Abstract
Exact solutions for stresses, strains, and displacements of a perforated rectangular plate by a central circular hole under both linearly varying in-plane normal stresses on two opposite edges and in-plane shear stresses acting on its entire outer boundary are investigated using the Airy stress function. The hoop stresses arising at the edge of the circular hole are also calculated and plotted. Stress concentration factors (the maximum non-dimensional hoop stresses) depending upon the size of the circular hole and the inplane loading condition are tabularized.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Fu, L.-S. (1996). A first course in elasticity, The Ohio State University.
Iwaki, T. and Miyao, K. (1980). “Stress concentrations in a plate with two unequal circular holes.” Int. J. Eng. Sci., Vol. 18, No. 8, pp. 1077–1090.
Kang, J.-H. (2014). “Exact solutions of stresses, strains, and displacements of a perforated rectangular plate by a central circular hole subjected to linearly varying in-plane normal stresses on two opposite edges.” Int. J. Mech. Sci., Vol. 84, pp. 18–24.
Li, F., He, Y. T., Fan, C. H., Li, H. P., and Zhang, H. X. (2008). “Investigation on three-dimensional stress concentration of LY12-CZ plate with two equal circular holes under tension.” Materials Sci. Eng., A. Vol. 483-484, No. 15, pp. 474–476.
Mal, A. K. and Singh, S. J. (1991). Deformation of elastic solids, Prentice-Hall, Englewood Cliffs.
Miyata, H. (1970). “Finite elastic deformations of an infinite plate perforated by two circular holes under biaxial tension.” Ingenieur-Archive, Vol. 39, No. 4, pp. 209–218.
Muskhelishvili, N. I. (1963). Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen, The Netherlands.
Peterson, R. E. (1974). Stress concentration factor, John Wiley and Sons, New York.
Radi, E. (2011). “Path-independent integrals around two circular holes in an infinite plate under biaxial loading conditions.” Int. J. Eng. Sci., Vol. 49, No. 9, pp. 893–914.
Savin, G. N. (1961). Stress concentration around holes, Pergamon Press, New York.
She, C. M. and Guo, W. L. (2007). “Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress.” Int. J. Fatig., Vol. 29, No. 2, pp. 330–335.
Theocaris, P. S. and Petrou, L. (1987). “The order of singularities and the stress intensity factors near corners of regular polygonal holes.” Int. J. Eng. Sci., Vol. 25, No. 7, pp. 821–832.
Timoshenko, S. P. and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed., McGraw-Hill, New York.
Woo, H.-Y., Leissa, A. W., and Kang, J.-H. (2014). “Exact solutions for stresses, strains, displacements, and the stress concentration factors of a perforated rectangular plate by a circular hole subjected to inplane bending moment on two opposite edges.” J. Eng. Mech., Vol. 140, No. 6, pp. 1–8.
Yang, L. H. and He, Y. Z. (2002). “Stress field analysis for infinite plate with rectangular opening.” J. Harbin Eng. Univ., Vol. 23, No. 2, pp. 106–110 in Chinese.
Yang, Z., Kim, C. B., Cho, C., and Beom, H. G. (2008). “The concentration of stress and strain in finite thickness elastic plate containing a circular hole.” Int. J. Solids Struct., Vol. 45, Nos. 3-4, pp. 713–731.
Yu, P. S., Guo, W. L., She, C. M., and Zhao, J. H. (2008). “The influence of Poisson’s ratio on thickness-dependent stress concentration at elliptic holes in elastic plates.” Int. J. Fatig., Vol. 30, No. 1, pp. 165–171.
Zhang, T., Liu, T. G., Zhao, Y., and Liu, J. X. (2002). “Analysis of stress field of finite plates weakened by holes.” J. Huazhong Univ. Sci. Tech., Vol. 30, pp. 87–89 in Chinese.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kang, JH. Exact deformation of a rectangular plate with a central circular hole under in-plane loads. KSCE J Civ Eng 20, 2492–2498 (2016). https://doi.org/10.1007/s12205-015-0510-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-015-0510-1