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Size-Dependent Hygro-Thermal Buckling of Porous FGM Sandwich Microplates and Microbeams Using a Novel Four-Variable Shear Deformation Theory

Mohammed Sobhy

Department of Mathematics and Statistics, Faculty of Science, King Faisal University, P. O. Box 400, Hofuf 31982, Saudi Arabia

Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

E-mail Address: msobhy@kfu.edu.sa

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https://doi.org/10.1142/S1758825120500179Cited by:38 (Source: Crossref)

Abstract

Based on a new shear deformation theory and the modified couple stress theory, in this paper, the hygro-thermal buckling of porous FGM sandwich microplates and microbeams is investigated. Unlike the classical elasticity theory, the present model involves a material length scale parameter, and, thereby, can capture the small size effect. The four-variable shear deformation theory with a new shape function is utilized to derive the governing stability equations for the microplates and microbeams from the principle of virtual work. The present microstructures are composed of three layers and subjected to hygro-thermal conditions. The core is assumed to be fully homogeneous and isotropic material. While, the face layers are made from porous functionally graded materials that vary only in the thickness direction. The governing equations are solved analytically to obtain the thermal buckling of FGM sandwich microplates and microbeams under humidity effects. The temperature rise and moisture concentration are graded uniformly, linearly or nonlinearly through the thickness. Comparison studies are made between the present results and those available in the literature to check the validity of the obtained formulations and results. Moreover, the effects played by the length scale parameter, power-law exponent, moisture concentration, core thickness and other parameters on the thermal buckling of microplates and microbeams are all investigated.

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References

Abazid, M. A., Alotebi, M. S. and Sobhy, M. [2018] “ A novel shear and normal deformation theory for hygrothermal bending response of FGM sandwich plates on Pasternak elastic foundation,” Structural Engineering and Mechanics 67(3), 219–232. Web of Science, Google Scholar
Abazid, M. A. and Sobhy, M. [2018] “ Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory,” Microsystem Technologies 24(2), 1227–1245. Web of Science, Google Scholar
Aifantis, E. C. [1999] “ Strain gradient interpretation of size effects,” Fracture Scaling 95, 1–4. Web of Science, Google Scholar
Akgoz, B. and Civalek, O. [2014] “ Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium,” International Journal of Engineering Science 85, 90–104. Web of Science, Google Scholar
Al-Basyouni, K. S., Tounsi, A. and Mahmoud, S. R. [2015] “ Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position,” Composite Structures 125, 621–630. Web of Science, Google Scholar
Alibeigloo, A. and Liew, K. M. [2014] “ Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity,” Composite Structures 113, 23–30. Web of Science, Google Scholar
Alibeigloo, A. and Noee, A. R. P. [2017] “ Static and free vibration analysis of sandwich cylindrical shell based on theory of elasticity and using DQM,” Acta Mechanica 228(12), 4123–4140. Web of Science, Google Scholar
Alzahrani, E. O., Zenkour, A. M. and Sobhy, M. [2013] “ Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium,” Composite Structures 105, 163–172. Web of Science, Google Scholar
Ansari, R., Gholami, R. and Sahmani, S. [2011] “ Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory,” Composite Structures 94(1), 221–228. Web of Science, Google Scholar
Ansari, R., Gholami, R. and Sahmani, S. [2014] “ Free vibration of size-dependent functionally graded microbeams based on the strain gradient reddy beam theory,” International Journal for Computational Methods in Engineering Science and Mechanics 15(5), 401–412. Google Scholar
Arbind, A. R. C. H. A. N. A., Reddy, J. N. and Srinivasa, A. R. [2014] “ Modified couple stress-based third-order theory for nonlinear analysis of functionally graded beams,” Latin American Journal of Solids and Structures 11(3), 459–487. Web of Science, Google Scholar
Asghari, M., Rahaeifard, M., Kahrobaiyan, M. H. and Ahmadian, M. T. [2011] “ The modified couple stress functionally graded Timoshenko beam formulation,” Materials and Design 32(3), 1435–1443. Web of Science, Google Scholar
Brush, D. O. and Almroth, B. O. [1975] Buckling of Bars, Plates, and Shells (McGraw-Hill, New York, 1975). Google Scholar
Chen, W. and Si, J. [2013] “ A model of composite laminated beam based on the global local theory and new modified couple-stress theory,” Composite Structures 103, 99–107. Web of Science, Google Scholar
Dehrouyeh-Semnani, A. M., Dehrouyeh, M., Torabi-Kafshgari, M. and Nikkhah-Bahrami, M. [2015] “ An investigation into size-dependent vibration damping characteristics of functionally graded viscoelastically damped sandwich microbeams,” International Journal of Engineering Science 96, 68–85. Web of Science, Google Scholar
Fleck, N. A., Muller, G. M., Ashby, M. F. and Hutchinson, J. W. [1994] “ Strain gradient plasticity: Theory and experiment,” Acta Metallurgica et Materialia 42(2), 475–487. Google Scholar
Fu, Y., Du, H. and Zhang, S. [2003] “ Functionally graded TiN/TiNi shape memory alloy films,” Materials Letters 57(20), 2995–2999. Web of Science, Google Scholar
Jung, W. Y., Park, W. T. and Han, S. C. [2014] “ Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory,” International Journal of Mechanical Sciences 87, 150–162. Web of Science, Google Scholar
Karama, M., Afaq, K. S. and Mistou, S. [2003] “ Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity,” International Journal of Solids and Structures 40(6), 1525–1546. Web of Science, Google Scholar
Kim, J. and Reddy, J. N. [2013] “ Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory,” Composite Structures 103, 86–98. Web of Science, Google Scholar
Lam, D. C., Yang, F., Chong, A. C. M., Wang, J. and Tong, P. [2003] “ Experiments and theory in strain gradient elasticity,” Journal of the Mechanics and Physics of Solids 51(8), 1477–1508. Web of Science, Google Scholar
Lamuta, C., Cupolillo, A., Politano, A., Aliev, Z. S., Babanly, M. B., Chulkov, E. V. and Pagnotta, L. [2016] “ Indentation fracture toughness of single-crystal Bi₂ Te₃ topological insulators,” Nano Research 9(4), 1032–1042. Web of Science, Google Scholar
Lin, H. G., Cao, D. Q. and Xu, Y. Q. [2018] “ Vibration, buckling and aeroelastic analyses of functionally graded multilayer graphene-nanoplatelets-reinforced composite plates embedded in piezoelectric layers,” International Journal of Applied Mechanics 10(03), 1850023. Link, Web of Science, Google Scholar
Meyers, C. A. and Hyer, M. W. [1991] “ Thermal buckling and postbuckling of symmetrically laminated composite plates,” Journal of Thermal Stresses 14(4), 519–540. Web of Science, Google Scholar
Meziane, M. A. A., Abdelaziz, H. H. and Tounsi, A. [2014] “ An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions,” Journal of Sandwich Structures and Materials 16(3), 293–318. Web of Science, Google Scholar
Mindlin, R. D. and Tiersten, H. F. [1962] “ Effects of couple-stresses in linear elasticity,” Archive for Rational Mechanics and Analysis 11(1), 415–448. Google Scholar
Mohammadi, M. and Mahani, M. F. [2015] “ An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories,” Acta Mechanica 226(10), 3477–3493. Web of Science, Google Scholar
Moita, J. S., Araújo, A. L., Soares, C. M. M. and Soares, C. A. M. [2018] “ Vibration analysis of functionally graded material sandwich structures with passive damping,” Composite Structures 183, 407–415. Web of Science, Google Scholar
Nateghi, A. and Salamat-talab, M. [2013] “ Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory,” Composite Structures 96, 97–110. Web of Science, Google Scholar
Nateghi, A., Salamat-talab, M., Rezapour, J. and Daneshian, B. [2012] “ Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory,” Applied Mathematical Modelling 36(10), 4971–4987. Web of Science, Google Scholar
Politano, A. and Chiarello, G. [2015] “ Probing the Young’s modulus and Poisson’s ratio in graphene/metal interfaces and graphite: A comparative study,” Nano Research 8(6), 1847–1856. Web of Science, Google Scholar
Radwan, A. F. [2019] “ Effects of non-linear hygrothermal conditions on the buckling of FG sandwich plates resting on elastic foundations using a hyperbolic shear deformation theory,” Journal of Sandwich Structures and Materials 21(1), 289–319. Web of Science, Google Scholar
Rahaeifard, M., Kahrobaiyan, M. H. and Ahmadian, M. T. [2009] “ Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials,” in 3rd International Conference on Micro and Nanosystems. DETC2009–86254, pp. 539–44. Google Scholar
Reddy, J. N. [1984] “ A simple higher-order theory for laminated composite plates,” Journal of Applied Mechanics 51(4), 745–752. Web of Science, Google Scholar
Sahmani, S. and Ansari, R. [2013] “ Size-dependent buckling analysis of functionally graded third-order shear deformable microbeams including thermal environment effect,” Applied Mathematical Modelling 37(23), 9499–9515. Web of Science, Google Scholar
Shariat, B. S. and Eslami, M. R. [2007] “ Buckling of thick functionally graded plates under mechanical and thermal loads,” Composite Structures 78(3), 433–439. Web of Science, Google Scholar
Shimpi, R. P. [2002] “ Refined plate theory and its variants,” AIAA Journal 40(1), 137–146. Web of Science, Google Scholar
Simsek, M., Kocaturk, T. and Akbas, S. D. [2013] “ Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory,” Composite Structures 95, 740–747. Web of Science, Google Scholar
Simsek, M. and Reddy, J. N. [2013] “ Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory,” International Journal of Engineering Science 64, 37–53. Web of Science, Google Scholar
Sobhy, M. [2013] “ Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions,” Composite Structures 99, 76–87. Web of Science, Google Scholar
Sobhy, M. [2014] “ Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions,” Acta Mechanica 225(9), 2521–2538. Web of Science, Google Scholar
Sobhy, M. [2015] “ Hygrothermal deformation of orthotropic nanoplates based on the state-space concept,” Composites Part B: Engineering 79, 224–235. Web of Science, Google Scholar
Sobhy, M. [2016a] “ Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory,” Appl. Math. Model 40, 85–99. Web of Science, Google Scholar
Sobhy, M. [2016b] “ An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment,” International Journal of Mechanical Sciences 110, 62–77. Web of Science, Google Scholar
Sobhy, M. and Alotebi, M. S. [2018] “ Transient hygrothermal analysis of FG sandwich plates lying on a visco-Pasternak foundation via a simple and accurate plate theory,” Arabian Journal for Science and Engineering 43(10), 5423–5437. Web of Science, Google Scholar
Sobhy, M. and Zenkour, A. M. [2018a] “ Nonlocal thermal and mechanical buckling of nonlinear orthotropic viscoelastic nanoplates embedded in a visco-pasternak medium,” International Journal of Applied Mechanics 10(08), 1850086. Link, Web of Science, Google Scholar
Sobhy, M. and Zenkour, A. M. [2018b] “ Thermal buckling of double-layered graphene system in humid environment,” Materials Research Express 5(1), 015028. Web of Science, Google Scholar
Sobhy, M. and Zenkour, A. M. [2019a] “ Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory,” Composite Structures 220, 289–303. Web of Science, Google Scholar
Sobhy, M. and Zenkour, A. M. [2019b] “ The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations,” Mechanics of Advanced Materials and Structures, https://doi.org/10.1080/ 15376494.2018.1482579. Web of Science, Google Scholar
Sobhy, M. and Zenkour, A. M. [2019c] “ A comprehensive study on the size-dependent hygrothermal analysis of exponentially graded microplates on elastic foundations,” Mechanics of Advanced Materials and Structures, https://doi.org/10.1080/ 15376494.2018.1499986. Web of Science, Google Scholar
Sun, Z. H., Wang, X. X., Soh, A. K., Wu, H. A. and Wang, Y. [2007] “ Bending of nanoscale structures: Inconsistency between atomistic simulation and strain gradient elasticity solution,” Computational Materials Science 40(1), 108–113. Web of Science, Google Scholar
Thai, H. T. and Choi, D. H. [2013] “ Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory,” Composite Structures 95, 142–153. Web of Science, Google Scholar
Thai, C. H., Ferreira, A. J. M., Lee, J. and Nguyen-Xuan, H. [2018] “ An efficient size-dependent computational approach for functionally graded isotropic and sandwich microplates based on modified couple stress theory and moving Kriging-based meshfree method,” International Journal of Mechanical Sciences 142, 322–338. Web of Science, Google Scholar
Thai, H. T. and Kim, S. E. [2013] “ A size-dependent functionally graded Reddy plate model based on a modified couple stress theory,” Composites Part B: Engineering 45(1), 1636–1645. Web of Science, Google Scholar
Thai, H. T. and Vo, T. P. [2013] “ A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory,” Composite Structures 96, 376–383. Web of Science, Google Scholar
Thai, H. T., Vo, T. P., Nguyen, T. K. and Lee, J. [2015] “ Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory,” Composite Structures 123, 337–349. Web of Science, Google Scholar
Touratier, M. [1991] “ An efficient standard plate theory,” International Journal of Engineering Science 29(8), 901–916. Web of Science, Google Scholar
Verre, S., Ombres, L. and Politano, A. [2017] “ Evaluation of the free-vibration frequency and the variation of the bending rigidity of graphene nanoplates: The role of the shape geometry and boundary conditions,” Journal of Nanoscience and Nanotechnology 17(12), 8827–8834. Web of Science, Google Scholar
Witvrouw, A. and Mehta, A. [2005] “ The use of functionally graded poly-SiGe layers for MEMS applications,” Mater Sci. Forum 492–493, 255–60. Web of Science, Google Scholar
Yaghoobi, H. and Yaghoobi, P. [2013] “ Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach,” Meccanica 48(8), 2019–2035. Web of Science, Google Scholar
Yang, F. A. C. M., Chong, A. C. M., Lam, D. C. C. and Tong, P. [2002] “ Couple stress based strain gradient theory for elasticity,” International Journal of Solids and Structures 39(10), 2731–2743. Web of Science, Google Scholar
Zenkour, A. M. [2005] “ A comprehensive analysis of functionally graded sandwich plates: Part 1. Deflection and stresses,” International Journal of Solids and Structures 42(18–19), 5224–5242. Web of Science, Google Scholar
Zenkour, A. M., Allam, M. N. M. and Sobhy, M. [2010] “ Effect of transverse normal and shear deformation on a fiber-reinforced viscoelastic beam resting on two-parameter elastic foundations,” International Journal of Applied Mechanics 2(01), 87–115. Link, Web of Science, Google Scholar
Zenkour, A. M. and Sobhy, M. [2010] “ Thermal buckling of various types of FGM sandwich plates,” Composite Structures 93(1), 93–102. Web of Science, Google Scholar
Zenkour, A. M. and Sobhy, M. [2011] “ Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory,” Journal of Thermal Stresses 34(11), 1119–1138. Web of Science, Google Scholar