Abstract
Governing equations based on the generalized kinematic hypotheses of Timoshenko and including the effect of transverse shears are used to predict the buckling of a medium-length thin laminated cylindrical shell under action of the external normal pressure. It is assumed that some of layers are made of a “soft” material so that the effective shear modulus turns out to be too less than the effective Young’s modulus for the laminate. Of all possible variants of boundary conditions, the boundary conditions corresponding to the simple support of edges with and without diaphragms in their planes are considered. For the case of the simply supported edges with diaphragms, the critical buckling pressure as well as the modes of buckling are found in an explicit form. If one of the edges is free from the diaphragm, the boundary-value problem is solved by using the asymptotic approach, a solution being constructed in the form of the superposition of functions describing the main stress state and the edge effect integrals. It is shown that the absence of the edge diaphragm accounts for the appearance of the edge transverse shears (non-classical edge effect integrals) whose decay rate is lower than that of the classical simple edge effect integrals. The effect of edge shears and diaphragms as well on both the critical buckling pressure and eigenform is studied for a laminated cylindrical shell with any number of layers regardless of materials used for laminae. As an example, the buckling of a cylindrical sandwich assembled from the ABS-plastic and magnetorheological elastomer under different levels of an applied magnetic field is examined.
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Librescu, L., Hause, T.: Recent developments in the modeling and behavior of advanced sandwich constructions: a survey. Compos. Struct. 48, 1–17 (2000)
Kardomateas, G.A.: Elasticity solutions for a sandwich orthotropic cylindrical shell under external pressure, internal pressure and axial force. AIAA J. 39, 713–7199 (2001)
Han, J.-H., Kardomateas, G.A., Simitses, G.J.: Elasticity, shell theory and finite element results for the buckling of long sandwich cylindrical shells under external pressure. Compos. Part B 35, 591–598 (2004)
Xie, Y.J., Yan, H.G., Liu, Z.M.: Buckling optimization of hybrid-fiber multilayer-sandwich cylindrical shells under external lateral pressure. Compos. Sci. Technol. 56, 1349–1353 (1996)
Mikhasev, G.I., Botogova, M.G., Korobko, E.V.: Theory of thin adaptive laminated shells based on magnetorheological materials and its application in problems on vibration suppression. In: Altenbach, H., Eremeyev, V.A. (eds.) Shell-like Structures. Advanced Structured Materials, vol. 15, pp. 727–750. Springer, Berlin (2011)
Kozlowska, J., Boczkowska, A., Czulak, A., Przybyszewski, B., Holeczek, K., Stanik, R., Gude, M.: Novel MRE/CFRP sandwich structures for adaptive vibration control. Smart Mater. Struct. 25, 035025 (2016)
Yeh, J.-Y.: Vibration and damping analysis of orthotropic cylindrical shells with electrorheological core layer. Aerosp. Sci. Technol. 15, 293–303 (2011)
Tanguy, M., Pyrzb, M., Ginestec, B., Chauchotd, P.: Optimal laminations of thin underwater composite cylindrical vessels. Compos. Struct. 58, 529–537 (2002)
Ohga, M., Wijenayaka, A.S., Croll, J.G.A.: Reduced stiffness buckling of sandwich cylindrical shells under uniform external pressure. Thin. Wall. Struct. 43, 1188–1201 (2005)
Malinowski, M., Belica, T., Magnucki, K.: Buckling and post-buckling behaviour of elastic seven-layered cylindrical shells—FEM study. Thin. Wall. Struct. 94, 478–484 (2015)
Kulikov, G.M., Plotnikova, S.V.: Advanced formulation for laminated composite shells: 3D stress analysis and rigid-body motions. Compos. Struct. 95, 236–246 (2013)
Bolotin, V.V., Novichkov, Yu. N: Mechanics of Multilayer Structures. Mashinostroenie, Moscow (1980). [in Russian]
Reddy, J.N.: An evaluation of equivalent-single-layer and layerwise theories of composite laminates. Compos. Struct. 25, 21–35 (1993)
Reddy, J.N., Robbins, D.H.: Theories and computational models for composite laminates. Appl. Mech. Rev. 47, 147–165 (1994)
Altenbach, H.: Theories for laminated and sandwich plates. A review. Mech. Compos. Mater. 34, 243–252 (1998)
Carrera, E.: Multilayered shell theories accounting for layerwise mixed description. Part 1: governing equations. AIAA J. 37, 1107–1116 (1999)
Carrera, E.: Developments, ideas, and evaluations based upon Reissners mixed variational theorem in the modeling of multilayered plates and shells. Appl. Mech. Rev. 54, 301–329 (2001)
Carrera, E.: Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch. Comput. Methods. Eng. 9, 87–140 (2002)
Fiedler, L., Lacarbonara, W., Vestroni, F.: A generalized higher-order theory for multi-layered, shear-deformable composite plates. Acta Mech. 209, 85–98 (2010)
Reddy, J.N., Arciniega, R.A.: Shear deformation plate and shell theories: from Stavsky to present. Mech. Adv. Mater. Struct. 11, 535–582 (2004)
Mantari, J.L., Oktem, A.S., Soares, C.G.: A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. Int. J. Solids Struct. 49, 43–53 (2012)
Thai, C.N., Ferreira, A.J.M., Wahab, M.A., Nguyen-Xuan, H.: A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis. Acta Mech. 227, 1225–1250 (2016)
Reissner, E., Wan, F.Y.M.: On the equations of linear shallow shell theory. Stud. Appl. Math. 48, 133–145 (1969)
Whitney, J.M.: The effect of boundary conditions on the response of laminated composites. J. Compos. Mater. 4, 192–203 (1970)
Dong, S.B., Tso, F.K.W.: On a laminated orthotropic shell theory including transverse shear deformation. J. Appl. Mech. 39, 1091–1097 (1972)
Chou, P.C., Carleone, J.: Transverse shear in laminated plate theories. AIAA J. 11, 1333–1336 (1973)
Reissner, E.: A consistent treatment of transverse shear deformation in laminated anisotropic plates. AIAA J. 10, 716–718 (1972)
Reddy, J.N., Liu, C.F.: A higher-order shear deformation theory of laminated elastic shells. Int. J. Eng. Sci. 23, 319–330 (1985)
Grigolyuk, E.I., Kulikov, G.M.: Multilayer Reinforced Shells: Calculation of Pneumatic Tires. Mashinostroenie, Moscow (1988). [in Russian]
Grigolyuk, E.I., Kulikov, G.M.: General direction of development of the theory of multilayered shells. Mech. Compos. Mater. 24, 231–241 (1988)
Kant, T., Swaminathan, K.: Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos. Struct. 56, 329–344 (2002)
Thakur, S.N., Ray, C., Chakraborty, S.: A new efficient higher-order shear deformation theory for a doubly curved laminated composite shell. Acta Mech. (2016). doi:10.1007/s00707-016-1693-3
Toorani, M.H., Lakis, A.A.: General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. J. Sound Vib. 237, 561–615 (2000)
Anastasiadis, J.S., Simitses, G.J.: Buckling of pressure-loaded, long, shear deformable, cylindrical laminated shells. Compos. Struct. 23, 221–231 (1993)
Mikhasev, G.I., Seeger, F., Gabbert, U.: Comparison of analytical and numerical methods for the analysis of buckling and vibrations of composite shell structures. In: (ed.) Proceedings of 5th Magdeburg Days of Mechanical Engineering. Otto-von-Guericke-University Magdeburg, pp. 175–183. Logos, Berlin (2001)
Wu, Z., Cheung, Y.K., Lo, S.H., Chen, W.: Effects of higher-order globallocal shear deformations on bending, vibration and buckling of multilayered plates. Compos. Struct. 82, 277–289 (2008)
Li, Z.-M., Lin, Z.-Q.: Non-linear buckling and postbuckling of shear deformable anisotropic laminated cylindrical shell subjected to varying external pressure loads. Compos. Struct. 92, 553–567 (2010)
Kheirikhah, M.M., Khalili, S.M.R., Fard, K.M.: Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory. Eur. J. Mech. A Solids 31, 54–66 (2012)
Grover, N., Maiti, D.K., Singh, B.N.: A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates. Compos. Struct. 95, 667–675 (2013)
Nguyen, T.N., Thai, C.H., Nguyen-Xuan, H.: On the general framework of high order shear deformation theories for laminated composite plate structures: a novel unified approach. Int. J. Mech. Sci. 110, 242–255 (2016)
Gol’denveizer, A.L.: Theory of Thin Elastic Shells. International Series of Monograph in Aeronautics and Astronautics. Pergamon Press, New York (1961)
Novozhilov, V.: Theory of Thin Shells. Wolters-Noordhoff, Groningen (1970)
Mikhasev, G.I., Altenbach, H., Korchevskaya, E.A.: On the influence of the magnetic field on the eigenmodes of thin laminated cylindrical shells containing magnetorheological elastomer. Compos. Struct. 113, 186–196 (2014)
Marguerre, K.: Zur Theorie der gekrümmten Platte grosser Formänderung. Jahrbuch 1939 der deutschen Akademie der Luftfahrtforschung, Bewrlin, Adlershof Bücherei. 1, 413–426 (1939)
Föppl, A.: Vorlesungen über technische Mechanik. 5. Oldenburg Verlag, München, 132–144 (1907)
von Kàrmán, T.: Festigkeitsprobleme im Maschinenbau. In: Encyk. d. Math. Wiss., vol. 4, pp. 311–385, Teubner, Leipzig (1910)
Tovstik, P.E., Smirnov, A.L.: Asymptotic Metods in the Buckling Theory of Elastic Shells. World Scientific, Singapore (2001)
Koiter, W.T.: On the nonlinear theory of thin elastic shells. Proc. Koninkl. Ned. Acad. Wetensch. 69, 1–54 (1966)
Mikhasev, G.I., Tovstik, P.E.: Localized Vibrations and Waves in Thin Shells. Asymptotic Methods. FIZMATLIT, Moscow (2009) (in Russian)
Southwell, R.: On the collapse of tubes by external pressure. Parts 1, 2, 3. Philos. Mag. Ser. 6 25, 687–697 (1913)
Mikhasev, G.I., Mlechka, I.R.: On the influence of boundary conditions and transverse shear on buckling of thin laminated cylindrical shells under external pressure. Facta Univ. Ser. Mech. Eng. 12, 95–106 (2014)
Korobko, E.V., Mikhasev, G.I., Novikova, Z.A., Zurauski, M.A.: On damping vibrations of three-layered beam containing magnetorheological elastomer. J. Intell. Mater. Syst. Struct. 23, 1019–1023 (2012)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, New York (2004)
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Mikhasev, G., Botogova, M. Effect of edge shears and diaphragms on buckling of thin laminated medium-length cylindrical shells with low effective shear modulus under external pressure. Acta Mech 228, 2119–2140 (2017). https://doi.org/10.1007/s00707-017-1825-4
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DOI: https://doi.org/10.1007/s00707-017-1825-4