Influence of Discretely Introduced Cutouts on the Buckling of Shallow Shells with Double Curvature

Document Type : Research Paper


Department of Computer Science, Saint Petersburg State University of Architecture and Civil Engineering, 4, 2nd Krasnoarmeyskaya st., Saint-Petersburg, 190005, Russia


The paper analyzes the influence of cutouts on the buckling of shallow shells with double curvature. Based on the Timoshenko-Reissner hypothesis, a mathematical model is presented that considers transverse shifts, material orthotropy, geometric nonlinearity and structural weakening by cutouts. Cutouts are specified discretely by single columnar functions. The computational algorithm is based on the Ritz method and the Newton method. The implementation of the algorithm is carried out in the Maple 2022 software package. To study the buckling, the Lyapunov criterion is adopted. Calculations of the buckling of flat shells of double curvature with square cuts, graphs of the dependence of deflections on loads and deflection fields are given. Accounting for the structural cutouts leads to a decrease in the critical load. At the same time, for the considered problems, it is found that the decrease in the critical load does not exceed 25 % for the cutout volume not exceeding 10 % of the shell volume.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Treshchev, A., Kuznetsova, V., Study of the Influence of the Kinetics of Hydrogen Saturation on the Stress-Deformed State of a Spherical Shell Made from Titanium Alloy, International Journal for Computational Civil and Structural Engineering, 18(2), 2022, 121–130. DOI: 10.22337/2587-9618-2022-18-2-121-130.
[2] Razov, I., Sokolov, V., Dmitriev, A., Ogorodnova, J., Parametric vibrations of the underground oil pipeline, E3S Web of Conference; ed. Malygina I., 363, 2022, 01038. DOI: 10.1051/e3sconf/202236301038.
[3] Kayumov, R.A., Shakirzyanov, F.R., Large Deflections and Stability of Low-Angle Arches and Panels During Creep Flow, Multiscale Solid Mechanics; ed. Altenbach H., Eremeyev V.A., Igumnov L.A., Cham: Springer International Publishing, 141, 2021, 237–248. DOI: 10.1007/978-3-030-54928-2_18.
[4] Kamenev, I.V., Semenov, A.A., Rationale of the use of the constructive anisotropy method in the calculation of shallow shells of double curvature, weakened holes, PNRPU Mechanics Bulletin, 2, 2016, 54–68. DOI: 10.15593/perm.mech/2016.2.05. (in Russian)
[5] Karpov, V.V., Models of the shells having ribs, reinforcement plates and cutouts, International Journal of Solids and Structures, 146, 2018, 117–135. DOI: 10.1016/j.ijsolstr.2018.03.024.
[6] Solovei, N.A., Krivenko, O.P., Malygina, O.A., Finite element models for the analysis of nonlinear deformation of shells stepwise-variable thickness with holes, channels and cavities, Magazine of Civil Engineering, 1(53), 2015, 56–69. DOI: 10.5862/MCE.53.6. (in Russian)
[7] Zakharova, Yu.V., Lokhmatova, L.G., Simulation of stress-strain state of defected composite shells, Engineering Journal: Science and Innovation, 11(59), 2016. DOI: 10.18698/2308-6033-2016-11-1552. (in Russian)
[8] Zhao, C., Niu, J., Zhang, Q., Zhao, C., Xie, J., Buckling behavior of a thin-walled cylinder shell with the cutout imperfections, Mechanics of Advanced Materials and Structures, 26(18), 2019, 1536–1542. DOI: 10.1080/15376494.2018.1444225.
[9] Dmitriev, V.G., Egorova, O.V., Zhavoronok, S.I., Rabinskii, L.N., Investigation of Buckling Behavior for Thin-Walled Bearing Aircraft Structural Elements with Cutouts by Means of Numerical Simulation, Russian Aeronautics, 61(2), 2018, 165–174. DOI: 10.3103/S1068799818020034.
[10] Yılmaz, H., Kocabaş, İ., Özyurt, E., Empirical equations to estimate non-linear collapse of medium-length cylindrical shells with circular cutouts, Thin-Walled Structures, 119, 2017, 868–878. DOI: 10.1016/j.tws.2017.08.008.
[11] Xia, Y., Wang, H., Zheng, G., Shen, G., Hu, P., Discontinuous Galerkin isogeometric analysis with peridynamic model for crack simulation of shell structure, Computer Methods in Applied Mechanics and Engineering, 398, 2022, 115193. DOI: 10.1016/j.cma.2022.115193.
[12] Ambati, M., Heinzmann, J., Seiler, M., Kästner, M., Phase‐field modeling of brittle fracture along the thickness direction of plates and shells, International Journal for Numerical Methods in Engineering, 123(17), 2022, 4094–4118. DOI: 10.1002/nme.7001.
[13] Wang, Y., Hu, J., Kennedy, D., Wang, J., Wu, J., Adaptive mesh refinement for finite element analysis of the free vibration disturbance of cylindrical shells due to circumferential micro-crack damage, Engineering Computations, 39(9), 2022, 3271–3295. DOI: 10.1108/EC-09-2021-0555.
[14] Giani, S., Hakula, H., Free vibration of perforated cylindrical shells of revolution: Asymptotics and effective material parameters, Computer Methods in Applied Mechanics and Engineering, 403, 2023, 115700. DOI: 10.1016/j.cma.2022.115700.
[15] Arbelo, M.A., Herrmann, A., Castro, S.G.P., Khakimova, R., Zimmermann, R., Degenhardt, R., Investigation of Buckling Behavior of Composite Shell Structures with Cutouts, Applied Composite Materials, 22(6), 2015, 623–636. DOI: 10.1007/s10443-014-9428-x.
[16] Gangadhar, L., Kumar, T.S., Finite Element Buckling Analysis of Composite Cylindrical Shell with Cutouts Subjected to Axial Compression, International Journal of Advanced Science and Technology, 89, 2016, 45–52. DOI: 10.14257/ijast.2016.89.06.
[17] Shen, K.-C., Yang, Z.-Q., Jiang, L.-L., Pan, G., Buckling and Post-Buckling Behavior of Perfect/Perforated Composite Cylindrical Shells under Hydrostatic Pressure, Journal of Marine Science and Engineering, 10(2), 2022, 278. DOI: 10.3390/jmse10020278.
[18] Ghanbari Ghazijahani, T., Jiao, H., Holloway, D., Structural behavior of shells with different cutouts under compression: An experimental study, Journal of Constructional Steel Research, 105, 2015, 129–137. DOI: 10.1016/j.jcsr.2014.10.020.
[19] Krishna, G.V., Narayanamurthy, V., Viswanath, C., Buckling behaviour of FRP strengthened cylindrical metallic shells with cut-outs, Composite Structures, 300, 2022, 116176. DOI: 10.1016/j.compstruct.2022.116176.
[20] Sohan, R., Likith, S., Sai, J., Vadlamani, S., Linear, nonlinear and post buckling analysis of a stiffened panel with cutouts, IOP Conference Series: Materials Science and Engineering, 1248(1), 2022, 012078. DOI: 10.1088/1757-899X/1248/1/012078.
[21] da Silveira, T., Pinto, V., Neufeld, J.P., Pavlovic, A., Rocha, L., dos Santos, E., Isoldi, L.A., Applicability Evidence of Constructal Design in Structural ‎Engineering: Case Study of Biaxial Elasto-Plastic Buckling of ‎Square Steel Plates with Elliptical Cutout, Journal of Applied and Computational Mechanics, 7(2), 2021, 922–934. DOI: 10.22055/jacm.2021.35385.2647.
[22] Keshav, V., Patel, S.N., Kumar, R., Watts, G., Effect of Cutout on the Stability and Failure of Laminated Composite Cylindrical Panels Subjected to In-Plane Pulse Loads, International Journal of Structural Stability and Dynamics, 22(08), 2022, 2250087. DOI: 10.1142/S0219455422500870.
[23] Dewangan, H.C., Panda, S.K., Hirwani, C.K., Numerical deflection and stress prediction of cutout borne damaged composite flat/curved panel structure, Structures, 31, 2021, 660–670. DOI: 10.1016/j.istruc.2021.02.016.
[24] Dewangan, H.C., Sharma, N., Panda, S.K., Thermomechanical loading and cut-out effect on static and dynamic responses of multilayered structure with TD properties, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(16), 2022, 9081–9094. DOI: 10.1177/09544062221089153.
[25] Li, Q., Wang, D.F., Influence of cutout position on buckling of large-scale thin-walled cylindrical shell of desulphurizing tower with welding induced imperfection under wind loading, Applied Mechanics and Materials, 687–691, 2014, 68–72. DOI: 10.4028/
[26] Labans, E., Bisagni, C., Celebi, M., Tatting, B., Gürdal, Z., Blom-Schieber, A., Rassaian, M., Wanthal, S., Bending of Composite Cylindrical Shells with Circular Cutouts: Experimental Validation, Journal of Aircraft, 56(4), 2019, 1534–1550. DOI: 10.2514/1.C035247.
[27] Gokyer, Y., Sonmez, F.O., Topology optimization of cylindrical shells with cutouts for maximum buckling strength, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45(1), 2023, 13. DOI: 10.1007/s40430-022-03941-w.
[28] Groh, R.M.J., Wu, K.C., Nonlinear Buckling and Postbuckling Analysis of Tow-Steered Composite Cylinders with Cutouts, AIAA Journal, 60(9), 2022, 5533–5546. DOI: 10.2514/1.J061755.
[29]      Shahani, A.R., Kiarasi, F., Numerical and Experimental Investigation on Post-buckling ‎Behavior of Stiffened Cylindrical Shells with Cutout subject to ‎Uniform Axial Compression, Journal of Applied and Computational Mechanics, 9(1), 2023, 25–44. DOI: 10.22055/jacm.2021.33649.2261.
[30] Li, Z., Cao, Y., Pan, G., Influence of geometric imperfections on the axially loaded composite conical shells with and without cutout, AIP Advances, 10(9), 2020, 095106. DOI: 10.1063/5.0021103.
[31] Kamaloo, A., Jabbari, M., Tooski, M.Y., Javadi, M., Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells, International Journal of Structural Stability and Dynamics, 20(01), 2020, 2050010. DOI: 10.1142/S0219455420500108.
[32] Kumar Chaubey, A., Kumar, A., Chakrabarti, A., Effect of multiple cutouts on shear buckling of laminated composite spherical shells, Materials Today: Proceedings, 21, 2020, 1155–1163. DOI: 10.1016/j.matpr.2020.01.065.
[33] Juhász, Z., Szekrényes, A., An analytical solution for buckling and vibration of delaminated composite spherical shells, Thin-Walled Structures, 148, 2020, 106563. DOI: 10.1016/j.tws.2019.106563.
[34] Semenov, A.A., Moskalenko, L.P., Karpov, V.V., Sukhoterin, M.V., Buckling of cylindrical panels strengthened with an orthogonal grid of stiffeners, Bulletin of Civil Engineers, 6(83), 2020, 117–125. DOI: 10.23968/1999-5571-2020-17-6-117-125. (in Russian)
[35] Karpov, V.V., Semenov, A.A., Refined model of stiffened shells, International Journal of Solids and Structures, 199, 2020, 43–56. DOI: 10.1016/j.ijsolstr.2020.03.019.