Abstract
We report an implementation of the Boundary Element Method (BEM) for half-space elasticity or Stokes problems with a plane interface (the boundary of the half space). With a proper choice of the singularity solution this plane interface, on which the displacement or velocity vector is zero, does not need to be discretized. For a large class of problems involving translating or rotating bodies a simplification of the boundary element formulation is possible, with a resulting improvement in the accuracy of the numerical results. The three-dimensional boundary element program was tested with the moving sphere problem and was found to be satisfactory in all cases.
Similar content being viewed by others
References
Banerjee, P.K.; Butterfield, R. (1981): Boundary element methods in engineering science. London: McGraw-Hill
Blake, J.R. (1971): A note on the image system for a Stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303–310
Brebbia, C.A.; Telles, J.C.F.; Wrobel, L.C. (1984): Boundary element techniques theory and applications in engineering. Berlin, Heidelberg, New York, Tokyo: Springer
Brenner, H. (1964): Effect of finite boundaries on the Stokes resistance of an arbitrary particle, part 2: Asymmetrical orientations. J. Fluid Mech. 18, 144–158
Das, P.C. (1978): A disc based block elimination technique used for the solution of non-symmetrical fully populated matrix system encountered in the boundary element method. In: Brebbia, C.A. (Ed): Recent advances in boundary element methods. London: Pentech Press 391–404
Ejike, U.B.C.O. (1970): Boundary effects due to body forces and body couples in the interior of a semi infinite elastic solid. Int. J. Eng. Sci.8, 909–924
Fichera, G. (1961): Linear elliptic equations of higher order in two independent variables and singular integral equations, with applications to anisotropic inhomogeneous elasticity. In: Langer, R.E. (Ed.): Proc. Conf. P.D.E. and Continuum Mechanics, pp 55–80. Madison, WI, Univ. Wisconsin Press
Hasimoto, H.; Sano, O. (1980): Stokeslets and eddies in creeping flow. Ann. Rev. Fluid Mech. 12, 335–363
Hess, J.L.; Smith, A.M.O. (1967): Calculation of potential flow about arbitrary bodies. In: Kucheman, D. (Ed.): Progress in aeronautical sciences, pp. 1–138. London: Pergamon Press
Lee, S.H.; Leal, L.G. (1980): Motion of a sphere in the presence of a plane interface, part 2: An exact solution in bipolar coordinates. J. Fluid Mech. 98, 193–224
Mindlin, R.D. (1936): Force at a point in the interior of a semi-infinite solid. Physics 7, 195–202
Phan-Thien, N. (1983): On the image system for the Kelvin-state. J. Elasticity 13, 231–235
Rizzo, F.J. (1967): An integral equation approach to boundary value problems of classical elastostatics. J. Appl. Math. 25, 83–95
Telles, J.C.F.; Brebbia, C.A. (1981): Boundary element solution for half-plane problems. Int. J. Solids Struct. 17, 1149–1158
Watson, J.O. (1975): Advanced implementation of the boundary element method for two- and three-dimensional elastostatics. In: Banerjee, P.K.; Butterfield, R. (Eds.): Developments in boundary element methods-1, pp. 31–63. London: Applied Science
Author information
Authors and Affiliations
Additional information
Communicated by R. I. Tanner and S. N. Aduri, November 1, 1985
Rights and permissions
About this article
Cite this article
Tran-Cong, T., Phan-Thien, N. Boundary element solution for half-space elasticity or stokes problem with a no-slip boundary. Computational Mechanics 1, 259–268 (1986). https://doi.org/10.1007/BF00273702
Issue Date:
DOI: https://doi.org/10.1007/BF00273702