Journal of Applied and Computational Mechanics
Strength of Steel Shell Cylindrical Panels Reinforced with an Orthogonal Grid of Stiffeners
Document Type : Research Paper
Author
Department of Computer Science, Saint Petersburg State University of Architecture and Civil Engineering, 4, 2nd Krasnoarmeyskaya st., Saint-Petersburg, 190005, Russia
Abstract
The paper presents an approach to the strength analysis in steel cylindrical panels reinforced from the concave side with an orthogonal grid of stiffeners. A mathematical model of the Timoshenko (Mindlin – Reissner) type is used. Transverse shears and geometric nonlinearity are taken into account. The stiffeners are introduced in two ways: using the method of refined discrete introduction (proposed by author) and the method of structural anisotropy. Computational algorithm based on the Ritz method and the best parameter continuation method. For strength analysis von Mises criterion is used. The values of the maximum permissible strength loss loads are shown for several variants of structures made of steel S345. The extension of areas of non-fulfillment of strength conditions according to the Mises criterion for the stiffened and unstiffened structures are shown.
Keywords
Main Subjects
Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
[1] Bischoff, M., Bletzinger, K.-U., Wall, W.A., Ramm, E., Models and Finite Elements for Thin-Walled Structures, In: Encyclopedia of Computational Mechanics, ed. Stein E., de Borst R., Hughes T.J.R. Chichester, UK: John Wiley & Sons, Ltd, 2004, 59–137. DOI: 10.1002/0470091355.ecm026.
[2] Godoy, L.A., Thin-Walled Structures with Structural Imperfections, Elsevier, 1996. DOI: 10.1016/B978-0-08-042266-4.X5000-3.
[3] Mamalis, A.G., Manolakos, D.E., Demosthenous, G.A., Ioannidis M.B., Crashworthiness of composite thin-walled structural components, Boca Raton; London; New York: CRC Press, Taylor & Francis Group, 2019.
[4] Fragassa, C., Minak, G., Pavlovic, A., Measuring deformations in the telescopic boom under static and dynamic load conditions, Facta Universitatis-Series Mechanical Engineering, 18(2), 2020, 315–328. DOI: 10.22190/FUME181201001F.
[5] Jaunky, N., Knight, N.F., Ambur, D.R., Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels, Composites Part B: Engineering, 27(5), 1996, 519–526. DOI: 10.1016/1359-8368(96)00032-7.
[6] Kidane, S., Li, G., Helms, J., Pang, S.-S., Woldesenbet, E., Buckling load analysis of grid stiffened composite cylinders, Composites Part B: Engineering, 34(1), 2003, 1–9. DOI: 10.1016/S1359-8368(02)00074-4.
[7] Wang, J.T.-S., Hsu, T.-M., Discrete analysis of stiffened composite cylindrical shells, AIAA Journal, 23(11), 1985, 1753–1761. DOI: 10.2514/3.9162.
[8] Meish, V.F., Meish, Yu.A., Pavlyuk, A.V., Dynamics of a Three-Layer Elliptic Cylindrical Shell Reinforced with Discrete Rings, International Applied Mechanics, 54(2), 2018, 172–179. DOI: 10.1007/s10778-018-0869-z.
[9] Qu, Y., Wu, S., Chen, Y., Hua, H., Vibration analysis of ring-stiffened conical-cylindrical-spherical shells based on a modified variational approach, International Journal of Mechanical Sciences, 69, 2013, 72–84. DOI: 10.1016/j.ijmecsci.2013.01.026.
[10] Sadeghifar, M., Bagheri, M., Jafari, A.A., Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity, Archive of Applied Mechanics, 81(7), 2011, 875–886. DOI: 10.1007/s00419-010-0457-0.
[11] Talebitooti, M., Ghayour, M., Ziaei-Rad, S., Talebitooti, R., Free vibrations of rotating composite conical shells with stringer and ring stiffeners, Archive of Applied Mechanics, 80(3), 2010, 201–215. DOI: 10.1007/s00419-009-0311-4.
[12] Troitsky, M.S., Stiffened plates: bending, stability, and vibrations, Elsevier Scientific Pub. Co., Amsterdam; New York, 1976.
[13] Reddy, A.D., Valisetty, R., Rehfield, L.W., Continuous filament wound composite concepts for aircraft fuselage structures, Journal of Aircraft, 22(3), 1985, 249–255. DOI: 10.2514/3.45115.
[14] Dung, D.V., Chan, D.Q., Analytical investigation on mechanical buckling of FGM truncated conical shells reinforced by orthogonal stiffeners based on FSDT, Composite Structures, 159, 2017, 827–841. DOI: 10.1016/j.compstruct.2016.10.006.
[15] Tu, T.M., Loi, N.V., Vibration Analysis of Rotating Functionally Graded Cylindrical Shells with Orthogonal Stiffeners, Latin American Journal of Solids and Structures, 13(15), 2016, 2952–2969. DOI: 10.1590/1679-78252934.
[16] Lanzo, A.D., Garcea, G., Koiter’s analysis of thin-walled structures by a finite element approach, International Journal for Numerical Methods in Engineering, 39(17), 1996, 3007–3031. DOI: 10.1002/(SICI)1097-0207(19960915)39:17<3007::AID-NME991>3.0.CO;2-S.
[17] Pinto, V.T., Oliveira Rocha, L.A., Fragassa, C., Domingues dos Santos, E., Isoldi, L.A., Multiobjective Geometric Analysis of Stiffened Plates under Bending through Constructal Design Method, Journal of Applied and Computational Mechanics, 6(SI), 2020, 1438–1449. DOI: 10.22055/jacm.2020.35248.2608.
[18] Bai, X., Xu, W., Ren, H., Li, J., Analysis of the influence of stiffness reduction on the load carrying capacity of ring-stiffened cylindrical shell, Ocean Engineering, 135, 2017, 52–62. DOI: 10.1016/j.oceaneng.2017.02.034.
[19] Chen, B., Liu, G., Kang, J., Li, Y., Design optimization of stiffened storage tank for spacecraft, Structural and Multidisciplinary Optimization, 36(1), 2008, 83–92. DOI: 10.1007/s00158-007-0174-7.
[20] Lene, F., Duvaut, G., Olivier-Mailhe, M., Ben Chaabane, S., Grihon, S., An advanced methodology for optimum design of a composite stiffened cylinder, Composite Structures, 91(4), 2009, 392–397. DOI: 10.1016/j.compstruct.2009.04.005.
[21] Reza Ghasemi, A., Tabatabaeian, A., Hadi Hajmohammad, M., Tornabene, F., Multi-Step Buckling Optimization Analysis of Stiffened and Unstiffened Polymer Matrix Composite Shells: A New Experimentally Validated Method, Composite Structures, 273, 2021, 114280. DOI: 10.1016/j.compstruct.2021.114280.
[22] Hao, P., Wang, B., Tian, K., Liu, H., Wang, Y., Niu, F., Zeng, D., Simultaneous buckling design of stiffened shells with multiple cutouts, Engineering Optimization, 49(7), 2017, 1116–1132. DOI: 10.1080/0305215X.2016.1235328.
[23] Wang, J., Li, Z.L., Yu, W., Structural similitude for the geometric nonlinear buckling of stiffened orthotropic shallow spherical shells by energy approach, Thin-Walled Structures, 138, 2019, 430–457. DOI: 10.1016/j.tws.2018.02.006.
[24] Cho, S.-R., Muttaqie, T., Do, Q.T., Park, S.H., Kim, S.M., So, H.Y., Sohn, J.M., Experimental study on ultimate strength of steel-welded ring-stiffened conical shell under external hydrostatic pressure, Marine Structures, 67, 2019, 102634. DOI: 10.1016/j.marstruc.2019.102634.
[25] Duarte, A.P.C., Díaz Sáez, A., Silvestre, N., Comparative study between XFEM and Hashin damage criterion applied to failure of composites, Thin-Walled Structures, 115, 2017, 277–288. DOI: 10.1016/j.tws.2017.02.020.
[26] Brauns, J., Skadins, U., Semi-analytical postbuckling strength analysis of anisotropic shell structures, IOP Conference Series: Materials Science and Engineering, 251, 2017, 012096. DOI: 10.1088/1757-899X/251/1/012096.
[27] Abrosimov, N.A., Novoseltseva, N.A., Computer Modeling of the Dynamic Strength of Metal-Plastic Cylindrical Shells Under Explosive Loading, Mechanics of Composite Materials, 53, 2017, 139–148. DOI: 10.1007/s11029-017-9648-x.
[28] Semenov, A.A., Analysis of the strength of shell structures, made from modern materials, according to various strength criteria, Diagnostics, Resource and Mechanics of Materials and Structures, 2018, 16–33. DOI: 10.17804/2410-9908.2018.1.016-033.
[29] Pavlovic, A., Sintoni, D., Fragassa, C., Minak, G., Multi-Objective Design Optimization of the Reinforced Composite Roof in a Solar Vehicle, Applied Sciences, 10(8), 2020, 2665. DOI: 10.3390/app10082665.
[30] 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.
[31] Li, G., de Miguel, A.G., Pagani, A., Zappino, E., Carrera, E., Finite beam elements based on Legendre polynomial expansions and node-dependent kinematics for the global-local analysis of composite structures, European Journal of Mechanics – A/Solids, 74, 2019, 112–123. DOI: 10.1016/j.euromechsol.2018.11.006.
[32] Yshii, L.N., Santana, R.C., Monteiro, F.A.C., Lucena Neto, E., Buckling of Cylindrical Panels by a Ritz Scheme, Proceedings of the XXXVIII Iberian Latin-American Congress on Computational Methods in Engineering, Brazil, 2017. DOI: 10.20906/CPS/CILAMCE2017-0613.
[33] Feng, K., Xu, J., Buckling Analysis of Composite Cylindrical Shell Panels by Using Legendre Polynomials Hierarchical Finite-Strip Method, Journal of Engineering Mechanics, 143(4), 2017, 04016121. DOI: 10.1061/(ASCE)EM.1943-7889.0001181.
[34] Qu, Y., Long, X., Wu, S., Meng, G., A unified formulation for vibration analysis of composite laminated shells of revolution including shear deformation and rotary inertia, Composite Structures, 98, 2013, 169–191. DOI: 10.1016/j.compstruct.2012.11.001.
[35] Monge, J.C., Mantari, J.L., A quasi-exact solution for the analysis of smart multilayered simply supported shallow shell panels, Composite Structures, 265, 2021, 113710. DOI: 10.1016/j.compstruct.2021.113710.
[36] Qu, Y., Chen, Y., Long, X., Hua, H., Meng, G., A modified variational approach for vibration analysis of ring-stiffened conical-cylindrical shell combinations, European Journal of Mechanics – A/Solids, 37, 2013, 200–215. DOI: 10.1016/j.euromechsol.2012.06.006.
[37] Kurylov, Ye., Amabili, M., Nonlinear vibrations of clamped-free circular cylindrical shells, Journal of Sound and Vibration, 330(22), 2011, 5363–5381. DOI: 10.1016/j.jsv.2011.05.037.
[38] Bakusov, P.A., Semenov, A.A., Stability of Toroidal Shell Segments at Variation of a Deflection Angle, PNRPU Mechanics Bulletin, 3, 2017, 17–36. DOI: 10.15593/perm.mech/2017.3.02. (in Russian)
[39] Semenov, A., Buckling of Shell Panels Made of Fiberglass and Reinforced with an Orthogonal Grid of Stiffeners, Journal of Applied and Computational Mechanics, 7(3), 2021, 1856–1861. DOI: 10.22055/jacm.2021.37768.3078.
)
