Assessment of Inverse Hyperbolic Zigzag Theory for Hygro-Thermomechanical Analysis of Laminated Composite and Sandwich Plates
Publication: Journal of Aerospace Engineering
Volume 33, Issue 5
Abstract
In the present work, the hygro-thermomechanical response on the static characteristics of symmetric and antisymmetric laminated composite and sandwich plates is obtained using the recently developed inverse hyperbolic zigzag theory (IHZZT). The framework of IHZZT inculcates the shear strain shape function assuming a nonlinear distribution of transverse shear stresses. It satisfies the necessary conditions of interlaminar stress continuity at the layer interfaces as well as the condition of zero transverse shear stresses at the top and bottom surfaces of the plates. The theory has seven unknown field variables, which are layer-independent. The displacement-based finite-element approach is employed, using the eight-noded isoparametric serendipity element, accounting for the continuity. A number of numerical examples are solved considering the effect of temperature, moisture concentration, span-thickness ratio, aspect ratio, boundary conditions, loading conditions, and variations in the number of layers. The results obtained in terms of deflections and stresses are validated with the exact results and results available in the existing literature. A few new results are produced here to establish a benchmark study for future research.
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 generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions.
Acknowledgments
The corresponding author acknowledges the support of “Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India” under Grant No. ECR/2016/001926.
References
Akhras, G., M. S. Cheung, and W. Li. 1994. “Finite strip analysis of anisotropic laminated composite plates using higher-order shear deformation theory.” Comput. Struct. 52 (3): 471–477. https://doi.org/10.1016/0045-7949(94)90232-1.
Akhras, G., and W. Li. 2007. “Spline finite strip analysis of composite plates based on higher-order zigzag composite plate theory.” Compos. Struct. 78 (1): 112–118. https://doi.org/10.1016/j.compstruct.2005.08.016.
Auricchio, F., and E. Sacco. 2003. “Refined first-order shear deformation theory models for composite laminates.” J. Appl. Mech. 70 (3): 381. https://doi.org/10.1115/1.1572901.
Bhar, A., S. S. Phoenix, and S. K. Satsangi. 2010. “Finite element analysis of laminated composite stiffened plates using FSDT and HSDT: A comparative perspective.” Compos. Struct. 92 (2): 312–321. https://doi.org/10.1016/j.compstruct.2009.08.002.
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.
Bhaskar, K., T. K. Varadan, and J. S. M. Ali. 1996. “Thermoelastic solutions for orthotropic and anisotropic composite laminates.” Compos. Part B: Eng. 27 (5): 415–420. https://doi.org/10.1016/1359-8368(96)00005-4.
Carrera, E. 2003. “Historical review of zig-zag theories for multilayered plates and shells.” Appl. Mech. Rev. 56 (3): 287. https://doi.org/10.1115/1.1557614.
Chalak, H. D., A. Chakrabarti, M. A. Iqbal, and A. H. Sheikh. 2012. “An improved C0 FE model for the analysis of laminated sandwich plate with soft core.” Finite Elem. Anal. Des. 56 (Sep): 20–31. https://doi.org/10.1016/j.finel.2012.02.005.
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.
Cook, R., D. Malkus, M. Plesha, and R. Witt. 2002. Concepts and applications of finite element analysis. Hoboken, NJ: Wiley.
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. 1987. “An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates.” J. Appl. Mech. 54 (3): 589–596. https://doi.org/10.1115/1.3173074.
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.
Ferreira, A. J. M. 2005. “Analysis of composite plates using a layerwise theory and multiquadrics discretization.” Mech. Adv. Mater. Struct. 12 (2): 99–112. https://doi.org/10.1080/15376490490493952.
Grover, N., B. N. Singh, and D. K. Maiti. 2013a. “Analytical and finite element modeling of laminated composite and sandwich plates: An assessment of a new shear deformation theory for free vibration response.” Int. J. Mech. Sci. 67 (Feb): 89–99. https://doi.org/10.1016/j.ijmecsci.2012.12.010.
Grover, N., B. N. Singh, and D. K. Maiti. 2013b. “New nonpolynomial shear-deformation theories for structural behavior of laminated-composite and sandwich plates.” AIAA J. 51 (8): 1861–1871. https://doi.org/10.2514/1.J052399.
Grover, N., B. N. Singh, and D. K. Maiti. 2014. “A general assessment of a new inverse trigonometric shear deformation theory for laminated composite and sandwich plates using finite element method.” J. Aerosp. Eng. 228 (10): 1788–1801. https://doi.org/10.1177/0954410013514742.
Joshan, Y. S., N. Grover, and B. N. Singh. 2017a. “Analytical modelling for thermo-mechanical analysis of cross-ply and angle-ply laminated composite plates.” Aerosp. Sci. Technol. 70 (Nov): 137–151. https://doi.org/10.1016/j.ast.2017.07.041.
Joshan, Y. S., N. Grover, and B. N. Singh. 2017b. “A new non-polynomial four variable shear deformation theory in axiomatic formulation for hygro-thermo-mechanical analysis of laminated composite plates.” Compos. Struct. 182 (Jun): 685–693. https://doi.org/10.1016/j.compstruct.2017.09.029.
Kant, T., S. S. Pendhari, and Y. M. Desai. 2008. “An efficient semi-analytical model for composite and sandwich plates subjected to thermal load.” J. Therm. Stresses 31 (1): 77–103. https://doi.org/10.1080/01495730701738264.
Kant, T., and S. M. Shiyekar. 2013. “An assessment of a higher order theory for composite laminates subjected to thermal gradient.” Compos. Struct. 96 (Feb): 698–707. https://doi.org/10.1016/j.compstruct.2012.08.045.
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. G. S. Achary. 2004. “An efficient higher order zigzag theory for laminated plates subjected to thermal loading.” Int. J. Solids Struct. 41 (16–17): 4661–4684. https://doi.org/10.1016/j.ijsolstr.2004.02.020.
Karama, M., K. S. Afaq, and S. Mistou. 2009. “A new theory for laminated composite plates.” J. Mater. Des. Appl. 223 (2): 53–62. https://doi.org/10.1243/14644207JMDA189.
Mantari, J. L., A. S. Oktem, and C. Guedes Soares. 2012a. “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.
Mantari, J. L., A. S. Oktem, and C. G. Soares. 2011. “Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory.” Compos. Struct. 94 (1): 37–49. https://doi.org/10.1016/j.compstruct.2011.07.020.
Mantari, J. L., A. S. Oktem, and C. G. Soares. 2012b. “A new higher order shear deformation theory for sandwich and composite laminated plates.” Compos. Part B: Eng. 43 (3): 1489–1499. https://doi.org/10.1016/j.compositesb.2011.07.017.
Mechab, B., I. Mechab, and S. Benaissa. 2012. “Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermo-mechanical loading.” Compos. Part B: Eng. 43 (3): 1453–1458. https://doi.org/10.1016/j.compositesb.2011.11.037.
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.
Pagano, N. J., and H. J. Hatfield. 1972. “Elastic behavior of multilayered bidirectional composites.” AIAA J. 10 (Jul): 931–933. https://doi.org/10.2514/3.50249.
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 (9–10): 602–610. https://doi.org/10.1016/j.finel.2008.02.001.
Patel, B. P., M. Ganapathi, and D. P. Makhecha. 2002. “Hygrothermal effects on the structural behaviour of thick composite laminates using higher-order theory.” Compos. Struct. 56 (1): 25–34. https://doi.org/10.1016/S0263-8223(01)00182-9.
Ramesh, S. S., C. M. Wang, J. N. Reddy, and K. K. Ang. 2009. “A higher-order plate element for accurate prediction of interlaminar stresses in laminated composite plates.” Compos. Struct. 91 (3): 337–357. https://doi.org/10.1016/j.compstruct.2009.06.001.
Ramtekkar, G. S., Y. M. Desai, and A. H. Shah. 2003. “Application of a three-dimensional mixed finite element model to the flexure of sandwich plate.” Comput. Struct. 81 (22–23): 2183–2198. https://doi.org/10.1016/S0045-7949(03)00289-X.
Reddy, J. N. 1984. “A simple higher-order theory for laminated composite plates.” J. Appl. Mech. 1984 (1): 745–752. https://doi.org/10.1115/1.3167719.
Reddy, J. N., and Y. S. Hsu. 1980. “Effects of shear deformation and anisotropy on the thermal bending of layered composite plates.” J. Therm. Stresses 3 (4): 475–493. https://doi.org/10.1080/01495738008926984.
Roque, C. M. C., A. J. M. Ferreira, and R. M. N. Jorge. 2005. “Modelling of composite and sandwich plates by a trigonometric layerwise deformation theory and radial basis functions.” Compos. Part B 36 (8): 559–572. https://doi.org/10.1016/j.compositesb.2005.05.003.
Sahoo, R., and B. N. Singh. 2013a. “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. 2013b. “A new shear deformation theory for the static analysis of laminated composite and sandwich plates.” Int. J. Mech. Sci. 75 (Oct): 324–336. https://doi.org/10.1016/j.ijmecsci.2013.08.002.
Sahoo, R., and B. N. Singh. 2014a. “A new trigonometric zigzag theory for buckling and free vibration analysis of laminated composite and sandwich plates.” Compos. Struct. 117 (1): 316–332. https://doi.org/10.1016/j.compstruct.2014.05.002.
Sahoo, R., and B. N. Singh. 2014b. “A new trigonometric zigzag theory for static analysis of laminated composite and sandwich plates.” Aerosp. Sci. Technol. 35 (1): 15–28. https://doi.org/10.1016/j.ast.2014.03.001.
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.
Sai Ram, K. S., and P. K. Sinha. 1991. “Hygrothermal effects on the bending characteristics of laminated composite plates.” Comput. Struct. 40 (4): 1009–1015. https://doi.org/10.1016/0045-7949(91)90332-G.
Sarangan, S., and B. N. Singh. 2017. “Evaluation of free vibration and bending analysis of laminated composite and sandwich plates using non-polynomial zigzag models: C0 Finite element formulation.” Aerosp. Sci. Technol. 68 (Sep): 496–508. https://doi.org/10.1016/j.ast.2017.06.001.
Sheikh, A. H., and A. Chakrabarti. 2003. “A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates.” Finite Elem. Anal. Des. 39 (9): 883–903. https://doi.org/10.1016/S0168-874X(02)00137-3.
Singh, S. K., and A. Chakrabarti. 2011. “Hygrothermal analysis of laminated composite plates by using efficient higher order shear deformation theory.” J. Solid Mech. 3 (1): 85–95.
Singh, S. K., A. Chakrabarti, P. Bera, and J. S. D. Sony. 2011. “An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup.” Latin Am. J. Solids Struct. 8 (2): 197–212. https://doi.org/10.1590/S1679-78252011000200006.
Thai, H.-T., and D.-H. Choi. 2013. “A simple first-order shear deformation theory for laminated composite plates.” Compos. Struct. 106 (Dec): 754–763. https://doi.org/10.1016/j.compstruct.2013.06.013.
Whitney, J. M. 1969. “The effect of transverse shear deformation on the bending of laminated plates.” J. Compos. Mater. 3 (3): 534–547. https://doi.org/10.1177/002199836900300316.
Zenkour, A. M. 2004. “Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading.” Compos. Struct. 65 (3–4): 367–379. https://doi.org/10.1016/j.compstruct.2003.11.012.
Zenkour, A. M. 2012. “Hygrothermal effects on the bending of angle-ply composite plates using a sinusoidal theory.” Compos. Struct. 94 (12): 3685–3696. https://doi.org/10.1016/j.compstruct.2012.05.033.
Zenkour, A. M., and R. A. Alghanmi. 2016. “Bending of symmetric cross-ply multilayered plates in hygrothermal environments.” Math. Models Eng. 2 (2): 94–107. https://doi.org/10.21595/mme.2016.17405.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 33 • Issue 5 • September 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Apr 19, 2018
Accepted: Apr 30, 2020
Published online: Jul 9, 2020
Published in print: Sep 1, 2020
Discussion open until: Dec 9, 2020
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.