs) enhanced also the interest in the development of numerical methods for the solution of boundary or initial-boundary value problems in nonhomogeneous continuous media. In FGMs, the composition and the volume fraction of the FGMs constituents vary gradually, giving a non-uniform microstructure with continuously graded macroproperties. Owing to the composite structure, the material properties are directionally dependent or anisotropic in general. The solution of transient heat conduction problems in anisotropic and non-homogeneous media is a complex task in general, even in the case of material linearity. In FEM formulations, the variational principles are

Keywords

integral equation methods, fundamental solutions, integral balance equation, meshless interpolation, Laplace transform, time stepping technique, heat conduction, functionally graded materials (FGMs), anisotropy