Summary
This work investigates the second order deformation of a uniformly thick incompressible isotropic elastic annulus with an axial cylindrical hole. The annulus is clamped at its outer edge and is subjected to a constant angular deformation on the interior boundary of the hole. The implicit mathematical solution is formulated in terms of finite Hankel transforms with Weber-Orr kernel functions which are then numerically inverted.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Signorini, A.: Ann. Mat. Pure Appl.30 (1949).
Green, A. E., Adkins, J. E.: Large elastic deformations, 2nd ed. Oxford: Oxford University Press 1970.
Green, A. E., Spratt, E. B.: Second-order effects in the deformation of elastic bodies. Proc. Roy. Soc. London Ser. A224, 347–361 (1954).
Spencer, A. J. M.: The static theory of finite elasticity. IMA J. Appl. Math.6, 164–200 (1970).
Selvadurai, A. P. S., Spencer, A. J. M.: Second-order elasticity with axial symmetry—I General theory. Int. J. Eng. Sci.10, 97–114 (1972).
Selvadurai, A. P. S.: Plain strain problems in second-order elasticity theory. Int. J. Nonlinear Mech.8, 551–563 (1973).
Selvadurai, A. P. S.: Second-order elastic effects in the torsion of a spherical annular region. Int. J. Eng. Sci.12, 295–310 (1974).
Haughton, D. M., Lindsay, K. A.: The second order deformation of a finite compressible isotropic elastic annulus subjected to circular shearing. Proc. Roy. Soc. London Ser. A (to appear).
Lindsay, K. A.: The second order deformation of an incompressible isotropic slab under torsion. Q.J.M.A.M. (in press).
Rivlin, R. S., Saunders, D. W.: Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber. Phil. Trans. Roy. Soc. London Ser. A243, 251–288 (1951).
Treloar, L. R. G.: The physics of rubber elasticity, 2nd ed. Oxford: Oxford University Press 1958.
Sneddon, I. N.: Finite Hankel transforms. Phil. Mag.37, 17–25 (1946).
Tranter, C. J.: Integral transforms in mathematical physics, 3rd ed. London: Chapman and Hall 1971.
Watson, G. N.: A treatise on the theory of Bessel functions, 2nd ed. Cambridge: Cambridge University Press 1944.
Davis, P. J., Rabinowitz, P.: Methods of numerical integration, 2nd ed. New York: Academic Press 1984.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Haughton, D.M., Lindsay, K.A. The second order deformation of a finite incompressible isotropic elastic annulus subjected to circular shearing. Acta Mechanica 104, 125–141 (1994). https://doi.org/10.1007/BF01170060
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01170060