# Investigation of Pre-buckling Stress Effect on Buckling Load Determination of Finite Rectangular Plates with Circular Cutout

Document Type: Research Paper

Authors

1 Faculty of Mechanical and Mechatronic Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

This paper investigates the buckling of finite isotropic rectangular plates with circular cutout under uniaxial and biaxial loading. The complex potential method is used to calculate the pre-buckling stress distribution around the cutout in the plate with finite dimensions. To satisfy the in-plane boundary conditions, the generalized complex-potential functions are introduced and a new method based on the boundary integral which has been obtained from the principle of virtual work is used to apply the boundary conditions at the plate edges. The potential energy of the plate is calculated by considering the first order shear deformation theory and the Ritz method is used to calculate the buckling load. The effects of cutout size, type of loading and different boundary conditions on the buckling load are investigated. Comparing of the calculated buckling loads with the finite element results shows the accuracy of the presented method for buckling analysis of the plates.

Keywords

### References

[1] Lekhnitskii S., 1968, Anisotropic Plates, Gordon and Breach Science, New York.
[2] Savin G. N., 1961,Stress Concentration Around Holes, Pergamon, New York.
[3] Sevenois R. D. B., Koussios S., 2014, Analytic methods for stress analysis of two-dimensional flat anisotropic plates with notches: an overview, Applied Mechanics Reviews 66: 060802.
[4] Lin C. C., Ko C. C., 1988, Stress and strength analysis of finite composite laminates with elliptical holes, Journal of Composite Materials 22: 373-385.
[5] Gao X. L., 1996, A general solution of an infinite elastic plate with an elliptic hole under biaxial loading, International Journal of Pressure Vessels and Piping 67: 95-104.
[6] Ukadgaonker V. G., Rao D. K. N., 2000, A general solution for stresses around holes in symmetric laminates under inplane loading, Composite Structures 49: 339-354.
[7] Xu X. W., Man H. C., Yue T. M., 2000, Strength prediction of composite laminates with multiple elliptical holes, International Journal of Solids and Structures 37: 2887-2900.
[8] Louhghalam A., Igusa T., Park C., Choi S., Kim K., 2011, Analysis of stress concentrations in plates with rectangular openings by a combined conformal mapping – Finite element approach, International Journal of Solids and Structures 48: 1991-2004.
[9] Nemeth M. P., stein M., Johnson E. R., 1986, An approximate buckling analysis for rectangular orthotropic plates with centrally located cutouts, NASA Technical Paper 1986: 1-18.
[10] Britt V. O., 1994, Shear and compression buckling analysis for anisotropic panels with elliptical cutouts, AIAA Journal 32: 2293-2299.
[11] Shakerley T. M., Brown C. J., 1996, Elastic buckling of plates with eccentrically positioned rectangular perforations, International Journal of Mechanical Sciences 38: 825-838.
[12] El-Sawy K. M., Nazmy A. S., 2001, Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes, Thin–Walled Structures 39: 983-998.
[13] Sabir A., Chow F., 1986, Elastic buckling of plates containing eccentrically located circular holes, Thin–Walled Structures 4: 135-149.
[14] Ghannadpour S. A. M., Najafi A., Mohammadi B., 2006, On the buckling behavior of cross-ply laminated composite plates due to circular/elliptical cutouts, Composite Structures 75: 3-6.
[15] Anil V., Upadhyay C. S., Iyengar N. G. R., 2007, Stability analysis of composite laminate with and without rectangular cutout under biaxial loading, Composite Structures 80: 92-104.
[16] Moen C. D., Schafer B. W., 2009, Elastic buckling of thin plates with holes in compression or bending, Thin–Walled Structures 47: 1597-1607.
[17] Kumar D., Singh S. B., 2013, Effects of flexural boundary conditions on failure and stability of composite laminate with cutouts under combined in-plane loads, Composites Part B: Engineering 45: 657-665.
[18] Kumar D., Singh S. B., 2012, Stability and failure of composite laminates with various shaped cutouts under combined in-plane loads, Composites Part B: Engineering 43: 142-149.
[19] Kumar D., Singh S. B., 2010, Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts, Composite Structures 92: 769-779.
[20] Aydin Komur M., Sonmez M., 2008, Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout, Mechanics Research Communications 35: 361-371.
[21] Prajapat K., Ray-Chaudhuri S., Kumar A., 2015, Effect of in-plane boundary conditions on elastic buckling behavior of solid and perforated plates, Thin–Walled Structures 90: 171-181.
[22] Barut A., Madenci E., 2010, A complex potential-variational formulation for thermo-mechanical buckling analysis of flat laminates with an elliptic cutout, Composite Structures 92: 2871-2884.
[23] Ovesy H. R., Fazilati J., 2012, Buckling and free vibration finite strip analysis of composite plates with cutout based on two different modeling approaches, Composite Structures 94: 1250-1258.
[24] Huang C., Leissa A., 2009, Vibration analysis of rectangular plates with side cracks via the Ritz method, Journal of Sound and Vibration 323: 974-988.
[25] Huang C., Leissa A., Chan C., 2011, Vibrations of rectangular plates with internal cracks or slits, International Journal of Mechanical Sciences 53: 436-445.
[26] Sadd M. H., 2005, Elasticity: Theory, Applications, and Numerics, Academic Press, India.
[27] Reddy J. N., 2006, Theory and Analysis of Elastic Plates and Shells, CRC Press.
[28] Bažant Z. P., Cedolin L., 2010, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, World Scientific.
[29] Kumar Y., 2017, The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review, Journal of Vibration and Control 2017: 1-23.
[30] Moreno-García P., Dos Santos J. V. A., Lopes H., 2017, A review and study on Ritz Method admissible functions with emphasis on buckling and free vibration of isotropic and anisotropic beams and plates, Archives of Computational Methods in Engineering 2017: 1-31.
[31] ABAQUS, 6.11. User’s manual, Dassault Systemes, 2011.