Modares Mechanical Engineering

Modares Mechanical Engineering

Bending Analysis of a Laminated Composite Plate under Transverse Loading, Steady-State Temperature Difference, and Transient Moisture Diffusion

Document Type : Original Article

Authors
Tara Mahmoudi
Ali Mohammad Baghestani
Mechanical Engineering Department, Babol Noshirvani University of Technology.
10.48311/mme.2026.123670.83112
Abstract
The combined effects of temperature and moisture variations, known as hygrothermal effects on the bending of a rectangular multilayer composite plate are investigated based on first-order shear deformation theory. The plate is subjected to transverse mechanical loading, temperature variation, and moisture diffusion. The time-dependent moisture distribution through the plate thickness is obtained using an analytical solution of Fick’s moisture diffusion equation. Owing to the slow moisture diffusion process in polymer-matrix composites, the plate bending is investigated quasi-statically based on the moisture distribution at a specified time. Using the semi-analytical Ritz method and the principle of minimum potential energy, the plate deflection is determined for different boundary conditions. The governing equations and solution method are validated by comparison with published results, followed by analyses of new cases. The effects of various parameters, including the length-to-width and length-to-thickness ratios, asymmetric stacking sequences, boundary conditions, and asymmetric moisture boundary conditions, on the plate deflection are investigated. The results show that increasing the length-to-width ratio increases the contribution of hygrothermal loading relative to mechanical loading to the plate deflection, whereas increasing the plate thickness reduces this contribution. In addition, in most cases, the moisture-induced deflection at one-tenth of the saturation time is greater than half of the deflection at saturation, highlighting the importance of considering time-dependent moisture diffusion.
Keywords
Composite Plate
Hygrothermal Analysis
Bending
Transient Moisture Diffusion
Subjects
[1] Y. J. Weitsman, Fluid Effects in Polymers and Polymeric Composites. Springer, 2011.
[2] C. H. Shen and G. S. Springer, "Moisture absorption and desorption of composite materials," Journal of Composite Materials, vol. 10, no. 1, pp. 2-20, 1976. doi: 10.1177/002199837601000101.
[3] M. Gholami, H. Afrasiab, A. M. Baghestani, and A. Fathi, "Hygrothermal degradation of elastic properties of fiber reinforced composites: A micro-scale finite element analysis," Composite Structures, vol. 266, p. 113819, 2021. doi: 10.1016/j.compstruct.2021.113819.
[4] G. S. Springer, "Environmental effects," in Reference Book for Composites Technology-2, S. M. Lee, Ed., Technomic Publishing Co., Inc., pp. 17-36, 1989.
[5] M. Gholami, H. Afrasiab, A. M. Baghestani, and A. Fathi, "Mechanical and failure analysis of thick composites under hygrothermal conditions by a novel coupled hygro-thermo-mechanical multiscale algorithm," Composites Science and Technology, vol. 230, p. 109773, 2022. doi: 10.1016/j.compscitech.2022.109773.
[6] A. Garg and H. D. Chalak, "A review on analysis of laminated composite and sandwich structures under hygrothermal conditions," Thin-Walled Structures, vol. 142, pp. 205-226, 2019. doi: 10.1016/j.tws.2019.05.005.
[7] B. Boukert, A. Benkhedda, E. B. Adda, and M. Khodjet-Kesba, "Hygrothermal stresses analysis of thick composite plates using high order theory under a Fick concentration distribution," Procedia Structural Integrity, vol. 17, pp. 37-43, 2019. doi: 10.1016/j.prostr.2019.08.006.
[8] N. Garg, K. Rahul Sanjay, R. Sahoo, P. R. Maiti, and B. N. Singh, "Assessment of inverse hyperbolic zigzag theory for hygro-thermomechanical analysis of laminated composite and sandwich plates," Journal of Aerospace Engineering, vol. 33, no. 5, p. 04020060, 2020. doi: 10.1061/(ASCE)AS.1943-5525.0001177.
[9] M. Sobhy and A. F. Radwan, "Influence of a 2D magnetic field on hygrothermal bending of sandwich CNTs-reinforced microplates with viscoelastic core embedded in a viscoelastic medium," Acta Mechanica, vol. 231, no. 1, pp. 71-99, 2020. doi: 10.1007/s00707-019-02531-7.
[10] N. S. Naik and A. S. Sayyad, "Analysis of laminated plates subjected to mechanical and hygrothermal environmental loads using fifth-order shear and normal deformation theory," International Journal of Applied Mechanics, vol. 12, no. 03, p. 2050028, 2020. doi: 10.1142/S1758825120500283.
[11] G. Tocci Monaco, N. Fantuzzi, F. Fabbrocino, and R. Luciano, "Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 43, no. 5, p. 274, 2021. doi: 10.1007/s40430-021-02992-9.
[12] N. S. Naik and A. S. Sayyad, "Higher-order displacement model for cylindrical bending of laminated and sandwich plates subjected to environmental loads," Mechanics of Advanced Composite Structures, vol. 8, no. 1, pp. 185-201, 2021. doi: 10.22075/macs.2020.20242.1253.
[13] A. Garg and H. D. Chalak, "Bending analysis of laminated sandwich plates under hygrothermal loadings," Materials Today: Proceedings, vol. 42, pp. 626-630, 2021. doi: 10.1016/j.matpr.2020.11.045.
[14] A. Gupta, S. Verma, and A. Ghosh, "Static and dynamic NURBS-based isogeometric analysis of composite plates under hygrothermal environment," Composite Structures, vol. 284, p. 115083, 2022. doi: 10.1016/j.compstruct.2021.115083.
[15] M. C. Maurya, S. M. Jawaid, and A. Chakrabarti, "Response of agglomerated SWCNT reinforced nanocomposite plate under Hygro-thermal loading," Mechanics of Advanced Composite Structures, vol. 11, no. 1, pp. 11-40, 2024. doi: 10.22075/macs.2023.29697.1472.
[16] N. Namazinia, A. Alibeigloo, and M. Karimiasl, "Free vibration and static analysis of sandwich composite plate with auxetic core and GPLRC facing sheets in hygrothermal environment," Forces in Mechanics, vol. 15, p. 100264, 2024. doi: 10.1016/j.finmec.2024.100264.
[17] M. Sobhy and A. F. Radwan, "Levy solution and state-space approach for hygro-thermo-magnetic bending of a cross-ply laminated plate on Kerr foundation under various loadings," Journal of Composite Materials, vol. 59, no. 1, pp. 3-28, 2025. doi: 10.1177/00219983241289492.
[18] L. L. Xu, C. P. Chen, and Y. F. Zheng, "Nonlinear bending responses of magneto-electro-elastic laminated nanoplates with flexomagnetoelectric effect in hygrothermal environments," Mechanics of Advanced Materials and Structures, vol. 33, no. 1, p. 2458775, 2026. doi: 10.1080/15376494.2025.2458775.
[19] J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, 2003.
[20] Y. J. Weitsman, "Effects of fluids on polymeric composites. A review," Government Research Announcements and Index (USA), vol. 100, 1994.
[21] A. C. Loos and G. S. Springer, "Moisture absorption of graphite-epoxy composites immersed in liquids and in humid air," Journal of Composite Materials, vol. 13, no. 2, pp. 131-147, 1979. doi: 10.1177/002199837901300205.
[22] A. Firouzian-Nejad, S. Ziaei-Rad, M. Moore, A modified shape function for calculating stable configurations and natural frequencies of bi-stable [0/90] composite laminates, Modares Mechanical Engineering, Vol. 16, No. 4, pp. 119-128, 2016 (In Persian).
[23] J. R. Vinson and R. L. Sierakowski, The behavior of structures composed of composite materials. Springer, 2006. doi: 10.1007/0-306-48414-5.
[24] K. Khorshidi, M. Balali, A. A. Ghadimi, Control forced vibrations of laminated composite rectangular plate resting on linear line support, Modares Mechanical Engineering,  Vol. 15, No. 9, pp. 95-104, 2015 (In Persian).
[25] Y. Kumar, "The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review," Journal of Vibration and Control, vol. 24, no. 7, pp. 1205-1227, 2018. doi: 10.1177/1077546317694724.
[26] K. M. Fard and A. M. Baghestani, "Free vibration analysis of deep doubly curved open shells using the Ritz method," Aerospace Science and Technology, vol. 69, pp. 136-148, 2017. doi: 10.1016/j.ast.2017.06.021.
[27] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions. Dover Publications, 1965.
[28] S. M. Ostadzadeh, A. M. Baghestani, H. Afrasiab, and M. Gholami, "Quasi-static bending analysis of composite laminated cylindrical panels under hygrothermal conditions," Thin-Walled Structures, vol. 203, p. 112227, 2024. doi: 10.1016/j.tws.2024.112227.
[29] D. J. Boll, W. D. Bascom, and B. Motiee, "Moisture absorption by structural epoxy-matrix carbon-fiber composites," Composites Science and Technology, vol. 24, no. 4, pp. 253-273, 1985. doi: 10.1016/0266-3538(85)90025-9.
[30] J. Crank, The mathematics of diffusion. Clarendon Press, 1979.
[31] H. S. Carslaw, J. C. Jaeger, and H. Feshbach, "Conduction of heat in solids," Physics Today, vol. 15, no. 11, pp. 74-76, 1962. doi: 10.1063/1.3057871.
[32] B. P. Patel, M. Ganapathi, and D. P. Makhecha, "Hygrothermal effects on the structural behaviour of thick composite laminates using higher-order theory," Composite Structures, vol. 56, no. 1, pp. 25-34, 2002. doi: 10.1016/S0263-8223(01)00182-9.
[33] P. Vaddadi, T. Nakamura, and R. P. Singh, "Transient hygrothermal stresses in fiber reinforced composites: a heterogeneous characterization approach," Composites Part A: Applied Science and Manufacturing, vol. 34, no. 8, pp. 719-730, 2003. doi: 10.1016/S1359-835X(03)00135-0.
[34] C. C. Chamis, "Simplified composite micromechanics equations of hygral, thermal, and mechanical properties," SAMPE Quarterly, vol. 15, no. 3, pp. 14-23, 1984.
[35] S. W. Tsai, "Double–Double: New family of composite laminates," AIAA Journal, vol. 59, no. 11, pp. 4293-4305, 2021.
 
 
 
Modares Mechanical Engineering
Volume 27, Issue 3
March 2026
Pages 265-282