Summary
The methods of images and Hankel transforms are used to construct solution to an axisymmetric boundary value problem of a semi-space of transversely isotropic (granular) material due to a point force applied at a distanceh beneath its stress free plane boundaryz=0. Exact closed form expressions are determined for the components of displacements and stresses throughout the interior of the granular semi-space. The solution is then used to derive the surface displacements due to a uniformly distributed force over a circle of radius ‘a’ with centre at (0, 0, −h) in the planez=−h of the semi-space. By a suitable choice of material constants and through a limit process as α1, α2 approach 1, the granular semi-space becomes isotropic and the corresponding results derived in this particular case agree with those presented in [14].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hearman, R. F. S.: An introduction to applied anisotropic elasticity. New York: Oxford University Press 1961.
Steeds, J. W.: Introduction to anisotropic elasticity theory of dislocations. New York: Oxford University Press 1973.
Musgrave, M. J. P.: Elastic waves in anisotropic media, in: Progress in Solid Mechanics, Vol. II. Amsterdam: North-Holland Publishing Company 1961.
Lekhnitskii, S. G.: Theory of elasticity of an anisotropic body, (trans. Fern, P.). San Francisco: Holden Day 1963.
Wang, S. S., Choi, I.: Boundary layer thermal stresses in angle-ply composite laminates. Modern Development in Composite Materials and Structures (Vinston, J. R., ed.), ASME, pp. 315–341 1979.
Chadwick, P., Smith, A.: Foundations of the theory of surface waves in anisotropic elastic materials. Advances in Applied Mechanics17, 303–389 (1977).
Sokolvskii, V. V.: Statics of granular media. London: Pergamon Press 1965.
Jenkins, J. T.: Static equilibrium of granular materials. J. Appl. Mech.42, 603 (1975).
Passman, S. L.: Mixtures of granular materials. Int. J. Engng. Sci.15, 117 (1977).
Ahmadi, G.: A generalized continuum theory for granular materials. Inter. Jour. Non. Mech.17, 21–33 (1982).
Misra, B., Sen, B. R.: Stresses and displacements in granular materials due to surface loads. Int. Jour. Engng. Sci.13, 743–761 (1975).
Mindlin, R. D.: Point force in the interior of an elastic semi-space. Physics7, 125 (1936).
Sharma, D. L.: A general solution of elastostatic equations in a half space. Jour. Math. Anal. Appl.21 (1), 99–111 (1968).
Sneddon, I. N.: Fourier transforms. New York: McGraw Hill Book Company 1951.
Author information
Authors and Affiliations
Additional information
With 2 Figures
Rights and permissions
About this article
Cite this article
Chowdhury, K.L. On the axisymmetric Mindlin's problem for a semi-space of granular material. Acta Mechanica 66, 145–159 (1987). https://doi.org/10.1007/BF01184290
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01184290