%0 Journal Article
%A Kanaun, Sergey
%D 2009
%I Begell House
%K elastic fields, heterogeneous medium, integral equations, Gaussian approximating functions, Toeplitz matrix, fast Fourier transform
%N 4
%P 263-276
%R 10.1615/IntJMultCompEng.v7.i4.30
%T Fast Calculation of Elastic Fields in a Homogeneous Medium with Isolated Heterogeneous Inclusions
%U http://dl.begellhouse.com/journals/61fd1b191cf7e96f,232871fc3b0df9a5,7193bb2d745d9103.html
%V 7
%X This work is devoted to the calculation of static elastic fields in a homogeneous medium with a finite number of isolated heterogeneous inclusions. First, the problem is reduced to the solution of integral equations for strain fields inside the inclusions. Then, Gaussian approximating functions are used for discretization of these equations. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. The method is mesh-free, and the coordinates of the approximating nodes is the only geometrical information required in the method. If such nodes compose a regular lattice, the matrix of the discretized problem will have Toeplitz structure. By the calculation of matrix-vector products with such matrices, the fast Fourier transform technique may be used. The latter essentially accelerates the process of the iterative solution of the disretized problem. The results of calculations of elastic fields in a 2-D medium with an isolated heterogeneous inclusion and with several inclusions are presented.
%8 2009-09-01