An Efficient Numerical Method for Calculation of Elastic and Thermo-Elastic Fields in a Homogeneous Medium with Several Heterogeneous Inclusions

Sergey Kanaun

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DOI: 10.4236/wjm.2011.12005                

Abstract

The work is devoted to calculation of static elastic and thermo-elastic fields in a homogeneous medium with a finite number of isolated heterogeneous inclusions. Firstly, the problem is reduced to the solution of inte-gral equations for strain and stress fields in the medium with inclusions. Then, Gaussian approximating func-tions are used for discretization of these equations. For such functions, the elements of the matrix of the dis-cretized problem are calculated in explicit analytical forms. The method is mesh free, and only the coordi-nates of the approximating nodes are the geometrical information required in the method. If such nodes compose a regular grid, the matrix of the discretized problem obtains the Toeplitz properties. By the calcula-tion of matrix-vector products with such matrices, the Fast Fourier Transform technique may be used. The latter accelerates essentially the process of the iterative solution of the disretized problem. The results of calculations of elastic fields in 3D-medium with an isolated spherical heterogeneous inclusion are compared with exact solutions. Examples of the calculation of elastic and thermo-elastic fields in the medium with several inclusions are presented.

Keywords

Elasticity, Heterogeneous Medium, Integral Equations, Gaussian Approximating Functions, Toeplitz Matrix, Fast Fourier Transform

Conflicts of Interest

The authors declare no conflicts of interest.

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