Bending Analysis of Sandwich Plates Subjected to Various Mechanical Loadings Using Quasi-Three-Dimensional Theory
Publication: Journal of Aerospace Engineering
Volume 35, Issue 4
Abstract
A quasi-three-dimensional (3D) theory considering transverse shear and normal deformation effects is presented for the static flexure of simply supported symmetric sandwich plates. The theory was developed based on the third- and fifth-order shear strain functions in terms of thickness coordinate. The displacement field accounts for nonlinear variation of in-plane displacements and transverse displacement through the plate thickness and enforces satisfying conditions of zero transverse shear stresses on the upper and lower surfaces of the plate. The present theory does not require the shear correction factor associated with the first-order shear deformation theory. Governing equations and boundary conditions were obtained using the principle of virtual work. The transverse shear and normal stresses were obtained from the stress equilibrium equations of theory of elasticity satisfying the continuity conditions at the layer interfaces and the stress-free boundary conditions at the top and bottom surfaces of the plate. The closed-form solutions for simply supported sandwich plates subjected to sinusoidal, uniform, and uniformly varying loads were obtained for various side to thickness ratios. The results of the present quasi-3D theory were compared with those of the exact theory, first- and third-order shear deformation theories, and the classical plate theory. Results showed that the present quasi-three-dimensional (3D) theory is in excellent agreement with the exact theory.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Belarbi, M. O., and A. Tati. 2015. “A new finite element model for the analysis of sandwich plates using combined theories.” Int. J. Struct. Eng. 6 (3): 212–239. https://doi.org/10.1504/IJSTRUCTE.2015.070719.
Bhaskar, K., and T. K. Varadan. 1989. “Refinement of higher-order laminated plate theories.” AIAA J. 27 (12): 1830–1831. https://doi.org/10.2514/3.10345.
Burton, W. S., and A. K. Noor. 1995. “Assessment of computational models for sandwich panels and shells.” Comput. Methods Appl. Mech. Eng. 124 (1–2): 125–151. https://doi.org/10.1016/0045-7825(94)00750-H.
Carlsson, L. A., and G. A. Kardomateas. 2011. “Classical and first-order shear deformation analysis of sandwich plates.” In Structural and failure mechanics of sandwich composites, 39–83. Dordrecht, Netherlands: Springer.
Carrera, E. 1998. “Mixed layer-wise models for multilayered plates analysis.” Compos. Struct. 43 (1): 57–70. https://doi.org/10.1016/S0263-8223(98)00097-X.
Carrera, E. 2002. “Theories and finite elements for multilayered, anisotropic, composite plates and shells.” Arch. Comput. Methods Eng. 9 (2): 87–140. https://doi.org/10.1007/BF02736649.
Carrera, E. 2005. “Transverse normal strain effects on thermal stress analysis of homogeneous and layered plates.” AIAA J. 43 (10): 2232–2242. https://doi.org/10.2514/1.11230.
Carrera, E., and S. Brischetto. 2009. “A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates.” Appl. Mech. Rev. 62 (1): 1–17. https://doi.org/10.1115/1.3013824.
Carrera, E., and L. Demasi. 2003. “Two benchmarks to assess two-dimensional theories of sandwich, composite plates.” AIAA J. 41 (7): 1356–1362. https://doi.org/10.2514/2.2081.
Chanda, A., and R. Sahoo. 2021a. “Accurate stress analysis of laminated composite and sandwich plates.” J. Strain Anal. Eng. Des. 56 (2): 96–111. https://doi.org/10.1177/0309324720921297.
Chanda, A., and R. Sahoo. 2021b. “Static and dynamic responses of simply supported sandwich plates using non-polynomial zigzag theory.” Structures 29 (Feb): 1911–1933. https://doi.org/10.1016/j.istruc.2020.11.062.
Cho, M., and R. R. Parmerter. 1992. “An efficient higher-order plate theory for laminated composites.” Compos. Struct. 20 (2): 113–123. https://doi.org/10.1016/0263-8223(92)90067-M.
Demasi, L. 2009. “ mixed plate theories based on the Generalized Unified Formulation. Part III: Advanced mixed high order shear deformation theories.” Compos. Struct. 87 (3): 183–194. https://doi.org/10.1016/j.compstruct.2008.07.011.
Di Sciuva, M. 1986. “Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model.” J. Sound Vib. 105 (3): 425–442. https://doi.org/10.1016/0022-460X(86)90169-0.
Di Sciuva, M. 1992. “Multilayered anisotropic plate models with continuous interlaminar stresses.” Compos. Struct. 22 (3): 149–167. https://doi.org/10.1016/0263-8223(92)90003-U.
Gajbhiye, P. D., V. Bhaiya, and Y. M. Ghugal. 2022. “Bending analysis of sandwich plate under concentrated force using quasi-three-dimensional theory.” AIAA J. 60 (1): 316–329. https://doi.org/10.2514/1.J060815.
Ganapathi, M., B. P. Patel, and D. P. Makhecha. 2004. “Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory.” Composites, Part B 35 (4): 345–355. https://doi.org/10.1016/S1359-8368(02)00075-6.
Ghugal, Y. M., and R. P. Shimpi. 2002. “A review of refined shear deformation theories of isotropic and anisotropic laminated plates.” J. Reinf. Plast. Compos. 21 (9): 775–813. https://doi.org/10.1177/073168402128988481.
Grover, N., D. K. Maiti, and B. N. Singh. 2013. “A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates.” Compos. Struct. 95 (Jan): 667–675. https://doi.org/10.1016/j.compstruct.2012.08.012.
Irfan, S., and F. Siddiqui. 2019. “A review of recent advancements in finite element formulation for sandwich plates.” Chin. J. Aeronaut. 32 (4): 785–798. https://doi.org/10.1016/j.cja.2018.11.011.
Kant, T., and K. Swaminathan. 2000. “Estimation of transverse/interlaminar stresses in laminated composites—A selective review and survey of current developments.” Compos. Struct. 49 (1): 65–75. https://doi.org/10.1016/S0263-8223(99)00126-9.
Kant, T., and K. Swaminathan. 2002. “Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory.” Compos. Struct. 56 (4): 329–344. https://doi.org/10.1016/S0263-8223(02)00017-X.
Kapuria, S., and G. S. Achary. 2004. “An efficient higher order zigzag theory for laminated plates subjected to thermal loading.” Int. J. Solids Struct. 41 (16): 4661–4684. https://doi.org/10.1016/j.ijsolstr.2004.02.020.
Kapuria, S., and S. D. Kulkarni. 2007. “An improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory for static analysis of composite and sandwich plates.” Int. J. Numer. Methods Eng. 69 (9): 1948–1981. https://doi.org/10.1002/nme.1836.
Kheirikhah, M. M., S. M. R. Khalili, and K. M. Fard. 2012. “Analytical solution for bending analysis of soft-core composite sandwich plates using improved high-order theory.” Struct. Eng. Mech. 44 (1): 15–34. https://doi.org/10.12989/sem.2012.44.1.015.
Kim, J.-S., and M. Cho. 2005. “Enhanced first-order shear deformation theory for laminated and sandwich plates.” J. Appl. Mech. 72 (6): 809–817. https://doi.org/10.1115/1.2041657.
Kirchhoff, G. 1850. “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe.” J. Reine Angew. Math. 1850 (40): 51–88. https://doi.org/10.1515/crll.1850.40.51.
Koiter, W. T. 1959. “A consistent first approximations in general theory of thin elastic shells.” In Proc., Symp. on the Theory of Thin Elastic Shells, 12–23. Amsterdam, Netherlands: North-Holland Publishing.
Kreja, I. 2011. “A literature review on computational models for laminated composite and sandwich panels.” Cent. Eur. J. Eng. 1 (1): 59–80. https://doi.org/10.2478/s13531-011-0005-x.
Krishna Murty, A. V. 1987. “Flexure of composite plates.” Compos. Struct. 7 (3): 161–177. https://doi.org/10.1016/0263-8223(87)90027-4.
Li, H., X. Zhu, Z. Mei, J. Qiu, and Y. Zhang. 2013. “Bending of orthotropic sandwich plates with a functionally graded core subjected to distributed loadings.” Acta Mech. Solida Sin. 26 (3): 292–301. https://doi.org/10.1016/S0894-9166(13)60027-0.
Li, X., and D. Liu. 1995. “A laminate theory based on global–local superposition.” Commun. Numer. Methods Eng. 11 (8): 633–641. https://doi.org/10.1002/cnm.1640110802.
Libove, C., and S. B. Batdorf. 1948. A general small-deflection theory for flat sandwich plates. Washington, DC: National Advisory Committee for Aeronautics.
Lo, K. H., R. M. Christensen, and E. M. Wu. 1977a. “A high-order theory of plate deformation—Part 1: Homogeneous plates.” J. Appl. Mech. 44 (4): 663–668. https://doi.org/10.1115/1.3424154.
Lo, K. H., R. M. Christensen, and E. M. Wu. 1977b. “A high-order theory of plate deformation—Part 2: Laminated plates.” J. Appl. Mech. 44 (4): 669–676. https://doi.org/10.1115/1.3424155.
Mahi, A., E. A. Adda Bedia, and A. Tounsi. 2015. “A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates.” Appl. Math. Modell. 39 (9): 2489–2508. https://doi.org/10.1016/j.apm.2014.10.045.
Mallikarjuna, and T. Kant. 1993. “A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches.” Compos. Struct. 23 (4): 293–312. https://doi.org/10.1016/0263-8223(93)90230-N.
Manjunatha, B. S., and T. Kant. 1992. “Comparison of 9 and 16 node quadrilateral elements based on higher-order laminate theories for estimation of transverse stresses.” J. Reinf. Plast. Compos. 11 (9): 968–1002. https://doi.org/10.1177/073168449201100902.
Mantari, J. L., A. S. Oktem, and C. Guedes Soares. 2012a. “A new higher order shear deformation theory for sandwich and composite laminated plates.” Composites, Part B 43 (3): 1489–1499. https://doi.org/10.1016/j.compositesb.2011.07.017.
Mantari, J. L., A. S. Oktem, and C. Guedes Soares. 2012b. “A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates.” Int. J. Solids Struct. 49 (1): 43–53. https://doi.org/10.1016/j.ijsolstr.2011.09.008.
Matsunaga, H. 2002. “Assessment of a global higher-order deformation theory for laminated composite and sandwich plates.” Compos. Struct. 56 (3): 279–291. https://doi.org/10.1016/S0263-8223(02)00013-2.
Mindlin, R. D. 1951. “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates.” J. Appl. Mech. 18 (1): 31–38. https://doi.org/10.1115/1.4010217.
Murthy, M. V. V. 1981. Improved transverse shear deformation theory for laminated anisotropic plates. Hampton, VA: National Aeronautics and Space Administration Langley Research Center.
Naik, N. S., and A. S. Sayyad. 2018. “2D analysis of laminated composite and sandwich plates using a new fifth-order plate theory.” Lat. Am. J. Solids Struct. 15 (9): 1–27. https://doi.org/10.1590/1679-78254834.
Natarajan, S., M. Haboussi, and G. Manickam. 2014. “Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets.” Compos. Struct. 113 (1): 197–207. https://doi.org/10.1016/j.compstruct.2014.03.007.
Nayak, A. K., R. A. Shenoi, and S. S. J. Moy. 2004. “Transient response of composite sandwich plates.” Compos. Struct. 64 (3–4): 249–267. https://doi.org/10.1016/S0263-8223(03)00135-1.
Noor, A. K., W. S. Burton, and C. W. Bert. 1996. “Computational models for sandwich panels and shells.” Appl. Mech. Rev. 49 (3): 155–199. https://doi.org/10.1115/1.3101923.
Pagano, N. J. 1970. “Exact solutions for rectangular bidirectional composites and sandwich plates.” J. Compos. Mater. 4 (1): 20–34. https://doi.org/10.1177/002199837000400102.
Pandit, M. K., A. H. Sheikh, and B. N. Singh. 2008. “An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core.” Finite Elem. Anal. Des. 44 (9): 602–610. https://doi.org/10.1016/j.finel.2008.02.001.
Pandya, B. N., and T. Kant. 1988. “Higher-order shear deformable theories for flexure of sandwich plates—Finite element evaluations.” Int. J. Solids Struct. 24 (12): 1267–1286. https://doi.org/10.1016/0020-7683(88)90090-X.
Plagianakos, T. S., and D. A. Saravanos. 2009. “Higher-order layerwise laminate theory for the prediction of interlaminar shear stresses in thick composite and sandwich composite plates.” Compos. Struct. 87 (1): 23–35. https://doi.org/10.1016/j.compstruct.2007.12.002.
Rao, M. K., and Y. M. Desai. 2004. “Analytical solutions for vibrations of laminated and sandwich plates using mixed theory.” Compos. Struct. 63 (3): 361–373. https://doi.org/10.1016/S0263-8223(03)00185-5.
Reddy, J. N. 1984a. “A refined nonlinear theory of plates with transverse shear deformation.” Int. J. Solids Struct. 20 (9): 881–896. https://doi.org/10.1016/0020-7683(84)90056-8.
Reddy, J. N. 1984b. “A simple higher-order theory for laminated composite plates.” J. Appl. Mech. 51 (4): 745–752. https://doi.org/10.1115/1.3167719.
Reissner, E. 1944. “On the theory of bending of elastic plates.” J. Math. Phys. 23 (1–4): 184–191. https://doi.org/10.1002/sapm1944231184.
Reissner, E. 1945. “The effect of transverse shear deformation on the bending of elastic plates.” J. Appl. Mech. 12 (2): A69–A77. https://doi.org/10.1115/1.4009435.
Robbins, D. H., Jr., and J. N. Reddy. 1993. “Modelling of thick composites using a layerwise laminate theory.” Int. J. Numer. Methods Eng. 36 (4): 655–677. https://doi.org/10.1002/nme.1620360407.
Sahoo, R., N. Grover, and B. N. Singh. 2019. “Nonpolynomial zigzag theories for random static analysis of laminated-composite and sandwich plates.” AIAA J. 57 (1): 437–447. https://doi.org/10.2514/1.J056519.
Sahoo, R., and B. N. Singh. 2013. “A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates.” Compos. Struct. 105 (Nov): 385–397. https://doi.org/10.1016/j.compstruct.2013.05.043.
Sahoo, R., and B. N. Singh. 2015. “Assessment of inverse trigonometric zigzag theory for stability analysis of laminated composite and sandwich plates.” Int. J. Mech. Sci. 101–102 (Oct): 145–154. https://doi.org/10.1016/j.ijmecsci.2015.07.023.
Sarangan, S., and B. N. Singh. 2016. “Higher-order closed-form solution for the analysis of laminated composite and sandwich plates based on new shear deformation theories.” Compos. Struct. 138 (Mar): 391–403. https://doi.org/10.1016/j.compstruct.2015.11.049.
Sayyad, A. S., and Y. M. Ghugal. 2014a. “Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory.” Struct. Eng. Mech. 51 (5): 867–891. https://doi.org/10.12989/sem.2014.51.5.867.
Sayyad, A. S., and Y. M. Ghugal. 2014b. “A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates.” Int. J. Mech. Mater. Des. 10 (3): 247–267. https://doi.org/10.1007/s10999-014-9244-3.
Shinde, B. M., and A. S. Sayyad. 2020. “Analysis of laminated and sandwich spherical shells using a new higher-order theory.” Adv. Aircr. Spacecraft Sci. 7 (1): 19–40. https://doi.org/10.12989/aas.2020.7.1.019.
Thai, C. H., M. Abdel Wahab, and H. Nguyen-Xuan. 2018. “A layerwise -type higher order shear deformation theory for laminated composite and sandwich plates.” C. R. Mec. 346 (1): 57–76. https://doi.org/10.1016/j.crme.2017.11.001.
Thai, C. H., A. J. M. Ferreira, S. P. A. Bordas, T. Rabczuk, and H. Nguyen-Xuan. 2014a. “Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory.” Eur. J. Mech. A Solids 43 (Jan): 89–108. https://doi.org/10.1016/j.euromechsol.2013.09.001.
Thai, H.-T., T.-K. Nguyen, T. P. Vo, and J. Lee. 2014b. “Analysis of functionally graded sandwich plates using a new first-order shear deformation theory.” Eur. J. Mech. A Solids 45 (May): 211–225. https://doi.org/10.1016/j.euromechsol.2013.12.008.
Toledano, A., and H. Murakami. 1987. “A composite plate theory for arbitrary laminate configurations.” J. Appl. Mech. 54 (1): 181–189. https://doi.org/10.1115/1.3172955.
Touratier, M. 1991. “An efficient standard plate theory.” Int. J. Eng. Sci. 29 (8): 901–916. https://doi.org/10.1016/0020-7225(91)90165-Y.
Vinson, J. R. 2001. “Sandwich structures.” Appl. Mech. Rev. 54 (3): 201–214. https://doi.org/10.1115/1.3097295.
Wang, X., and G. Shi. 2014. “A simple and accurate sandwich plate theory accounting for transverse normal strain and interfacial stress continuity.” Compos. Struct. 107 (Jan): 620–628. https://doi.org/10.1016/j.compstruct.2013.08.033.
Whitney, J. M. 1972. “Stress analysis of thick laminated composite and sandwich plates.” J. Compos. Mater. 6 (3): 426–440. https://doi.org/10.1177/002199837200600301.
Xiang, S., K. M. Wang, Y. T. Ai, Y. D. Sha, and H. Shi. 2009. “Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories.” Compos. Struct. 91 (1): 31–37. https://doi.org/10.1016/j.compstruct.2009.04.029.
Zenkour, A. M. 2007. “Three-dimensional elasticity solution for uniformly loaded cross-ply laminates and sandwich plates.” J. Sandwich Struct. Mater. 9 (3): 213–238. https://doi.org/10.1177/1099636207065675.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 35 • Issue 4 • July 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Sep 23, 2021
Accepted: Jan 28, 2022
Published online: Mar 16, 2022
Published in print: Jul 1, 2022
Discussion open until: Aug 16, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.