Elastic buckling of a generalized cylindrical sandwich panel under axial compression

• Autorzy: Magnucki Krzysztof , Magnucka Ewa , Wittenbeck Leszek

Identyfikatory

DOI

10.24425/bpasts.2023.144623

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to buckling problem of an axially compressed generalized cylindrical sandwich panel and rectangular sandwich plate. The continuous variation of mechanical properties in thickness direction of the structures is assumed. The generalized theory of deformation of the straight line normal to the neutral surface is applied. The analytical model of this sandwich panel is elaborated. Three differential equations of equilibrium of this panel based on the principle of stationary potential energy are obtained. This system of equations is analytically solved and the critical load is derived. Moreover, the limit transformation of the sandwich panel to a sandwich rectangular plate is presented. The critical loads of the example cylindrical panels and rectangular plates are derived.

Słowa kluczowe

EN

cylindrical sandwich panel; rectangular sandwich plate; elastic buckling

PL

panel warstwowy cylindryczny; płyta warstwowa prostokątna; płyta typu sandwich prostokątna; wyboczenie elastyczne

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 2
• Strony: art. no. e144623
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Magnucki Krzysztof

• Łukasiewicz Research Network – Poznan Institute of Technology, Rail Vehicles Center, ul. Warszawska 181, 61-055 Poznan, Poland

• https://orcid.org/0000-0003-2251-4697

autor

Magnucka Ewa

• Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60-965 Poznan, Poland

• https://orcid.org/0000-0002-6349-5579

autor

Wittenbeck Leszek

• Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60-965 Poznan, Poland

• https://orcid.org/0000-0003-3223-5704

Bibliografia

• [1] A.M. Zenkour, “Generalized shear deformation theory for bending analysis of functionally graded plates,” Appl. Math. Model., vol. 30, no. 1, pp. 67–84, 2006, doi: 10.1016/j.apm.2005.03.009.
• [2] W. Szyc, Z. Laszczyk, and K. Magnucki, “Elastic buckling of an axially compressed sandwich cylindrical panel with three edges simply supported and one edge free,” Thin-Walled Struct., vol. 44, no. 8, pp. 910–918, 2006, doi: 10.1016/j.tws.2006.07.004.
• [3] M.K. Pandit, B.N. Singh, and A.H. Sheikh, “Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory,” Thin-Walled Struct., vol. 46, no. 11, pp. 1183–1191, 2008, doi: 10.1016/j.tws.2008.03.002.
• [4] E. Carrera and S. Brischetto, “A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates,” Appl. Mech. Rev., vol. 62, no. 1, p. 010803, 2009, doi: 10.1115/1.3013824.
• [5] H.S. Shen, Functionally graded materials: Nonlinear analysis of plates and shells, CRC Press Taylor & Francis Group, Boca Raton London New York, 2009.
• [6] J.N. Reddy, “Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates,” Int. J. Eng. Sci., vol. 48, no. 11, pp. 1507–1518, 2010, doi: 10.1016/j.ijengsci.2010.09.020.
• [7] E. Carrera, S. Brischetto, M. Cinefra, and M. Soave, “Effects of thickness stretching in functionally graded plates and shells,” Compos. Part B-Eng., vol. 42, no. 2, pp. 123–133, 2011, doi: 10.1016/j.compositesb.2010.10.005.
• [8] T. Belica, M. Malinowski, and K. Magnucki, “Dynamic stability of an isotropic metal foam cylindrical shell subjected to external pressure and axial compression,” J. Appl. Mech., vol. 78, no. 4, p. 041003, 2011, doi: 10.1115/1.4003768.
• [9] T. Belica and K. Magnucki, “Stability of a porous-cellular cylindrical shell subjected to combined loads,” J. Theor. Appl. Mech., vol. 51, no. 4, pp. 927–936, 2013.
• [10] M. Malinowski, T. Belica, and K. Magnucki, “Buckling and post-buckling behaviour of elastic seven-layered cylindrical shells – FEM study,” Thin-Walled Struct., vol. 94, pp. 478–484, 2015, doi: 10.1016/j.tws.2015.05.017.
• [11] E. Magnucka-Blandzi and K. Magnucki, “Buckling and post-buckling behaviour of shallow – nearly flat cylindrical panels under axial compression,” Bull. Pol. Acad. Sci.-Tech. Sci., vol. 64, no. 3, pp. 655–658, 2016, doi: 10.1515/bpasts-2016-0074.
• [12] F.A. Fazzolari, “Stability analysis of FGM sandwich plates by using variable-kinematics Ritz models,” Mech. Adv. Mater. Struct., vol. 23, no. 9, pp. 1104–1113, 2016, doi: 10.1080/15376494.2015.1121559.
• [13] A.S. Rezaei and A.R. Saidi, “Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous–cellular plates,” Compos. Part B-Eng., vol. 91, pp. 361–370, 2016, doi: 10.1016/j.compositesb.2015.12.050.
• [14] S. Abrate and M. Di Sciuva, “Equivalent single layer theories for composite and sandwich structures: a review,” Compos. Struct., vol. 179, pp. 482–494, 2017, doi: 10.1016/j.compstruct.2017.07.090.
• [15] V. Birman and G.A. Kardomateas, “Review of current trends in research and applications of sandwich structures,” Compos. Part B-Eng., vol. 142, pp. 221–240, 2018, doi: 10.1016/j.compositesb.2018.01.027.
• [16] K. Magnucki, “Elastic buckling of a cylindrical panel with symmetrically varying mechanical properties – Analytical study,” Compos. Struct., vol. 204, pp. 217–222, 2018, doi: 10.1016/j.compstruct.2018.07.073.
• [17] M.R. Eslami, Buckling and post-buckling of beams, plates, and shells, Springer International Publishing AG, 2018.
• [18] K. Magnucki, D. Witkowski, and E. Magnucka-Blandzi, “Buckling and free vibrations of rectangular plates with symmetrically varying mechanical properties – Analytical and FEM studies,” Compos. Struct., vol. 220, pp. 355–361, 2019, doi: 10.1016/j.compstruct.2019.03.082.
• [19] K. Magnucki, W. Stawecki, and J. Lewinski, “Axisymmetric bending of a circular plate with symmetrically varying mechanical properties under a concentrated force,” Steel Compos. Struct., vol. 34, no. 6, pp. 795–802, 2020, doi: 10.12989/SCS.2020.34.6.795.
• [20] K. Magnucki, J. Lewinski, and E. Magnucka-Blandzi, “A shear deformation theory of beams of bisymmetrical cross sections based on the Zhuravsky shear stress formula,” Eng. Trans., vol. 68, no. 4, pp. 353–370, 2020, doi: 10.24423/ENGTRANS.1174.20201120.
• [21] K. Magnucki and E. Magnucka-Blandzi, “Generalization of a sandwich structure model: Analytical studies of bending and buckling problems of rectangular plates,” Compos. Struct., vol. 255, pp. 112944, 2021, doi: 10.1016/j.compstruct.2020.112944.
• [22] E. Carrera, M.D. Demirbas, and R. Augello, “Evaluation of stress distribution of isotropic, composite, and FG beams with different geometries in nonlinear regime via Carrera-Unified Formulation and Lagrange polynomial expansions,” Appl. Sci., vol. 11, no. 22, p. 10627, 2021, doi: 10.3390/app112210627.
• [23] B. Wu, A. Pagani, W.Q. Chen, and E. Carrera, “Geometrically nonlinear refined shell theories by Carrera Unified Formulation,” Mech. Adv. Mater. Struct., vol. 28, no. 16, pp. 1721–1741, 2021, doi: 10.1080/15376494.2019.1702237.
• [24] C.M. Twinkle and J. Pitchaimani, “Static stability and vibration behavior of graphene platelets reinforced porous sandwich cylindrical panel under non-uniform edge loads using semi-analytical approach,” Compos. Struct., vol. 280, p. 114837, 2022, doi: 10.1016/j.compstruct.2021.114837.
• [25] K. Magnucki, E. Magnucka-Blandzi, and L. Wittenbeck, “Bending of a generalized circular sandwich plate under a concentrated force with consideration of an improved shear deformation theory,” Arch. Mech., vol. 74, no. 4, pp. 267–282, 2022, doi: 10.24423/AOM.4074.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).