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Exact deformation of a rectangular plate with a central circular hole under in-plane loads

  • Structural Engineering
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KSCE Journal of Civil Engineering Aims and scope

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.

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References

  • Fu, L.-S. (1996). A first course in elasticity, The Ohio State University.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Mal, A. K. and Singh, S. J. (1991). Deformation of elastic solids, Prentice-Hall, Englewood Cliffs.

    MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Muskhelishvili, N. I. (1963). Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen, The Netherlands.

    MATH  Google Scholar 

  • Peterson, R. E. (1974). Stress concentration factor, John Wiley and Sons, New York.

    Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Savin, G. N. (1961). Stress concentration around holes, Pergamon Press, New York.

    MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Timoshenko, S. P. and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed., McGraw-Hill, New York.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Architectural Engineering, Chung-Ang University, Seoul, 06974, Korea

    Jae-Hoon Kang

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  1. Jae-Hoon Kang
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Correspondence to Jae-Hoon Kang.

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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

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  • DOI: https://doi.org/10.1007/s12205-015-0510-1

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