Buckling of Square and Circular Perforated Square Plates under Uniaxial Loading

Abstract

This paper aims to investigate the critical buckling loads of uniaxially loaded simply supported square thin plates with central circular and square holes in terms of some parameters like hole shapes, slenderness ratios and total hole areas. In this study, buckling analyses of perforated plates with different hole shapes of perforation and slenderness ratios were carried out. For this purpose, plate models with seven different total hole areas were examined together with the non-perforated plate. The total hole area ratios in the models are 0.79%, 3.14%, 7.07%, 12.57%, 19.63%, 28.27% and 38.48%, respectively. The total hole areas of the models with square holes are arranged to be the same as the models with circular holes to compare the results among circular and square perforated plates properly. The models were established by using the finite-element (FE) software ANSYS using Shell-181 elements which are 4-node structural shell elements. The comparisons on critical buckling loads between square and circular perforated results show that the buckling load for the plates with square holes is higher than for the plates with circular holes.

Keywords

• Buckling
• Perforated plates
• Finite element
• Square perforated
• Circular perforated

Tek Eksenli Yükleme Altındaki Kare ve Dairesel Delikli Kare Plakların Burkulması

Abstract

Bu makale, merkezi dairesel ve kare deliklere sahip tek eksenli yüklü basit mesnetli kare ince plakların kritik burkulma yüklerini delik şekilleri, narinlik oranları ve toplam delik alanları gibi bazı parametreler açısından incelemeyi amaçlamaktadır. Bu çalışmada, farklı delik şekillerine ve narinlik oranlarına sahip delikli plakların burkulma analizleri yapılmıştır. Bu amaçla boşluksuz plak ile beraber yedi farklı boşluk oranına sahip plak modelleri incelenmiştir. Modellerdeki boşluk oranları sırasıyla %0.79, %3.14, %7.07, %12.57, %19.63, %28.27 ve %38.48 şeklindedir. Dairesel ve kare delikli plaklar arasındaki sonuçları doğru bir şekilde karşılaştırabilmek için kare delikli modellerin toplam delik alanları, dairesel delikli modellerle aynı olacak şekilde düzenlenmiştir. Modeller, kütüphanesinde bulunan 4 düğüm noktalı yapısal kabuk elemanı olan Shell-181 elemanları kullanılarak sonlu elemanlar yazılımı ANSYS ile analiz edilmiştir. Elde edilen sonuçlar, aynı boşluk alanına sahip kare delikli plakaların burkulma yüklerinin dairesel delikli plakalara göre daha yüksek olduğunu göstermiştir.

Keywords

• Burkulma
• Delikli plaklar
• Sonlu eleman
• Kare delik
• Dairesel delik.

References

1. Albayrak, U., & Saraçoğlu, M. H. (2018). Analysis of Regular Perforated Metal Ceiling Tiles. International Journal of Engineering and Technology, 10(6), 440–446. doi: 10.7763/ijet.2018.v10.1099
2. Bader Al-Amar Mohammed S Hassan AL-Araji, Q. H. (2017). Buckling of Perforated and Unperforated Stiffened Plate. In Journal of Babylon University/Engineering Sciences.
3. Brown, C J. (1990). Elastic buckling of perforated plates subjected to concentrated loads. Computers and Structures, 36(6), 1103–1109.
4. Brown, Christopher J, Yettram, A. L., & Burnett, M. (1987). Stability of Plates with Rectangular Holes. Journal of Structural Engineering, 113(5), 1111–1116. doi: 10.1061/(ASCE)0733-9445(1987)113:5(1111)
5. Bryan, G. H. (1891). On the stability of a plane plate under thrusts in its own plane with applications to the buckling of the sides of a ship. Proceedings of London Mathematics Society, 54–67.
6. da Silveira, Thiago, Torres Pinto, V., Pedro Sarasol Neufeld, J., Pavlovic, A., Alberto Oliveira Rocha, L., Domingues dos Santos, E., & André Isoldi, L. (2021). Applicability evidence of constructal design in structural engineering: case study of biaxial elasto-plastic buckling of square steel plates with elliptical cutout. J. Appl. Comput. Mech, 7(2), 922–934. doi: 10.22055/JACM.2021.35385.2647
7. 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. Retrieved from www.elsevier.com/locate/tws
8. El-Sawy, K. M., Nazmy, A. S., & Martini, M. I. (2004). Elasto-plastic buckling of perforated plates under uniaxial compression. Thin-Walled Structures, 42(8), 1083–1101. doi: 10.1016/J.TWS.2004.03.002

9. Fu, W., & Wang, B. (2022). A semi-analytical model on the critical buckling load of perforated plates with opposite free edges. Original Research Article Proc IMechE Part C: J Mechanical Engineering Science, 236(9), 4885–4894. doi: 10.1177/09544062211056890
10. Guo, Y., & Yao, X. (2021). Buckling Behavior and Effective Width Design Method for Thin Plates with Holes under Stress Gradient. doi: 10.1155/2021/5550749
11. Karakaya, C. (2022). Numerical investigation on perforated sheet metals under tension loading. Open Chemistry, 20(1), 244–253. doi: 10.1515/chem-2022-0142
12. Kim, J. H., Park, D. H., Kim, S. K., Kim, J. D., & Lee, J. M. (2021). Lateral deflection behavior of perforated steel plates: Experimental and numerical approaches. Journal of Marine Science and Engineering, 9(5). doi: 10.3390/jmse9050498
13. Komur, M. A. (2011). Elasto-plastic buckling analysis for perforated steel plates subject to uniform compression. Mechanics Research Communications, 38(2), 117–122. doi: 10.1016/J.MECHRESCOM.2011.01.001
14. Komur, M. A., & Sonmez, M. (2008). Elastic buckling of perforated plates subjected to linearly varying in-plane loading. Structural Engineering and Mechanics, 28(3), 353–356. doi: 10.12989/SEM.2008.28.3.353
15. Maiorana, E., Pellegrino, C., & Modena, C. (2008). Linear buckling analysis of perforated plates subjected to localised symmetrical load. Engineering Structures, 30(11), 3151–3158. doi: 10.1016/J.ENGSTRUCT.2008.04.024
16. Maiorana, E., Pellegrino, C., & Modena, C. (2009). Non-linear analysis of perforated steel plates subjected to localised symmetrical load. Journal of Constructional Steel Research, 65(4), 959–964. doi: 10.1016/J.JCSR.2008.03.018
17. Narayanan, R., & der Avanessian, N. G. V. (1984). Elastic buckling of perforated plates under shear. Thin-Walled Structures, 2(1), 51–73. doi: 10.1016/0263-8231(84)90015-6
18. Rezaeepazhand, J., & Sabori, H. (2008). Buckling of perforated plates repaired with composite patches. Key Engineering Materials, 385–387, 377–380. Trans Tech Publications Ltd. doi: 10.4028/www.scientific.net/kem.385-387.377
19. Saraçoğlu, M. H., & Albayrak, U. (2016). Linear static analysis of perforated plates with round and staggered holes under their self-weights. Research on Engineering Structures & Materials, 2(1), 39–47. doi: 10.17515/resm2015.25me0910
20. Saraçoğlu, M. H., Uslu, F., & Albayrak, U. (2020). Stress and displacement analysis of perforated circular plates. Challenge Journal of Structural Mechanics, 6(3), 150. doi: 10.20528/cjsmec.2020.03.006
21. Saraçoğlu, M., Uslu, H., & Albayrak, F. (2021). Investigation of Hole Shape Effect on Static Analysis of Perforated Plates with Staggered Holes. International Journal of Engineering and Innovative Research, 3(2), 133–144. doi: 10.47933/ijeir.883510
22. Seifi, R., Chahardoli, S., & Akhavan Attar, A. (2017). Axial buckling of perforated plates reinforced with strips and middle tubes. Mechanics Research Communications, 85, 21–32. doi: 10.1016/J.MECHRESCOM.2017.07.015
23. Shakerley, T. M., & Brown, C. J. (1996). Elastic buckling of plates with eccentrically positioned rectangular perforations. International Journal of Mechanical Sciences, 38(8–9), 825–838. doi: 10.1016/0020-7403(95)00107-7
24. Shanmugam, N. E., Thevendran, V., & Tan, Y. H. (1999). Design formula for axially compressed perforated plates. Thin-Walled Structures, 34(1), 1–20. doi: 10.1016/S0263-8231(98)00052-4
25. Silveira, T., Neufeld, J. P. S., Rocha, L. A. O., Santos, E. D., & Isoldi, L. A. (2021). Numerical analysis of biaxial elasto-plastic buckling of perforated rectangular steel plates applying the Constructal Design method. IOP Conf. Ser.: Mater. Sci. Eng. doi: 10.1088/1757-899X/1048/1/012017
26. Soares Junior, R.A., Palermo Junior, L., & Wrobel, L.C. (2019). Buckling of perforated plates using the dual reciprocity boundary element method. In Boundary Elements and other Mesh Reduction Methods XLII (Vol. 126, pp. 89–100). WIT Press. doi: doi:10.2495/BE420081
27. Soleimanian, S., Davar, A., Jam, J. E., Zamani, M. R., & Beni, M. H. (2020). Thermal buckling and thermal induced free vibration analysis of perforated composite plates: a mathematical model. Mechanics of Advanced Composite Structures, 7, 15–23. doi: 10.22075/macs.2019.16556.1181
28. Swanson Analysis System Inc., A. (2005). ANSYS User’s manual.
29. Timoshenko, S. , Woinowsky-Krieger, S. (1959). Theory of Plates and Shells. In McGraw-Hill, Inc. McGraw-Hill, Inc.
30. Yanli, G., Xiaoqing, S., Xiao, L., Xingyou, Y., Zhifan, X., Bin, X., Jianyi, S. (2019). Elastic buckling of thin plate with circular holes in bending. E3S Web of Conferences, 136, 3–8. doi: 10.1051/e3sconf/201913604043