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Chati, M. K.; Mukherjee, S.

Evaluation of gradients on the boundary using fully regularized hypersingular boundary integral equations. (English) Zbl 0949.74076

Acta Mech. 135, No. 1-2, 41-55 (1999).
An elegant way of calculation of gradients on the boundary of a body is presented. It starts from the hypersingular boundary integrals regularized by using simple solutions or modes. The method is currently limited to the calculation of gradients at regular points on the boundary at which the gradients of primary variables are continuous. The iterative scheme developed in the paper is shown to be extremely robust for the calculations of the gradients. The method is tested on two Laplace problems and two problems in linear elasticity.
Reviewer: Ján Sládek (Bratislava)

Cited in 8 Documents

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity

Keywords:

potential problem; regularization; regular integrals; gradients; hypersingular boundary integrals; iterative scheme; Laplace problems; linear elasticity
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References:

[1] Banerjee, P. K.: The boundary element methods in engineering, 2nd ed. New York: McGraw-Hill 1994.
[2] Chandra, A., Mukherjee, S.: Boundary element methods in manufacturing Oxford: Oxford University Press 1997.
[3] Krishnaswamy, G., Schmerr, L. W., Rudolphi, T. J., Rizzo, F. J.: Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. J. Appl. Mech. Trans. ASME57, 404-414 (1990). · Zbl 0729.73251 · doi:10.1115/1.2892004
[4] Chien, C. C., Rajiyah, H., Atluri, S. N.: On the evaluation of hyper-singular integrals arising in the boundary element method for linear elasticity. Comput. Mech.8, 57-70 (1991). · Zbl 0733.73066 · doi:10.1007/BF00370548
[5] Guiggiani, M., Krishnaswamy, G., Rudolphi, T. J., Rizzo, F. J.: A general algorithm for the num solution of hypersingular boundary integral equations. J. Appl. Mech. Trans. ASME59, 604-614 (1992). · Zbl 0765.73072 · doi:10.1115/1.2893766
[6] Rudolphi, T. J.: The use of simple solutions in the regularization of hypersingular boundary integral equations. Math. Comput. Modell.15, 269-278 (1991). · Zbl 0728.73081 · doi:10.1016/0895-7177(91)90071-E
[7] Lutz, E., Gray, L. J., Ingraffea, A. R.: Indirect evaluation of surface stress in the boundary element method. IABEM-90: Symposium of the International Association for Boundary Elements, pp. 339-348, Rome, Oct. 1990.
[8] Guiggiani, M.: Hyeprsingular formulation for boundary stress evaluation. Eng. Anal. Bond. Elem.13, 169-179 (1994). · doi:10.1016/0955-7997(94)90019-1
[9] Dong, Y. F., Gea, H. C.: A non-hypersingular boundary integral formulation for displacement gradients in linear elasticity. Acta Mech.129, 187-205 (1998). · Zbl 0911.73008 · doi:10.1007/BF01176745
[10] Cruse, T. A., Richardson, J. D.: Non-singular Somigliana stress identities in elasticity. Int. J. Numer. Meth. Eng.39, 3273-3304 (1996). · Zbl 0886.73005 · doi:10.1002/(SICI)1097-0207(19961015)39:19<3273::AID-NME999>3.0.CO;2-7
[11] Kane, J. H.: Boundary element analysis in engineering continuum mechanics. Englewood Cliffs: Prentice-Hall 1994.
[12] Cruse, T. A., Van Buren, W.: Three-dimensional elastic stress analysis of a fracture specimen with an edge crack. Int. J. Fract. Mech.7, 1-15 (1971).
[13] Sladek, V., Sladek, J.: Computation of stresses by BEM in 2-D elastostatics. Acta Techn. CSA31, 523-525 (1986).
[14] Toh, K. C., Mukherjee, S.: Hypersingular and finite part integrals in the boundary element method. Int. J. Solids Struct.31, 2299-2312 (1994). · Zbl 0946.74584 · doi:10.1016/0020-7683(94)90153-8
[15] Krishnaswamy, G., Rizzo, F. J., Rudolphi, T. J.: Hypersingular boundary integral equations: their occurence, interpretation, regularization and computation. In: Developments in boundary elements method (Banerjee, P. K., Kobayashi, S., eds.), pp. 207-252. London: Elsevier 1992.
[16] Rizzo, F. J.: An integral equation approach to boundary value problems of classical elastostatics. Q. Appl. Math.25, 83-95 (1967). · Zbl 0158.43406
[17] Timoshenko, S. P., Goodier, J. N.: Theory of elasticity, 3rd ed. New York: McGraw-Hill 1970. · Zbl 0266.73008
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