Exact Solutions for Stresses, Strains, Displacements, and Stress Concentration Factors of a Perforated Rectangular Plate by a Circular Hole Subjected to In-Plane Bending Moment on Two Opposite Edges
Publication: Journal of Engineering Mechanics
Volume 140, Issue 6
Abstract
Exact solutions for stresses, strains, displacements, and the stress concentration factors of a perforated rectangular plate by a circular hole subjected to in-plane bending moment on two opposite edges are investigated by two-dimensional theory of elasticity using the Airy stress function. The hoop stresses, strains, and displacements occurring at the edge of the circular hole are computed and plotted. Comparisons are made for the hoop stresses and the stress concentration factors from the current study and rectangular plates with a circular hole under uniaxial and biaxial uniform tensions and pure shear loading.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aksu, G., and Ali, R. (1976). “Determination of dynamic characteristics of rectangular plates with cut-outs using finite difference formulation.” J. Sound Vib., 44(1), 147–158.
Aydin Komur, M. (2011). “Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression.” Mech. Res. Commun., 38(2), 117–122.
Aydin Komur, M., and Sonmez, M. (2008). “Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout.” Mech. Res. Commun., 35(6), 361–371.
Azhari, M., Shahidi, A. R., and Saadatpour, M. M. (2005). “Local and post local buckling of stepped and perforated thin plates.” Appl. Math. Model., 29(7), 633–652.
Azizian, Z. G., and Roberts, T. M. (1983). “Buckling and elasto-plastic collapse of perforated plates.” Proc., Int. Conf. on Instability and Plastic Collapse of Steel Structures, Granada, London, 392–398.
Boay, C. G. (1996). “Free vibration of laminated plates with a central circular hole.” Compos. Struct., 35(4), 357–368.
Brown, C. J. (1990). “Elastic buckling of perforated plates subjected to concentrated loads.” Comput. Struct., 36(6), 1103–1109.
Brown, C. J., and Yettram, A. L. (1986). “The elastic stability of square perforated plates under combination of bending, shear and direct load.” Thin-Walled Struct., 4(3), 239–246.
Brown, C. J., Yettram, A. L., and Burnett, M. (1987). “Stability of plates with rectangular holes.” J. Struct. Eng., 1111–1116.
Chakherlou, T. N., and Abazadeh, B. (2011). “Estimation of fatigue life for plates including pre-treated fastener holes using different multiaxial fatigue criteria.” Int. J. Fatigue, 33(3), 343–353.
Chan, R. W. K., Albermani, F., and Kitipornchai, S. (2013). “Experimental study of perforated yielding shear panel device for passive energy dissipation.” J. Constr. Steel Res., 91, 14–25.
Chau, K. T., and Wang, Y. B. (1999). “A new boundary integral formulation for plane elastic bodies containing cracks and holes.” Int. J. Solids Struct., 36(14), 2041–2074.
Cheng, B., and Zhao, J. (2010). “Strengthening of perforated plates under uniaxial compression: Buckling analysis.” Thin-Walled Struct., 48(12), 905–914.
Cheng, C. J., and Fan, X. J. (2001). “Nonlinear mathematical theory of perforated viscoelastic thin plates with its applications.” Int. J. Solids Struct., 38(36–37), 6627–6641.
Dalessandro, J. A. (1976). “Structural considerations for a Tokamak fusion reactor.” Nucl. Eng. Des., 39(1), 141–151.
El-Sawy, K. M., and Martini, M. I. (2007). “Elastic stability of bi-axially loaded rectangular plates with a single circular hole.” Thin-Walled Struct., 45(1), 122–133.
El-Sawy, K. M., and Nazmy, A. S. (2001). “Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes.” Thin-Walled Struct., 39(12), 983–998.
El-Sawy, K. M., Nazmy, A. S., and Martini, M. I. (2004). “Elasto-plastic buckling of perforated plates under uniaxial compression.” Thin-Walled Struct., 42(8), 1083–1101.
Fu, L.-S. (1996). A first course in elasticity, Ohio State Univ., Columbus, OH.
Geannakakes, G. N. (1990). “Vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi-analytical finite strip method.” J. Sound Vib., 137(2), 283–303.
Iwaki, T., and Miyao, K. (1980). “Stress concentrations in a plate with two unequal circular holes.” Int. J. Eng. Sci., 18, 1077–1090.
Lacarac, V., Smith, D. J., Pavier, M. J., and Priest, M. (2000). “Fatigue crack growth from plain and cold expanded holes in aluminium alloys.” Int. J. Fatigue, 22(3), 189–203.
Lam, K. Y., Hung, K. C., and Chow, S. T. (1989). “Vibration analysis of plates with cutouts by the modified Rayleigh-Ritz method.” Appl. Acoust., 28(1), 49–60.
Laura, P. A. A., Romanelli, E., and Rossi, R. E. (1997). “Transverse vibrations of simply supported rectangular plates with rectangular cutouts.” J. Sound Vib., 202(2), 275–283.
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.” Mater. Sci. Eng. A, 483–484, 474–476.
Liew, K. M., Hung, K. C., and Lim, M. K. (1993a). “Method of domain decomposition in vibrations of mixed edge anisotropic plates.” Int. J. Solids Struct., 30(23), 3281–3301.
Liew, K. M., Hung, K. C., and Lim, M. K. (1993b). “Roles of domain decomposition method in plate vibrations—Treatment of mixed discontinuous periphery boundaries.” Int. J. Mech. Sci., 35(7), 615–632.
Liew, K. M., Hung, K. C., and Sum, Y. K. (1995). “Flexural vibration of polygonal plates: treatments of sharp re-entrant corners.” J. Sound Vib., 183, 221–238.
Liew, K. M., Kitipornchai, S., Leung, A. Y. T., and Lim, C. W. (2003). “Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method.” Int. J. Mech. Sci., 45(5), 941–959.
Liew, K. M., Ng, T. Y., and Kitipornchai, S. (2001). “A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation.” Int. J. Solids Struct., 38(28–29), 4937–4954.
Liew, K. M., and Sum, Y. K. (1998). “Vibration of plates having orthogonal straight edges with clamped boundaries.” J. Eng. Mech., 184–192.
Liu, F. L., and Liew, K. M. (1999a). “Differential quadrature element method: A new approach for free vibration analysis of polar Mindlin plates having discontinuities.” Comput. Methods Appl. Mech. Eng., 179(3–4), 407–423.
Liu, F. L., and Liew, K. M. (1999b). “Vibration analysis of discontinuous Mindlin plates by differential quadrature element method.” J. Vib. Acoust., 121(2), 204–208.
Liu, Y., Xin, H., He, J., Xue, D., and Ma, B. (2013). “Experimental and analytical study on fatigue behavior of composite truss joints.” J. Constr. Steel Res., 83, 21–36.
Maiorana, E., Pellegrino, C., and Modena, C. (2008). “Linear buckling analysis of perforated plates subjected to localized symmetrical load.” Eng. Struct., 30(11), 3151–3158.
Maiorana, E., Pellegrino, C., and Modena, C. (2009a). “Elastic stability of plates with circular and rectangular holes subjected to axial compression and bending moment.” Thin-Walled Struct., 47(3), 241–255.
Maiorana, E., Pellegrino, C., and Modena, C. (2009b). “Non-linear analysis of perforated steel plates subjected to localized symmetrical load.” J. Constr. Steel Res., 65(4). 959–964.
Moen, C. D., and Schafer, B. W. (2009). “Elastic buckling of thin plates with holes in compression or bending.” Thin-Walled Struct., 47(12), 1597–1607.
Muskhelishvili, N. I. (1963). Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen, Netherlands.
Narayanan, R., and Avanessian, N. G. V. (1984). “Elastic buckling of perforated plated under shear.” Thin-Walled Struct., 2(1), 51–73.
Narayanan, R., and Chow, F. Y. (1984). “Ultimate capacity of uniaxially compressed perforated plates.” Thin-Walled Struct., 2(3), 241–264.
Narayanan, R., and Darwish, I. Y. S. (1985). “Strength of slender webs having non-central holes.” The Structural Engineer, 63(15), 57–61.
Narayanan, R., and Rockey, K. C. (1981). “Ultimate load capacity of plate girders with webs containing circular cut-outs.” Proc. Inst. Civ. Eng., 71(3), 845–862.
Nemeth, M. (1996). “Buckling and postbuckling behavior of laminated composite plates with a cutout.” NASA Technical Paper 3587, National Aeronautics and Space Administration (NASA) Langley Research Center, Hampton, VA.
Paik, J. K. (2007a). “Ultimate strength of perforated steel plates under edge shear loading.” Thin-Walled Struct., 45(3), 301–306.
Paik, J. K. (2007b). “Ultimate strength of steel plates with a single circular hole under axial compressive loading along short edges.” Ships Offshore Struct., 2(4), 355–360.
Paik, J. K. (2008). “Ultimate strength of perforated steel plates under combined biaxial compression and edge shear loads.” Thin-Walled Struct., 46(2), 207–213.
Pan, E. N. (1997). “A general boundary element analysis of 2-D linear elastic fracture mechanics.” Int. J. Fract., 88(1), 41–59.
Peterson, R. E. (1974). Stress concentration factor, Wiley, New York.
Roberts, T. M., and Azizian, Z. G. (1984). “Strength of perforated plates subjected to in-plane loading.” Thin-Walled Struct., 2(2), 153–164.
Rockey, K. C., Anderson, R. G., and Cheung, Y. K. (1967). “The behavior of square shear webs having circular hole.” Proc., Int. Conf. on Thin-Walled Structures, Crosby Lockwood, London, 148–169.
Sabir, A. B., and Davies, T. G. (1997). “Natural frequencies of square plates with reinforced central holes subjected to inplane loads.” Thin-Walled Struct., 28(3–4), 337–353.
Saleem, M., Toubal, L., Zitoune, R., and Bougherara, H. (2013). “Investigating the effect of machining processes on the mechanical behavior of composite plates with circular holes.” Compos., Part A Appl. Sci. Manuf., 55, 169–177.
Savin, G. N. (1961). Stress concentration around holes, Pergamon Press, New York.
Shakerley, T. M., and Brown, C. J. (1996). “Elastic buckling of plates with eccentrically positioned rectangular perforations.” Int. J. Mech. Sci., 38(8-9), 825–838.
Shanmugam, N. E., Lian, V. T., and Thevendran, V. (2002). “Finite element modeling of plate girders with web openings.” Thin-Walled Struct., 40(5), 443–464.
Shanmugam, N. E., and Narayanan, R. (1982). “Elastic buckling of perforated square plates for various loading and edge conditions.” Proc., Int. Cof. on Finite Element Methods, Gordon and Breach, Shanghai, China, 241–245.
Shanmugam, N. E., Thevendran, V., and Tan, Y. H. (1999). “Design formula for axially compressed perforated plates.” Thin-Walled Struct., 34(1), 1–20.
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. Fatigue, 29(2), 330–335.
Sivakumar, K., Iyengar, N. G. R., and Deb, K. (1999a). “Free vibration of laminated composite plates with cutout.” J. Sound Vib., 221(3), 443–470.
Sivakumar, K., Iyengar, N. G. R., and Deb, K. (1999b). “Optimum design of laminated composite plates with cutouts undergoing large amplitude oscillations.” Adv. Compos. Mater, 8(4), 295–316.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed., McGraw Hill, New York.
Tokiyoshi, T., Kawashima, F., Igari, T., and Kino, H. (2001). “Crack propagation life prediction of a perforated plate under thermal fatigue.” Int. J. Press. Vessels Piping, 78(11–12), 837–845.
Toshihiro, I., and Kayzu, M. (1980). “Stress concentrations in a plate with two unequal circular holes.” Int. J. Eng. Sci., 18(8), 1077–1090.
Yang, B., and Park, D. H. (1999). “Analysis of plates with curved boundaries using isoparametric strip distributed transfer functions.” Int. J. Numer. Methods Eng., 44(1), 131–146.
Yang, B., and Zhou, J. (1996). “Semi-analytical solution of 2-D elasticity problems by the strip distributed transfer function method.” Int. J. Solids Struct., 33(27), 3983–4005.
Yang, L. H. and He, Y. Z. (2002). “Stress field analysis for infinite plate with rectangular opening.” J. Harbin Eng. Univ., 23, 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., 45(3–4), 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. Fatigue, 30(1), 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., 30, 87–89 (in Chinese).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 6 • June 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 3, 2013
Accepted: Oct 16, 2013
Published online: Oct 18, 2013
Published in print: Jun 1, 2014
Discussion open until: Jun 16, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.