Journal of Machinery Manufacture and Reliability

, Volume 46, Issue 6, pp 542–553 | Cite as

Simulation of 3-D Deformable Bodies Dynamics by Spectral Boundary Integral Equation Method

Mechanics of Machines
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Abstract

The study of the dynamics of inhomogeneous elastically deformable media under conditions of stationary and transient loading processes is based on the integral representation of the corresponding boundary value problems with time-dependent fundamental solutions and a combination of methods for solving boundary integral equations with Fourier transforms. Theoretical bases of methods for solving boundary integral equations focused on effective numerical implementation and application flexibility are presented. The accuracy of the proposed approach is discussed. Three-dimensional applied problems are solved in support of the effectiveness of the developed method.

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References

  1. 1.
    Giagopulos, D. and Natsiavas, S., Hybrid (numerical-experimental) modeling of complex structures with linear and nonlinear components, Nonlin. Dyn., 2007, vol. 47, no. 1, pp. 193–217.MATHGoogle Scholar
  2. 2.
    Wrobel, L.C. and Aliabadi, M.H., The Boundary Element Method, John Wiley & Sons, 2007.MATHGoogle Scholar
  3. 3.
    Boundary Element Analysis: Mathematical Aspects and Applications, Schanz, M. and Steinbach, O., Eds., Berlin, Heidelberg: Springer-Verlag, 2007.Google Scholar
  4. 4.
    Colton, D., The inverse scattering problem for time-harmonic acoustic waves, SIAM Rev., 1984, vol. 26, pp. 323–350.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Gesualdo, A., Guarracino, F., Mallardo, V., et al., Flaw identification in elastic solids: theory and experiments, Extracta Math., 1997, vol. 12, no. 1, pp. 61–86.MathSciNetMATHGoogle Scholar
  6. 6.
    Petushkov, V.A., Numerical implementation of boundary integral equations method with respect to nonlinear problems of fracture and deformation mechanics for volumetric bodies, in Sb. nauchnykh trudov ITPM SO AN SSSR Modelirovanie v mekhanike (Collection of Scientific Papers of Khristianovich Institute of Theoretical and Applied Mechanics of Siberian Branch of Soviet Academy of Sciences. Simulation in Mechanics), Novosibirsk, 1989, vol. 3(20), no. 1, pp. 133–156.Google Scholar
  7. 7.
    Rjasanow, S. and Steinbach, O., The Fast Solution of Boundary Integral Equations, Heidelberg: Springer, 2007.MATHGoogle Scholar
  8. 8.
    Liu, Y.J., Mukherjee, S., Nishimura, N., Schanz, M., et al., Recent advances and emerging applications of the boundary element method, Appl. Mech. Rev., 2012, vol. 64, p. 38. doi doi 10.1115/1.4005491CrossRefGoogle Scholar
  9. 9.
    Kupradze, V.D. and Burchuladze, T.V., Dynamical problems in elasticity and thermoelasticity theory, in Itogi nauki i tekhniki. Seriya sovremennye problemy matematiki (Results of Science and Engineering. Series: Modern Problems of Mechanics), Moscow: VINITI, 1975, vol. 7, pp. 163–294.MATHGoogle Scholar
  10. 10.
    Costabel, M., Time-dependent problems with the boundary integral equation method, in Encyclopedia of Computational Mechanics, John Wiley & Sons, 2004, pp. 703–721.Google Scholar
  11. 11.
    Petushkov, V.A., Transient processes in nonlinear deformed mediums: researching on the base of integral concepts and discrete fields method, Vestn. Samarsk. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki, 2016, vol. 20, no. 3, pp. 1–24.Google Scholar
  12. 12.
    Beskos, D.E., Boundary element methods in dynamic analysis: part II (1986–1996), Appl. Mech. Rev., 1997, vol. 50, pp. 149–197.CrossRefGoogle Scholar
  13. 13.
    Petushkov, V.A. and Potapov, A.I., Numerical solutions for 3D dynamical problems in elasticity theory, in Sb. dokladov Sed’mogo Vsesoyuznogo s”ezda po teoreticheskoi i prikladnoi mekhanike (Proc. 7th All-Union Meeting on Theoretical and Applied Mechanics), Moscow: MSU, 1991, p.286.Google Scholar
  14. 14.
    Manolis, G.D., A comparative study on three boundary element method approaches to problems in elastodynamics, Int. J. Num. Meth. Eng., 1983, vol. 19, no. 1, pp. 73–91.CrossRefMATHGoogle Scholar
  15. 15.
    Phan, A.V., Guduru, V., Salvadori, A., and Gray, L.J., Frequency domain analysis by the exponential window method and SGBEM for elastodynamics, Comput. Mech., 2011, vol. 48, no. 5, pp. 615–630.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Mertins, A., Signal Analysis Wavelets, Filter Banks, Time-Frequency Transforms and Applications, Chichester: John Wiley & Sons, 1999.MATHGoogle Scholar
  17. 17.
    Wheeler, L.T. and Sternberg, E., Some theorems in classical elastodynamics (uniqueness theorems and elastodynamic equations for homogeneous and isotropic elastic media), Arch Rational Mech. Anal., 1968, vol. 31, no. 1, pp. 51–90.MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Fata, S.N., Treatment of domain integrals in boundary element methods, Appl. Num. Math., 2012, vol. 62, no. 6, pp. 720–735.MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Strang, G. and Fix, G., An Analysis of the Finite Element Method, Englewood Cliffs, NJ: Prentice-Hall, 1973.MATHGoogle Scholar
  20. 20.
    Petushkov, V.A. and Zysin, V.I., MEGRE-3D application program package for numerical simulation of nonlinear processes of deformation and fracture of volumetric bodies. Algorithms and implementation in ES operation system, in Sb. Pakety prikladnykh programm: Programmnoe obespechenie matematicheskogo modelirovaniya (Collection of Papers. Application Program Package: Mathematical Simulation Software Support), Moscow: Nauka, 1992, pp. 111–126.Google Scholar
  21. 21.
    GiD. The Personal Pre and Post Processor (ver. 11), Barcelona: CIMNE, 1998.Google Scholar
  22. 22.
    Petushkov, V.A., Konstruktsii i metody rascheta vodo-vodyanykh energeticheskikh reaktorov (Structure and Methods for Calculating Water-to-Water Energy Reactors), Moscow: Nauka, 1987.Google Scholar
  23. 23.
    Kramer, S.L., Geotechnical Earthquake Engineering, New Jersey: Prentice-Hall, 1996.Google Scholar

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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Blagonravov Institute of Mechanical EngineeringMoscowRussia

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