Bending of a generalized circular sandwich plate under a concentrated force with consideration of an improved shear deformation theory

• Autorzy: Magnucki K. , Magnucka-Blandzi E. , Wittenbeck L.

Identyfikatory

DOI

10.24423/aom.4074

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to an axisymmetric bending problem of a generalized circular sandwich plate with continuous variation of mechanical properties in the thickness direction of the core. The plate is clamped and carries a concentrated force in its center. The improved shear deformation theory of the normal straight line to the neutral surface is elaborated. The deformation of this normal straight line is graphically presented for the exemplary sandwich structures of the plate. Two differential equation of equilibrium of the plate are obtained based on the principle of stationary potential energy. This system of equations is analytically solved and the maximum deflection of the example plates are derived. Moreover, the deformation of the normal strain line and the maximum deflection of the plate are calculated numerically (FEM). Results of these calculations are compared.

Słowa kluczowe

EN

circular sandwich plate; shear deformation theory; axisymmetric bending

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2022
• Tom: Vol. 74, nr 4
• Strony: 267--282
• Opis fizyczny: Bibliogr. 23 poz., rys., wykr.

Twórcy

autor

Magnucki K.

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

autor

Magnucka-Blandzi E.

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

autor

Wittenbeck L.

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

Bibliografia

• 1. E. Carrera, Developments, ideas, and evaluations based upon Reissner’s Mixed Variational Theorem in the modeling of multilayered plates and shells, Applied Mechanics Reviews, 54, 4, 301–329, 2001.
• 2. E.S. Ventsel, T. Krauthammer, Thin plates and shells: theory, analysis, and applications, Marcel Dekker, New York, Basel, 2001.
• 3. J.R. Vinson, Sandwich Structures, Applied Mechanics Reviews, 54, 3, 201–214, 2001.
• 4. F. Auricchio, E. Sacco, Refined first-order shear deformation theory models for composite laminates, Journal of Applied Mechanics, 70, 3, 381–390, 2003.
• 5. E. Carrera, Historical review of Zig-Zag theories for multilayered plates and shells, Applied Mechanics Reviews, 56, 3, 287–308, 2003.
• 6. J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, CRC Press, Boca Raton, London, New York, Washington, 2004.
• 7. M. Yang, P. Qiao, Higher-order impact modeling of sandwich structures with flexible core, International Journal of Solids and Structures, 42, 20, 5460–5490, 2005.
• 8. A.M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, 30, 1, 67–84, 2006.
• 9. E. Carrera, S. Brischetto, A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Applied Mechanics Reviews, 62, 1, 2009.
• 10. P. Jasion, E. Magnucka-Blandzi, W. Szyc, K. Magnucki, Global and local buc kling of sandwich circular and beam-rectangular plates with metal foam core, Thin-Walled Structures, 61, 154–161, 2012.
• 11. K. Magnucki, P. Jasion, E. Magnucka-Blandzi, P. Wasilewicz, Theoretical and experimental study of a sandwich circular plate under pure bending, Thin-Walled Structures, 79, 1–7, 2014.
• 12. I. Senjanovic, N. Hadzic, N. Vladimir, D.-S. Cho, Natural vibrations of thick circular plate based on the modified Mindl in theory, Archives of Mechanics, 66, 6, 389–409, 2014.
• 13. C.H. Thai, A.J. M. Ferreira, S.P.A. Bordas, T. Rabczuk, H. Nguyen-Xuan, Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory, European Journal of Mechanics - A/Solids, 43, 89–108, 2014.
• 14. S. Sarangan, B.N. Singh, Higher-order closed-form solution for the analysis of laminatem composite and sandwich plates based on new shear deformation theories, Composite Structures, 138, 391–403, 2016.
• 15. S. Abrate, M. Di Sciuva, Equivalent single layer theories for composite and Sandwich structures: a review, Composite Structures, 179, 482–494, 2017.
• 16. R. Meksi, S. Benyoucef, A. Mahmoudi, A. Tounsi, E.A.A. Bedia, S.R. Mahmoud, An analytical solution for bending, buckling and vibration responses of FGM Sandwich plates, Journal of Sandwich Structures & Materials, 21, 2, 727–757, 2017.
• 17. N. Naderi Beni, M. Botshekanan Dehkordi, An extension of Carrera unified formulation in polar coordinate for analysis of circular sandwich plate with FGM core Rusing GDQ method, Composite Structures, 185, 421–434, 2018.
• 18. D. Zarga, A. Tounsi, A.A. Bousahla, F. Bourada, S.R. Mahmoud, Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory, Steel and Composite Structures, 32, 3, 389–410, 2019.
• 19. A. Boussoula, B. Boucham, M. Bourada, F. Bourada, A. Tounsi, A.A. Bousahla, A. Tounsi, A simple nth-order shear deformation theory for thermomechanical Bendig analysis of different configurations of FG sandwich plates, Smart Structures and Systems, 25, 2, 197–218, 2020.
• 20. K. Magnucki, J. Lewinski, E. Magnucka-Blandzi, A shear deformation theory of beams with bisymmetrical cross-sections based on the Zhuravsky shear stress formula, Engineering Transactions, 68, 4, 353–370, 2020.
• 21. K. Magnucki, J. Lewinski, E. Magnucka-Blandzi, An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction, Acta Mechanica, 231, 10, 4381–4395, 2020.
• 22. K. Magnucki, W. Stawecki, J. Lewinski, Axisymmetric bending of a circular plate with symmetrically varying mechanical properties under a concentrated force, Steel and Composite Structures, 34, 6, 795–802, 2020.
• 23. M. H. Karimi, F. Fallah, Analytical non-linear analysis of functionally graded Sandwich solid/annular sector plates, Composite Structures, 275, 114420, 2021.

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).