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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v7.i4.30
pages 263-276

Fast Calculation of Elastic Fields in a Homogeneous Medium with Isolated Heterogeneous Inclusions

Sergey Kanaun
Mechanical Engineering Department, Technological Institute of Monterrey, Mexico

RÉSUMÉ

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.

RÉFÉRENCES

  1. Chew, W., Waves and Fields in Inhomogeneous Media.

  2. Peterson, A., Ray, S., and Mittra, R., Computational Methods for Electromagnetics.

  3. Chang, H., Greengard, L., and Rokhlin, V., A Fast Adaptive Multipole Algorithm in Three Dimensions. DOI: 10.1006/jcph.1999.6355

  4. Gumerov, N., Duraiswami, R., and Borovikov, E., Data Structure, Optimal Choice of Parameters, and Complexity Results for Generalized Multilevel Fast Multipole Methods in d-Dimensions.

  5. Alpert, B., Belkin, G., Coifman, R., and Rokhlin, V., Wavelet Bases for the Fast Solution of Second Kind Integral Equations. DOI: 10.1137/0914010

  6. Dahmen, W., Proessdorf, S., and Schneider, R., Wavelet Approximation Methods for Pseudodifferential Equations II: Matrix Compression and Fast Algorithms. DOI: 10.1007/BF02072014

  7. Maz’ya, V. and Schmidt, G., Approximate Approximation.

  8. Kanaun, S., Romero, V., and Bernal, J., A New Numerical Method for the Solution of the Second Boundary Value Problem of Elasticity for Bodies with Cracks. DOI: 10.1023/A:1007659329025

  9. Kanaun, S. and Romero, V., Boundary Point Method in the Dynamic Problems of Elasticity for Plane Areas with Cracks. DOI: 10.1023/A:1012389906648

  10. Kanaun, S., A Method for the Solution of the Diffraction Problem on Perfectly Conducting Screens. DOI: 10.1006/jcph.2001.6974

  11. Kanaun, S. and Babaii, S., A Numerical Method for the Solution of Thermo and Electro Static Problems for a Medium with Isolated Inclusions. DOI: 10.1016/j.jcp.2003.07.010

  12. Kanaun, S. and Levin, V, Self-Consistent Methods for Composites.

  13. Mikhlin, S., Multi-Dimensional Singular Integrals and Integral Equations.

  14. Press, W., Flannery, B., Teukolsky, S., and Vetterling, W., Numerical Recipes in FORTRAN: The Art of Scientific Computing.

  15. Golub, G. and Van Loan, C., Matrix Computations.

  16. Kanaun, S., Fast Solution of 3D-Elasticity Problem of a Planar Crack of Arbitrary Shape. DOI: 10.1007/s10704-008-9208-4


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