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USE OF ISOTROPIC FUNDAMENTAL SOLUTIONS FOR HEAT CONDUCTION IN ANISOTROPIC MEDIA

M.M. PEREZ (Wessex Institute of Technology, University of Portsmouth, Ashurst Lodge, Ashurst, Southampton, UK. On leave from: Departmento de Engenharia Mecânica, Universidade Federal de Uberlândia, 38400 Uberlândia, MG, Brazil)
L.C. WROBEL (Wessex Institute of Technology, University of Portsmouth, Ashurst Lodge, Ashurst, Southampton, UK)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 January 1993

92

Abstract

A numerical formulation for solving homogeneous anisotropic heat conduction problems based on the use of an isotropic fundamental solution is presented in detail. The analysis is carried out assuming a generic position of the coordinate axes, which may not coincide with the principal directions of orthotropy of the material. The two primary integral equations of the method are derived from the governing differential equation of the problem. Then, the numerical procedure is developed by rewriting the internal degrees of freedom that arise from the domain discretization in terms of the boundary nodes and solving the resulting system of linear equations for the boundary unknowns only. Special attention is given to the differentiation of singular integrals which yields additional terms as well as to the evaluation of the resulting Cauchy principal value integral. The main feature of the proposed formulation is its generality, which makes possible its direct extension to solve the problem of three‐dimensional heat conduction in anisotropic media and, foremost, to three‐dimensional orthotropic and anisotropic elasticity or elastoplasticity.

Keywords

Citation

PEREZ, M.M. and WROBEL, L.C. (1993), "USE OF ISOTROPIC FUNDAMENTAL SOLUTIONS FOR HEAT CONDUCTION IN ANISOTROPIC MEDIA", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 3 No. 1, pp. 49-62. https://doi.org/10.1108/eb017515

Publisher

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MCB UP Ltd

Copyright © 1993, MCB UP Limited

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