Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Direct boundary integral equation method in the theory of elasticity


Author: S. V. Kuznetsov
Journal: Quart. Appl. Math. 53 (1995), 1-8
MSC: Primary 73C35; Secondary 35Q72, 73V10
DOI: https://doi.org/10.1090/qam/1315444
MathSciNet review: MR1315444
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Abstract | References | Similar Articles | Additional Information

Abstract: The Direct Boundary Integral Equation Method (BIEM), which leads to second-kind singular integral equations for all types of commonly used boundary-value problems of the theory of elasticity, is formulated. The exposition is applied to anisotropic bodies with arbitrary elastic anisotropy.


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  • [1] C. A. Brebbia, Topics in Boundary Element Research. Vol. 1 . Basic Principles and Applications, Springer-Verlag, Berlin, 1984
  • [2] V. D. Kupradze and M. A. Alexidze, On one applied method for solution of some boundary-value problems, Soobshch. Akad. Nauk Gruz in SSR 30, 529-536 (1963) (Russian)
  • [3] V. D. Kupradze and M. A. Alexidze, Method of functional equations for approximate solutions of some boundary-value problems, Zh. Vychisl. Mat. i Mat. Fiz. 4, 683-715 (1964) (Russian)
  • [4] V. D. Kupradze, On approximate solution for problems of mathematical physics, Uspekhi Mat. Nauk (2) 22, 59-107 (1967) (Russian)
  • [5] M. A. Alexidze, On completeness of some functional systems, Differentsial'nye Uravneniya 3, 1766-1771 (1967) (Russian)
  • [6] A. B. Bakushinsky, Notes on Kupradze-Alexidze's method, Differentsial'nye Uravneniya 6, 1298-1301 (1970) (Russian)
  • [7] P. S. Theocaris, N. Karayanopoulos, and G. Tsamasphyros, A numerical method for the solution of static and dynamic three-dimensional elasticity problems, Comput. & Structures 16, 777-784 (1983)
  • [8] R. Mathon and R. L. Johnston, The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM J. Numer. Anal. 14, 638-650 (1977)
  • [9] F. J. Rizzo, An integral equation approach to boundary value problems of classical elastostatics, Quart. Appl. Math. 25, 83-95 (1967)
  • [10] A. C. Kaya and F. Erdogan, On the solution of integral equations with strongly singular kernels, Quart. Appl. Math. 45, 105-122 (1987)
  • [11] P. A. Martin, End-point behaviour of solutions to hypersingular integral equations, Proc. Roy. Soc. London Ser. A 432, 301-320 (1991)
  • [12] E. Kroner, Das Fundamentalintegral der anisotropen elastischen Differentialgleichungen, Z. Phys. 136, 402-410 (1953)
  • [13] V. D. Kupradze and M. O. Basheleishvili, New integral equations of the theory of elasticity for anisotropic elastic bodies, Soobshch. Akad. Nauk Gruzin. SSR 15, 327-334 (1954) (Russian)
  • [14] S. Helgason, The Radon Transform, Birkhäuser, Boston, 1980
  • [15] I. M. Lifshitz and L. N. Rosenzveig, On construction of Green's tensor for the main equation of the theory of elasticity in the case of an unbounded elasto-anisotropic medium, Zh. Eksper. Teoret. Fiz. 17, 783-791 (1947) (Russian)
  • [16] R. Burridge, The singularity on the plane lids of the wave surface of elastic media with cubic symmetry, Quart. J. Mech. Appl. Math. 20, 41-56 (1967)
  • [17] J. R. Willis, A polarization approach to the scattering of elastic waves, I. Scattering by a single inclusion, J. Mech. Phys. Solids 28, 287-305 (1980)
  • [18] R. B. Wilson and T. A. Cruse, Efficient implementation of anisotropic three dimensional boundary-integral equation stress analysis, Internat. J. Numer. Methods Engrg. 12, 1383-1397 (1978)
  • [19] S. Bochner, Harmonic Analysis and the Theory of Probability, Univ. Calif. Press, Berkeley, 1955
  • [20] S. V. Kuznetzov, Fundamental solutions for Lamé's equations of anisotropic media, Izv. Akad. Nauk SSSR Mekh. Tver. Tela (4), 50-54 (1989) (Russian)
  • [21] S. V. Kuznetzov, Fundamental solutions for equations of statics in the case of two variables, Izv. Vyssh. Uchebn. Zaved. Mat. (7), 32-34 (1991) (Russian)
  • [22] S. V. Kuznetzov, Dislocation interaction energy in anisotropic media, Prikl. Mat. Mekh. 55, 894-897 (1991) (Russian)
  • [23] V. D. Kupradze et al., Three-Dimensional Problems of Elasticity and Thermoplasticity, North-Holland, Amsterdam, 1979
  • [24] F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators. Vol. 1 , Pseudodifferential Operators, Plenum Press, New York, 1982
  • [25] S. V. Kuznetzov, On discrete spectrum of singular integral operators in the theory of elasticity, Izv. Vyssh. Uchebn. Zaved. Mat. (5), 26-29 (1991) (Russian)
  • [26] S. V. Kuznetzov, Green and Newmann's tensors in mechanics of anisotropic media, Prikl. Mekh. 27, 58-62 (1991) (Russian)
  • [27] Pham The Lai, Potentiels elastiques; tenseurs de Green et de Neumann, J. Mech. 6, 211-242 (1967)
  • [28] N. M. Kublanovskaya, Application of the analytical prolongation in numerical analysis by the use of change of variables, Trudy Mat. Inst. Steklov. 53, 145-185 (1959) (Russian)

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DOI: https://doi.org/10.1090/qam/1315444
Article copyright: © Copyright 1995 American Mathematical Society


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