Abstract
In the present study, flexural behaviour of laminated composite plate with porosity presented using improved third-order shear deformation theory. Present theory ensures transverse shear stress continuity at each layer interface in addition to zero transverse shear stresses at top and bottom of plate. C0 finite-element (FE) formulation developed of the present theory. This is the first attempt to study the laminated composite plate with porosity using the present advanced theory. The present improved third-order theory incorporating transverse shear stress continuity at each layer interface predicts better results than third-order shear deformation theory and first-order shear deformation theory. Authors for the present study developed an in-house FORTRAN code. The effects of material properties, orientation angle of the fibre, and sequence of laminated plate with porosity on stresses and deflection are studied. The comparison with the existing literature predicts the accuracy and robustness of present work.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig13_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig14_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig15_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig16_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig17_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig18_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig19_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig20_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig21_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig22_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig23_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig24_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42107-022-00523-y/MediaObjects/42107_2022_523_Fig25_HTML.png)
Similar content being viewed by others
References
Abdelmalek, A., Bouazza, M., Zidour, M., & Benseddiq, N. (2017). Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: A micromechanical approach. Iranian Journal of Science and Technology Transactions of Mechanical Engineering. https://doi.org/10.1007/s40997-017-0140-y
Akbaş, ŞD. (2017a). Nonlinear static analysis of functionally graded porous beams under thermal effect. Coupled Systems Mechanics, 4, 399–415.
Akbaş, ŞD. (2017b). Vibration and static analysis of functionally graded porous plates. Journal of Applied and Computational Mechanics, 3(3), 199–207. https://doi.org/10.22055/jacm.17.21540.1107
Akbaş, ŞD. (2017c). Nonlinear static analysis of functionally graded porous beams under thermal effect. Coupled Systems Mechanics, 4, 399–415.
Akbaş, ŞD. (2017d). Forced vibration analysis of functionally graded porous deep beams. Composite Structures. https://doi.org/10.1016/j.compstruct.2017.12.013
Akbaş, ŞD. (2019). Longitudinal forced vibration analysis of porous a nanorod. Mühendislik Bilimleri Ve Tasarım Dergisi, 7(4), 736–743. https://doi.org/10.21923/jesd.553328
Akbas, S. D., & Akbas, S. D. (2019). Hygrothermal post-buckling analysis of laminated composite beams. International Journal of Applied Mechanic. https://doi.org/10.1142/S1758825119500091
Alnujaie, A., Akbaş, ŞD., Eltaher, M. A., & Assie, A. E. (2021). Damped forced vibration analysis of layered functionally graded thick beams with porosity. Smart Structures and Systems. https://doi.org/10.12989/sss.2021.27.4.679
Amoushahi, H., & Goodarzian, F. (2018). Thin-Walled Structures Dynamic and buckling analysis of composite laminated plates with and without strip delamination under hygrothermal effects using finite strip method. Thin Walled Structures, 131(June), 88–101. https://doi.org/10.1016/j.tws.2018.06.030
Arumugam, A. B., Rajamohan, V., Pandey, A., & Sudhagar, P. E. (2017). Finite element vibration analysis of rotating laminated composite beam with varying cross-section using HSDT. International Journal on Interactive Design and Manufacturing, 11(3), 703–712. https://doi.org/10.1007/s12008-016-0364-x
Arumugam, A. B., Subramani, M., Dalakoti, M., **dal, P., Selvaraj, R., & Khalife, E. (2021). Dynamic characteristics of laminated composite CNT reinforced MRE cylindrical sandwich shells using HSDT. Mechanics Based Design of Structures and Machines. https://doi.org/10.1080/15397734.2021.1950550
Bahrami, A., & Nosier, A. (2007). Interlaminar hygrothermal stresses in laminated plates. International Journal of Solids and Structures, 44(25–26), 8119–8142. https://doi.org/10.1016/j.ijsolstr.2007.06.004
Belarbi, M., Sid, M., Houari, A., Hirane, H., Daikh, A. A., Pierre, S., Bordas, A., Génie, L. D., & Biskra, U. D. (2022). On the finite element analysis of functionally graded sandwich curved beams via a new refined higher shear deformation theory. Composite Structures, 279, 4715.
Benkhedda, A., Tounsi, A., & Adda Bedia, E. A. (2008). Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates. Composite Structures, 82(4), 629–635. https://doi.org/10.1016/j.compstruct.2007.04.013
Biswal, M., Sahu, S. K., & Asha, A. V. (2016). Hygrothermal effects on buckling of composite shell-experimental and FEM results. Steel Composite Structure. https://doi.org/10.12989/scs.2016.22.6.1445
Can, N., Kurgan, N., & Hassan, A. (2020). Buckling analysis of functionally graded plates using finite element analysis. International Journal of Engineering and Applied Sciences, 12(1), 43–56.
Chen, D., Yang, J., & Kitipornchai, S. (2017). Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams. Composites Science and Technology. https://doi.org/10.1016/j.compscitech.2017.02.008
Cinefra, M., Petrolo, M., Li, G., & Carrera, E. (2017). Variable kinematic shell elements for composite laminates accounting for hygrothermal effects. Journal of Thermal Stresses, 40, 5739. https://doi.org/10.1080/01495739.2017.1360165
Demirhan, P. A., & Taskin, V. (2019). Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach. Composites, Part B: Engineering. https://doi.org/10.1016/j.compositesb.2018.12.020
Ghayesh, M. H. (2019). International journal of engineering science viscoelastic dynamics of axially FG microbeams. International Journal of Engineering Science, 135, 75–85. https://doi.org/10.1016/j.ijengsci.2018.10.005
Ghayesh, M. H., Kazemirad, S., Darabi, M. A., & Woo, P. (2012). Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system. Archive of Applied Mechanics, 2012, 317–331. https://doi.org/10.1007/s00419-011-0558-4
Hunungare, P. (2017). Numerical Analysis of hygrothermal effect on laminated composite plates Pranoti Hunungare. International Research Journal of Engineering and Technology, 2017, 1984–1991.
Journal, A. I., Gupta, A., & Talha, M. (2018). Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates. Mechanics Based Design of Structures and Machines. https://doi.org/10.1080/15397734.2018.1449656
Kant, T., & Swaminathan, K. (2002). Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Composite Structures, 56(4), 329–344. https://doi.org/10.1016/S0263-8223(02)00017-X
Kumar, R., Lal, A., Singh, B. N., & Singh, J. (2019). Meshfree approach on buckling and free vibration analysis of porous FGM plate with proposed IHHSDT resting on the foundation. Curved and Layered Structures, 6, 192–211.
Li, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W., & Liu, M. (2018). Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets. Composite Structures, 204(January), 114–130. https://doi.org/10.1016/j.compstruct.2018.07.059
Lo, S. H., Zhen, W., Cheung, Y. K., & Wanji, C. (2010). Hygrothermal effects on multilayered composite plates using a refined higher order theory. Composite Structures, 92(3), 633–646. https://doi.org/10.1016/j.compstruct.2009.09.034
Merdaci, S., Adda, H. M., Hakima, B., & Dimitri, R. (2021). Higher-order free vibration analysis of porous functionally graded plates. Journal of Composites Science, 5, 305.
Merdaci, S., & Belghoul, H. (2019). High-order shear theory for static analysis of functionally graded plates with porosities. Comptes Rendus Mecanique, 347(3), 207–217. https://doi.org/10.1016/j.crme.2019.01.001
Merdaci, S., & Mostefa, A. H. (2020). Influence of porosity on the analysis of sandwich plates FGM using of high order shear-deformation theory. Frattura Ed Integrita Strutturale, 14(51), 199–214. https://doi.org/10.3221/IGF-ESIS.51.16
Naik, N. S., & Sayyad, A. S. (2020). Analysis of laminated plates subjected to mechanical and hygrothermal environmental loads using fifth-order shear and normal deformation theory. International Journal of Applied Mechanics, 12, 3. https://doi.org/10.1142/S1758825120500283
Natarajan, S., Deogekar, P. S., Manickam, G., & Belouettar, S. (2014). Hygrothermal effects on the free vibration and buckling of laminated composites with cutouts. Composite Structure, 108, 848–855. https://doi.org/10.1016/j.compstruct.2013.10.009
Noor, A. K., & Scott Burton, W. (1990). Three-dimensional solutions for antisymmetrically laminated anisotropic plates. Journal of Applied Mechanics, 57(1), 182–188. https://doi.org/10.1115/1.2888300
Pagano, N. J. (1970). Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials, 4(1), 20–34. https://doi.org/10.1177/002199837000400102
Panda, H. S., Sahu, S. K., & Parhi, P. K. (2013). Hygrothermal effects on free vibration of delaminated woven fiber composite plates–numerical and experimental results. Composite Structures, 96, 502–513. https://doi.org/10.1016/j.compstruct.2012.08.057
Parhi, P. K., Bhattacharyya, S. K., & Sinha, P. K. (2001). Hygrothermal effects on the dynamic behavior of multiple delaminated composite plates and shells. Journal of Sound and Vibration, 248(2), 195–214. https://doi.org/10.1006/jsvi.2000.3506
Patel, B. P., Ganapathi, M., & Makhecha, D. P. (2002). Hygrothermal effects on the structural behaviour of thick composite laminates using higher-order theory. Composite Structures, 56(1), 25–34. https://doi.org/10.1016/S0263-8223(01)00182-9
Pervez, T., Seibi, A. C., & Al-Jahwari, F. K. S. (2005). Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory. Composite Structures, 71(3–4), 414–422. https://doi.org/10.1016/j.compstruct.2005.09.014
Qian, L. F., Batra, R. C., & Chen, L. M. (2004). Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method. Composites Part B: Engineering, 35(6–8), 685–697. https://doi.org/10.1016/j.compositesb.2004.02.004
Ram, K. S. S., & Sinha, P. K. (1992). Hygrothermal effects on the free vibration of laminated composite plates. Journal of Sound and Vibration, 158(1), 133–148. https://doi.org/10.1016/0022-460X(92)90669-O
Reddy, J. N. (1984). A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics, Transactions ASME, 51(4), 745–752. https://doi.org/10.1115/1.3167719
Saidi, A. R., Bahaadini, R., & Majidi-mozafari, K. (2019). On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading. Composites, Part B: Engineering. https://doi.org/10.1016/j.compositesb.2019.01.074
Saidi, A. R., & Naderi, A. (2017). Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. https://doi.org/10.1177/0954406217716197
Sheikh, A. H., & Chakrabarti, A. (2003). A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates. Finite Elements in Analysis and Design, 39(9), 883–903. https://doi.org/10.1016/S0168-874X(02)00137-3
Shen, H. S. (2001). Hygrothermal effects on the postbuckling of shear deformable laminated plates. International Journal of Mechanical Sciences, 43(5), 1259–1281. https://doi.org/10.1016/S0020-7403(00)00058-8
Shen, H.-S. (2002). Hygrothermal effects on the nonlinear bending of shear deformable laminated plates. Journal of Engineering Mechanics, 128(4), 493–496. https://doi.org/10.1061/(asce)0733-9399(2002)128:4(493)
Shukla, V., & Singh, J. (2020). Modeling and analysis of cross-ply and angle-ply laminated plates under patch loads using RBF based meshfree method and new HSDT. Computers and Mathematics with Applications, 79(8), 2240–2257. https://doi.org/10.1016/j.camwa.2019.10.026
Singh, B. N., & Verma, V. K. (2009). Hygrothermal effects on the buckling of laminated composite plates with random geometric and material properties. Journal of Reinforced Plastics and Composites, 28(4), 409–427. https://doi.org/10.1177/0731684407084991
Singh, S. K., & Chakrabarti, A. (2011). Hygrothermal analysis of laminated composite plates by using efficient higher order shear deformation theory. Journal of Reinforced Plastics and Composites, 3(1), 85–95.
Slimane, M., Mostefa, H., Mohamed, M., & Hakima, B. (2020). ScienceDirect effects of even pores distribution of functionally graded plate porous rectangular and square. Procedia Structural Integrity, 26, 35–45. https://doi.org/10.1016/j.prostr.2020.06.006
Static, I. O. F. (2017). Static analysis of a composite laminated plate static analysis of a composite laminated plate.
Subramani, M., Arumugam, A. B., & Ramamoorthy, M. (2017). Vibration analysis of carbon fiber reinforced laminated composite skin with glass honeycomb sandwich beam using HSDT. Periodica Polytechnica Mechanical Engineering, 61(3), 213–224. https://doi.org/10.3311/PPme.9747
Tran, T. T., Pham, Q., & Nguyen-thoi, T. (2020). Dynamic analysis of functionally graded porous plates resting on elastic foundation taking into mass subjected to moving loads using an edge-based smoothed finite element method. Hindawi Shock and Vibration, 2020, 8853920. https://doi.org/10.1155/2020/8853920
Wang, X., Dong, K., & Wang, X. Y. (2005). Hygrothermal effect on dynamic interlaminar stresses in laminated plates with piezoelectric actuators. Composite Structures, 71(2), 220–228. https://doi.org/10.1016/j.compstruct.2004.10.004
Wang, Y. Q., & Zu, J. W. (2017). Vibration characteristics of moving sigmoid functionally graded plates containing porosities. International Journal of Mechanics and Materials in Design. https://doi.org/10.1007/s10999-017-9385-2
Wattanasakulpong, N., & Ungbhakorn, V. (2014). Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology, 32(1), 111–120. https://doi.org/10.1016/j.ast.2013.12.002
Wosu, S. N., Hui, D., & Daniel, L. (2012). Composites: Part B Hygrothermal effects on the dynamic compressive properties of graphite/epoxy composite material. Composites, Part B: Engineering, 43(3), 841–855. https://doi.org/10.1016/j.compositesb.2011.11.045
Yüksel, Y. Z., & Akbaş, D. (2021). Hygrothermal stress analysis of laminated composite porous plates. Structural Engineering and Mechanics, 80(1), 1–13. https://doi.org/10.12989/sem.2021.80.1.001
Zenkour, A. M. (2018). A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities. Composite Structures. https://doi.org/10.1016/j.compstruct.2018.05.147
Ziya, Y. (2018). Free vibration analysis of a cross-ply laminated plate in thermal environment. International Journal of Engineering and Applied Sciences, 10(3), 176–189.
Funding
This research received no specific grant from any funding agency.
Author information
Authors and Affiliations
Contributions
First author have done the research work and analyses all the results. Second author have provided the guidelines, ideas and formatted the entire paper.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kumar, R., Kumar, A. Flexural analysis of laminated composite porous plate. Asian J Civ Eng 24, 673–692 (2023). https://doi.org/10.1007/s42107-022-00523-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42107-022-00523-y