Hygro-thermo-mechanical bending of symmetric and asymmetric FGM Sandwich Plates with/without middle core Resting on Pasternak Foundation
Document Type : Research Paper
Authors
Civil Engineering and Public Works Department, Faculty of Technology, Djillali Liabes University, Sidi Bel Abbes 22000, Algeria
Abstract
The bending of sandwich plates made of functionally graded material (FGM) that are supported by variable two-parameter elastic foundations under hygro-thermo-mechanical loads is covered in this paper. This study's methodology was based on refined trigonometric shear deformable plate theory (RTSDT) and four-variable refined plate theory. The governing equation was then obtained by introducing the virtual work principle and solving it using a Navier solution. We evaluated our intriguing results with several models found in the literature after we had obtained them. Lastly, we talked about the influence of the elastic foundation parameters, the plate aspect ratio, the power-law index, temperature and moisture differential, and the layer thickness ratio on symmetrical and asymmetrical plates, with or without a middle core.
Keywords
- functionally graded materials
- symmetrical sandwich plate
- asymmetrical sandwich plate
- middle core
- thermo-mechanical bending
- deflection and stress
Main Subjects
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[2] R. A. Alghanmi, R. H. Aljaghthami, A Four-Variable Shear Deformation Theory for the Static Analysis of FG Sandwich Plates with Different Porosity Models, Mathematical and Computational Applications, Vol. 29, No. 2, pp. 20, 2024.
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[9] S. Merdaci, A. H. Mostefa, Influence of porosity on the analysis of sandwich plates FGM using of high order shear-deformation theory, Frattura ed Integrità Strutturale, Vol. 14, No. 51, pp. 199-214, 2019/11/25/, 2019. en
[10] B. Adhikari, P. Dash, B. N. Singh, Buckling analysis of porous FGM sandwich plates under various types nonuniform edge compression based on higher order shear deformation theory, Composite Structures, Vol. 251, pp. 112597, 2020/11//, 2020. en
[11] E. Njim, S. Bakhy, M. Al-Waily, Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation, Archives of Materials Science and Engineering, Vol. 111, No. 2, pp. 49-65, 2021.
[12] J. Liu, C. Hao, W. Ye, F. Yang, G. Lin, Free vibration and transient dynamic response of functionally graded sandwich plates with power-law nonhomogeneity by the scaled boundary finite element method, Computer Methods in Applied Mechanics and Engineering, Vol. 376, pp. 113665, 2021/04/01/, 2021. en
[13] N. Sharma, P. Kumar Swain, D. Kumar Maiti, B. Nath Singh, Vibration and uncertainty analysis of functionally graded sandwich plate using layerwise theory, AIAA Journal, Vol. 60, No. 6, pp. 3402-3423, 2022.
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[16] L. Kurpa, T. Shmatko, J. Awrejcewicz, G. Timchenko, I. Morachkovska, Analysis of free vibration of porous power-law and sigmoid functionally graded sandwich plates by the R-functions method, Journal of Applied and Computational Mechanics, Vol. 9, No. 4, pp. 1144-1155, 2023.
[17] K. Swaminathan, S. Hirannaiah, T. Rajanna, Vibration and stability characteristics of functionally graded sandwich plates with/without porosity subjected to localized edge loadings, Mechanics Based Design of Structures and Machines, Vol. 51, No. 11, pp. 6254-6292, 2023.
[18] P. Van Vinh, A. Tounsi, Free vibration characteristics of three-phases functionally graded sandwich plates using novel nth-order shear deformation theory, Computers and Concrete, Vol. 33, No. 1, pp. 27-39, 2024.
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[20] Z. Huang, M. Han, X. Wang, F. Chu, Free Vibration of Functionally Graded Material Sandwich Plates with Soft Core, Journal of Vibration Engineering & Technologies, Vol. 12, No. 3, pp. 5119-5131, 2024.
[21] A. M. Zenkour, M. Sobhy, Thermal buckling of various types of FGM sandwich plates, Composite Structures, Vol. 93, No. 1, pp. 93-102, 2010/12//, 2010. en
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[23] A. Benbakhti, M. B. Bouiadjra, N. Retiel, A. Tounsi, A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates, Steel Compos. Struct, Vol. 22, No. 5, pp. 975-999, 2016.
[24] D. Li, Z. Deng, G. Chen, H. Xiao, L. Zhu, Thermomechanical bending analysis of sandwich plates with both functionally graded face sheets and functionally graded core, Composite Structures, Vol. 169, pp. 29-41, 2017/06//, 2017. en
[25] S. J. Singh, S. P. Harsha, Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach, Thin-Walled Structures, Vol. 150, pp. 106668, 2020/05//, 2020. en
[26] A. A. Daikh, I. Bensaid, A. M. Zenkour, Temperature dependent thermomechanical bending response of functionally graded sandwich plates, Engineering Research Express, Vol. 2, No. 1, pp. 015006, 2020/01/06/, 2020. en
[27] S. Mahmoud, E. Ghandourah, A. Algarni, M. Balubaid, A. Tounsi, F. Bourada, On thermo-mechanical bending response of porous functionally graded sandwich plates via a simple integral plate model, Archives of Civil and Mechanical Engineering, Vol. 22, No. 4, pp. 186, 2022.
[28] M. Han, Z. Li, Z. Huang, X. Wang, W. Gao, Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates, Materials, Vol. 16, No. 13, pp. 4683, 2023.
[29] M. Han, J. Huang, Z. Huang, X. Wang, Bending Analysis of Asymmetric Functionally Graded Material Sandwich Plates in Thermal Environments, Materials, Vol. 16, No. 13, pp. 4682, 2023.
[30] S. Natarajan, G. Manickam, Bending and vibration of functionally graded material sandwich plates using an accurate theory, Finite Elements in Analysis and Design, Vol. 57, pp. 32-42, 2012.
[31] E. Reissner, On tranverse bending of plates, including the effect of transverse shear deformation, 1974.
[32] J. N. Reddy, A Simple Higher-Order Theory for Laminated Composite Plates, Journal of Applied Mechanics, Vol. 51, No. 4, pp. 745-752, 1984/12/01/, 1984.
[33] M. Touratier, An efficient standard plate theory, International Journal of Engineering Science, Vol. 29, No. 8, pp. 901-916, 1991/01/01/, 1991. en
[34] I. M. Mudhaffar, A. Tounsi, A. Chikh, M. A. Al-Osta, M. M. Al-Zahrani, S. U. Al-Dulaijan, Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation, in Proceeding of, Elsevier, pp. 2177-2189.
[35] Y. Beldjelili, A. Tounsi, S. R. Mahmoud, Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory, Smart Structures and Systems, Vol. 18, No. 4, pp. 755-786, 2016/10//, 2016.
[36] D. Li, Z. Deng, H. Xiao, Thermomechanical bending analysis of functionally graded sandwich plates using four-variable refined plate theory, Composites Part B: Engineering, Vol. 106, pp. 107-119, 2016.
[37] A. A. Daikh, A. M. Zenkour, Bending of Functionally Graded Sandwich Nanoplates Resting on Pasternak Foundation under Different Boundary Conditions, Journal of Applied and Computational Mechanics, Vol. 6, No. Special Issue, 2020 décembre, 2020. en
[2] R. A. Alghanmi, R. H. Aljaghthami, A Four-Variable Shear Deformation Theory for the Static Analysis of FG Sandwich Plates with Different Porosity Models, Mathematical and Computational Applications, Vol. 29, No. 2, pp. 20, 2024.
[3] M. Koizumi, FGM activities in Japan, Composites Part B: Engineering, Vol. 28, No. 1-2, pp. 1-4, 1997/01//, 1997. en
[4] A. D. Kerr, Elastic and viscoelastic foundation models, 1964.
[5] T. A. Anderson, A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere, Composite Structures, Vol. 60, No. 3, pp. 265-274, 2003.
[6] H. H. Abdelaziz, H. A. Atmane, I. Mechab, L. Boumia, A. Tounsi, A. B. E. Abbas, Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory, Chinese Journal of Aeronautics, Vol. 24, No. 4, pp. 434-448, 2011/08//, 2011. en
[7] Q. Li, V. P. Iu, K. P. Kou, Three-dimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration, Vol. 311, No. 1-2, pp. 498-515, 2008/03//, 2008. en
[8] A. Keddouri, L. Hadji, A. Tounsi, Static analysis of functionally graded sandwich plates with porosities, Advances in materials Research, Vol. 8, No. 3, pp. 155-177, 2019/09/25/, 2019. en
[9] S. Merdaci, A. H. Mostefa, Influence of porosity on the analysis of sandwich plates FGM using of high order shear-deformation theory, Frattura ed Integrità Strutturale, Vol. 14, No. 51, pp. 199-214, 2019/11/25/, 2019. en
[10] B. Adhikari, P. Dash, B. N. Singh, Buckling analysis of porous FGM sandwich plates under various types nonuniform edge compression based on higher order shear deformation theory, Composite Structures, Vol. 251, pp. 112597, 2020/11//, 2020. en
[11] E. Njim, S. Bakhy, M. Al-Waily, Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation, Archives of Materials Science and Engineering, Vol. 111, No. 2, pp. 49-65, 2021.
[12] J. Liu, C. Hao, W. Ye, F. Yang, G. Lin, Free vibration and transient dynamic response of functionally graded sandwich plates with power-law nonhomogeneity by the scaled boundary finite element method, Computer Methods in Applied Mechanics and Engineering, Vol. 376, pp. 113665, 2021/04/01/, 2021. en
[13] N. Sharma, P. Kumar Swain, D. Kumar Maiti, B. Nath Singh, Vibration and uncertainty analysis of functionally graded sandwich plate using layerwise theory, AIAA Journal, Vol. 60, No. 6, pp. 3402-3423, 2022.
[14] H. Georges, G. Meyer, C. Mittelstedt, W. Becker, 2D Elasticity solution for sandwich panels with functionally graded lattice cores, Composite Structures, Vol. 300, pp. 116045, 2022.
[15] I. Benameur, Y. Beldjelili, A. Tounsi, Analytical and finite element method for the bending analysis of the thick porous functionally graded sandwich plate including thickness stretching effect, Structural Engineering and Mechanics, Vol. 85, No. 5, pp. 593-605, 2023/01/01/, 2023. en
[16] L. Kurpa, T. Shmatko, J. Awrejcewicz, G. Timchenko, I. Morachkovska, Analysis of free vibration of porous power-law and sigmoid functionally graded sandwich plates by the R-functions method, Journal of Applied and Computational Mechanics, Vol. 9, No. 4, pp. 1144-1155, 2023.
[17] K. Swaminathan, S. Hirannaiah, T. Rajanna, Vibration and stability characteristics of functionally graded sandwich plates with/without porosity subjected to localized edge loadings, Mechanics Based Design of Structures and Machines, Vol. 51, No. 11, pp. 6254-6292, 2023.
[18] P. Van Vinh, A. Tounsi, Free vibration characteristics of three-phases functionally graded sandwich plates using novel nth-order shear deformation theory, Computers and Concrete, Vol. 33, No. 1, pp. 27-39, 2024.
[19] L. Hadji, V. Plevris, R. Madan, H. Ait Atmane, Multi-directional functionally graded sandwich plates: buckling and free vibration analysis with refined plate models under various boundary conditions, Computation, Vol. 12, No. 4, pp. 65, 2024.
[20] Z. Huang, M. Han, X. Wang, F. Chu, Free Vibration of Functionally Graded Material Sandwich Plates with Soft Core, Journal of Vibration Engineering & Technologies, Vol. 12, No. 3, pp. 5119-5131, 2024.
[21] A. M. Zenkour, M. Sobhy, Thermal buckling of various types of FGM sandwich plates, Composite Structures, Vol. 93, No. 1, pp. 93-102, 2010/12//, 2010. en
[22] A. Tounsi, M. S. A. Houari, S. Benyoucef, E. A. Adda Bedia, A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates, Aerospace Science and Technology, Vol. 24, No. 1, pp. 209-220, 2013, 2013.
[23] A. Benbakhti, M. B. Bouiadjra, N. Retiel, A. Tounsi, A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates, Steel Compos. Struct, Vol. 22, No. 5, pp. 975-999, 2016.
[24] D. Li, Z. Deng, G. Chen, H. Xiao, L. Zhu, Thermomechanical bending analysis of sandwich plates with both functionally graded face sheets and functionally graded core, Composite Structures, Vol. 169, pp. 29-41, 2017/06//, 2017. en
[25] S. J. Singh, S. P. Harsha, Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach, Thin-Walled Structures, Vol. 150, pp. 106668, 2020/05//, 2020. en
[26] A. A. Daikh, I. Bensaid, A. M. Zenkour, Temperature dependent thermomechanical bending response of functionally graded sandwich plates, Engineering Research Express, Vol. 2, No. 1, pp. 015006, 2020/01/06/, 2020. en
[27] S. Mahmoud, E. Ghandourah, A. Algarni, M. Balubaid, A. Tounsi, F. Bourada, On thermo-mechanical bending response of porous functionally graded sandwich plates via a simple integral plate model, Archives of Civil and Mechanical Engineering, Vol. 22, No. 4, pp. 186, 2022.
[28] M. Han, Z. Li, Z. Huang, X. Wang, W. Gao, Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates, Materials, Vol. 16, No. 13, pp. 4683, 2023.
[29] M. Han, J. Huang, Z. Huang, X. Wang, Bending Analysis of Asymmetric Functionally Graded Material Sandwich Plates in Thermal Environments, Materials, Vol. 16, No. 13, pp. 4682, 2023.
[30] S. Natarajan, G. Manickam, Bending and vibration of functionally graded material sandwich plates using an accurate theory, Finite Elements in Analysis and Design, Vol. 57, pp. 32-42, 2012.
[31] E. Reissner, On tranverse bending of plates, including the effect of transverse shear deformation, 1974.
[32] J. N. Reddy, A Simple Higher-Order Theory for Laminated Composite Plates, Journal of Applied Mechanics, Vol. 51, No. 4, pp. 745-752, 1984/12/01/, 1984.
[33] M. Touratier, An efficient standard plate theory, International Journal of Engineering Science, Vol. 29, No. 8, pp. 901-916, 1991/01/01/, 1991. en
[34] I. M. Mudhaffar, A. Tounsi, A. Chikh, M. A. Al-Osta, M. M. Al-Zahrani, S. U. Al-Dulaijan, Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation, in Proceeding of, Elsevier, pp. 2177-2189.
[35] Y. Beldjelili, A. Tounsi, S. R. Mahmoud, Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory, Smart Structures and Systems, Vol. 18, No. 4, pp. 755-786, 2016/10//, 2016.
[36] D. Li, Z. Deng, H. Xiao, Thermomechanical bending analysis of functionally graded sandwich plates using four-variable refined plate theory, Composites Part B: Engineering, Vol. 106, pp. 107-119, 2016.
[37] A. A. Daikh, A. M. Zenkour, Bending of Functionally Graded Sandwich Nanoplates Resting on Pasternak Foundation under Different Boundary Conditions, Journal of Applied and Computational Mechanics, Vol. 6, No. Special Issue, 2020 décembre, 2020. en
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Volume 56, Issue 1
January 2025Pages 43-68
- Receive Date: 16 August 2024
- Revise Date: 30 August 2024
- Accept Date: 08 September 2024