Article Sidebar
Main Article Content
In this study, the Hu–Washizu variational principle was employed to derive a three-dimensional system of partial differential equations, which governs the stability of an anisotropic body. This system was expressed in the cylindrical coordinate system. The analytical Bubnov–Galerkin method was employed to reduce it to a one-dimensional one. The solution of the one-dimensional problem in the direction of the normal to the median surface of the shell structure was carried out using the numerical method of discrete orthogonalisation. The present study investigates the values of critical loads of external lateral pressure for an anisotropic cylindrical shell made of a fibrous composite and the same shell with a layer of a functionally graded material. The study investigates the dependence of the critical loads on the angle of rotation of the main elastic directions of the unidirectional fibrous material and the number of its layers. The findings of this study demonstrate that incorporating a functionally graded material layer has the potential to enhance the critical loads of the structure.
Article Details
Abovsky, N. P., Andreev, N. P. & Deruga, A. P. (1978). Variatsionnyye printsipy teorii uprugosti i teorii obolochek. Moskva: Nauka.
Ambartsumyan, S. A. (1974). Obshchaya teoriya anizotropnykh obolochek. Moskva: Nauka.
Bazhenov, V. A., Kryvenko, O. P. & Solovey, M. O. (2010). Neliniyne deformuvannya ta stiykist pruzhnykh obolonok neodnoridnoyi struktury. Kyiv: Vipol.
Bazhenov, V. A., Semenyuk, M. P. & Trach, V. M. (2010). Neliniyne deformuvannya, stiykist i zakrytychna povedinka anizotropnykh obolonok. Kyiv: Karavela.
Grigorenko, Ya. M. & Kryukov, N. N. (1988). Chislennoye resheniye zadach statiki gibkikh sloistykh obolochek s peremennymi parametrami. Kyiv: Naukova Duma.
Guz, A. N. (1986). Osnovy trekhmernoy teorii ustoychivosti deformiruyemykh tel. Kyiv: Vishcha shkola.
Guz, A. N. & Babich, I. Yu. (1980). Trekhmernaya teoriya ustoychivosti sterzhney, plastin i obolochek. Kyiv: Vishcha shkola.
Guz, A. N. & Babich, I. Yu. (1985). Prostranstvennyye zadachi teorii uprugosti i plastichnosti. Vol. 4: Trekhmernaya teoriya ustoychivosti deformiruyemykh tel. Kyiv: Naukova Duma.
Kołakowski, Z. & Mania, R. (2012). Semi-analytical method versus the FEM for analysis of the local post-buckling of thin-walled composite structures. Composite Structures, 97, 99–106. https://doi.org/10.1016/j.compstruct.2012.10.035 (Crossref)
Kowal-Michalska, K. & Mania, R. (2013). Static and Dynamic Thermomechanical Buckling Loads of Functionally Graded Plates. Mechanics and Mechanical Engineering, 17 (1), 99–112.
Kryvenko, O. P., Lizunov, P. P., Vorona, Y. V. & Kalashnikov, O. B. (2024). Modeling of Nonlinear Deformation, Buckling, and Vibration Processes of Elastic Shells in Inhomogeneous Structure. International Applied Mechanics, 60 (4), 464–478. https://doi.org/10.1007/s10778-024-01298-2 (Crossref)
Lanczos, C. (1986). The Variational Principles of Mechanics (Dover Books on Physics). Dover Publications.
Lee, Y., Zhao, X. & Reddy, J. N. (2010). Postbuckling analysis of functionally graded plates subject to compressive and thermal loads. Computer Methods in Applied Mechanics and Engineering, 199 (25–28), 1645‒1653. https://doi.org/10.1016/j.cma.2010.01.008 (Crossref)
Lekhnitskii, S. G. (1981). Theory of Elasticity of an Anisotropic Body. Dagenham: Central Books.
Lubin, G. (2013). Handbook of Composites. Springer Science & Business Media.
Novozhilov, V. V. (1961). Theory of elasticity [translated to English by J. L. Lusher]. Elsevier.
Podvornyi, A. V., Semenyuk, N. P. & Trach, V. M. (2017). Stability of Inhomogeneous Cylindrical Shell under Distributed External Pressure in the Spatial Statement. International Applied Mechanics, 53 (6), 623–638. https://doi.org/10.1007/s10778-018-0845-7 (Crossref)
Reddy, J. N. (2000). Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 47 (1), 663–684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/33.0.CO;2-8 (Crossref)
Semenyuk, N. P., Trach, V. M. & Podvornyi, A. V. (2019). Spatial Stability of Layered Anisotropic Cylindrical Shells Under Compressive Loads. International Applied Mechanics, 55 (2), 211–221. https://doi.org/10.1007/s10778-019-00951-5 (Crossref)
Semenyuk, N. P., Trach, V. M. & Podvornyi, A. V. (2023). Stress–strain state of a thick-walled anisotropic cylindrical shell. International Applied Mechanics, 59 (1), 79–89. https://doi.org/10.1007/s10778-023-01201-5 (Crossref)
Shen, H-S. (2009). Functionally graded materials: nonlinear analysis of plates and shells. Boca Raton–London–New York: CRC Press Taylor & Francis Group.
Tonti, E. (1967). Variational principles in elastostatics. Meccanica, 2, 201–208. https://doi.org/10.1007/BF02153074 (Crossref)
Trach, V. M., Podvorny, A. V. & Zhukova, N. B. (2023). Stiykist netonkykh anizotropnykh tsylindrychnykh obolonok v prostoroviy postanovtsi pid rozpodilenym boko [Stability of non-thin anisotropic cylindrical shells in a spatial setting under distributed lateral pressure]. Bulletin of the Taras Shevchenko National University of Kyiv, Series Physical and Mathematical Sciences, 2, 152–155. https://doi.org/10.17721/1812-5409.2023/2 (Crossref)
Trach, V. M., Podvorny, A. V. & Khoruzhiy, M. M. (2019). Deformuvannya ta stiykist netonkykh anizotropnykh obolonok. Kyiv: Karavela.
Trach, V., Semenuk, M. & Podvornyi, A. (2016). Stability of anisotropic cylindrical shells in three-dimensional state under axial compression. Acta Scientiarum Polonorum. Architectura, 15 (4), 169–183.
Washizu, K. (1982). Variational Methods in Elasticity and Plasticity. Pergamon Press.
Yamaki, N. (1968/1969). Buckling of Circular Cylindrical Shells under External Pressure. Reports of the Institute of High Speed Mechanics, Thoku University, 20, 35–55.
Zienkiewicz, O. C. (1972). Metoda elementów skończonych. Warszawa: Arkady.
Downloads
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.