A Comprehensive Study on the Effects of the Boundary Conditions on the Elastic Buckling Capacity of a Perforated Plate

Subject Areas : Mechanical Engineering

Sadegh  Ghorbanhosseini ¹ (Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan, Iran)
Saeed  Yaghoubi ² (Department of Mechanical Engineering, Shoushtar Branch, Islamic Azad University, Shoushtar, Iran)
Mohammad Reza  Bahrambeigi ³ (Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran)

Received: 2020-11-10 Accepted : 2021-03-14 Published : 2021-09-01

Keywords: Boundary conditions, Perforated rectangular plates, FEM, stiffener, buckling capacity,

Abstract :

Nowadays, different industries are using sheets, plates, and shells as important parts of their components. Because of their small thickness compare to other dimensions, their structural safety requires more attention. Therefore, increasing their strength and intensifying their resistance against any kind of failure type could be introduced as an important problem for enhancing the structural safety. Buckling is one of the most significant failure type that should be considered in the stability of any parts such as sheet metals. Thus, investigation of the buckling capacity of the sheet metals is remarkable. On the other hand, the existence of discontinuity like holes and notches in sheet metals can decrease their buckling capacity, significantly. In current study, based on Finite Element Method (FEM), ABAQUS/Explicit has been employed to determine the elastic buckling capacity in a perforated rectangular sheet metal with different boundary conditions on its edges. Afterward, the effect of the hole position and the plate aspect ratios (plate length/plate width) on the buckling capacity of sheet metal was studied. Finally, in order to enhance the sheet metal buckling capacity, two different types of stiffeners were used. The outcomes showed that the maximum buckling coefficient is related to the sheet metal which have four clamped edges. Moreover, For all boundary conditions, the buckling coefficient does not change significantly for the sheet metals with aspect ratio of more than 4. Also, stiffener type 2 increased the buckling capacity of sheet metal up to 83%.

References:

• Vahabi, H., Esmaeili Golmakani, M., and Mobasher, I., Buckling Analysis of Orthotropic Annular Graphene Sheet with Various Boundary Conditions in an Elastic Medium, International Journal of Advanced Design and Manufacturing Technology, Vol. 13, No. 2, 2020, pp. 73-90.


• Timoshenko, S. P., Gere, J. M., Theory of Elastic Stability, 2rd ed, McGraw-Hill, New York, 1961, 319-356.


• Brown, C. J., Yettram, A. L., The Elastic Stability of Square Perforated Plates Under Combinations of Bending, Shear and Direct Load, Thin-Walled Structures, Vol. 4, No. 3, 1986, 239-246, DOI: https://doi.org/10.1016/0263-8231(86)90005-4.


• Brown, C. J., Yettram, A. L., and Burnett, M., Stability of Plates with Rectangular Holes, Journal of Structural Engineering, Vol. 113, No. 5, 1987, pp. 1111-1116, DOI: https://doi.org/10.1061/0733-9445(1987)113:5(1111).


• Brown, C. J., Elastic Buckling of Perforated Plates Subjected to Concentrated Loads, Computers & Structures, Vol. 36, No. 6, 1990, pp. 1103-1109, DOI: https://doi.org/10.1016/0045-7949(90)90218-Q.


• Shakerley, T., Brown, C., Elastic Buckling of Plates with Eccentrically Positioned Rectangular Perforations, International Journal of Mechanical Sciences, Vol. 38, No. 8-9, 1996, pp. 825-838, DOI: https://doi.org/10.1016/0020-7403(95)00107-7.


• Wang, C., Xiang, Y., Kitipornchai, S., and Liew, K. M., Buckling Solutions for Mindlin Plates of Various Shapes, Engineering Structures, Vol. 16, No. 2, 1994, pp. 119-127, DOI: https://doi.org/10.1016/0141-0296(94)90037-X.


• Byklum, E., Amdahl, J., A Simplified Method for Elastic Large Deflection Analysis of Plates and Stiffened Panels Due to Local Buckling, Thin-Walled Structures, Vol. 40, No. 11, 2002, pp. 925-953, DOI: https://doi.org/10.1016/S0263-8231(02)00042-3.


• Matsunaga, H., Buckling Instabilities of Thick Elastic Plates Subjected to In-Plane Stresses, Computers & Structures, Vol. 62, No. 1, 1997, pp. 205-214, DOI: https://doi.org/10.1016/S0045-7949(96)00239-8.


• Bert, C. W., Devarakonda, K. K., Buckling of Rectangular Plates Subjected to Nonlinearly Distributed In-plane Loading, International Journal of Solids and Structures, Vol. 40, No. 16, 2003, pp. 4097-4106, DOI: https://doi.org/10.1016/S0020-7683(03)00205-1.


• Sabir, A., Chow, F., Elastic buckling of Flat Panels Containing Circular and Square Holes, Granada Publishing Ltd, 1983, pp. 311-321.


• Azizian, Z., Roberts, T., Buckling and Elastoplastic Collapse of Perforated Plates, Instability and Plastic Collapse of Steel Structures, 1983, pp. 322-328.


• El-Sawy, K. M., Nazmy, A. S., Effect of Aspect Ratio on the Elastic Buckling of Uniaxially Loaded Plates with Eccentric Holes, Thin-Walled Structures, Vol. 39, No. 12, 2001, pp. 983-998, DOI: https://doi.org/10.1016/S0263-8231(01)00040-4.


• Shanmugam, N., Thevendran, V., and Tan, Y., Design Formula for Axially Compressed Perforated Plates, Thin-Walled Structures, Vol. 34, No. 1, 1999, pp. 1-20, https://doi.org/10.1016/S0263-8231(98)00052-4.


• El-Sawy, K. M., Martini, M. I., Elastic Stability of Bi-axially Loaded Rectangular Plates with a Single Circular Hole, Thin-Walled Structures, Vol. 45, No. 1, 2007, pp. 122-133, DOI: https://doi.org/10.1016/j.tws.2006.11.002.


• Shariati, M., Majd Sabeti, A. M., and Gharooni, H., A Numerical and Experimental Study on Buckling and Post-buckling of Cracked Plates under Axial Compression Load, Journal of Computational & Applied in Mechanical Engineering, Vol. 4, No. 1, 2014, pp. 43-54, DOI: https://dx.doi.org/10.22061/jcarme.2014.71.


• Komur, M. A., Sonmez, M., Elastic Buckling Behavior of Rectangular Plates with Holes Subjected to Partial Edge Loading, Journal of Constructional Steel Research, Vol. 112, 2015, pp. 54-60, DOI: https://doi.org/10.1016/j.jcsr.2015.04.020.


• Prajapat, K., Ray-Chaudhuri, S., and Kumar, A., Effect of In-plane Boundary Conditions on Elastic Buckling Behavior of Solid and Perforated Plates, Thin-Walled Structures, Vol. 90, 2015, pp. 171-181, DOI: https://doi.org/10.1016/j.tws.2014.12.015.


• Seifi, R., Chahardoli, S., and Attar, A. A., Axial Buckling of Perforated Plates Reinforced with Strips and Middle Tubes, Mechanics Research Communications, Vol. 85, 2017, pp. 21-32, DOI: https://doi.org/10.1016/j.mechrescom.2017.07.015.


• Azmi, M. R., Yatim, M. Y. M., Esa, A., and Badaruzzaman, W. W., Experimental Studies on Perforated Plate Girders with Inclined Stiffeners, Thin-Walled Structures, Vol. 117, 2017, pp. 247-256, DOI: https://doi.org/10.1016/j.tws.2017.04.021.


• Pham, C. H., Shear Buckling of Plates and Thin-walled Channel Sections with Holes, Journal of Constructional Steel Research, Vol. 128, 2017, pp. 800-811, DOI: https://doi.org/10.1016/j.jcsr.2016.10.013.


• Abolghasemi, S., Eipakchi, H. R., and Shariati, M., Investigation of Pre-buckling Stress Effect on Buckling Load Determination of Finite Rectangular Plates with Circular Cutout, Journal of Solid Mechanics, Vol. 10, No. 4, 2018, pp. 816-830.


• Abolghasemi, S., Eipakchi, H., and Shariati, M., An Analytical Solution for Buckling of Plates with Circular Cutout Subjected to Non-uniform In-plane Loading, Archive of Applied Mechanics, Vol. 89, No. 12, 2019, pp. 2519-2543, DOI: https://doi.org/10.1007/s00419-019-01592-3.


• Soltani, H. M., Kharazi, M., Plastic Buckling and Post Buckling Analysis of Plates Using 3D Incompatible and Standard Elements, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2019, pp. 1-23, DOI: https://doi.org/10.1007/s40997-019-00316-w.