The nonlinear static bending analysis of microplates resting on imperfect Pasternak elastic foundations is carried out in this paper. The finite element method based on the modified couple stress theory is used to derive the nonlinear finite element formulations. The present theory and mathematical model are validated by comparisons of this work’s results with those of other reputable publications, which show a very good agreement. The influences of length-scale parameter, nonlinearity, elastic foundation parameters, imperfect foundations, and boundary conditions on the nonlinear static bending response of microplates are then explored. The computed data of this study is very intriguing, particularly the interaction of the microplate with the imperfect elastic foundation, and this helps us better understand the mechanical behavior of this structure.
Révisé le :
Accepté le :
Publié le :
Nguyen Thai Dung 1 ; Le Minh Thai 1 ; Tran Van Ke 2 ; Truong Thi Huong Huyen 2 ; Phung Van Minh 2
CC-BY 4.0
@article{CRMECA_2022__350_G1_121_0,
author = {Nguyen Thai Dung and Le Minh Thai and Tran Van Ke and Truong Thi Huong Huyen and Phung Van Minh},
title = {Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory},
journal = {Comptes Rendus. M\'ecanique},
pages = {121--141},
publisher = {Acad\'emie des sciences, Paris},
volume = {350},
year = {2022},
doi = {10.5802/crmeca.105},
language = {en},
}
TY - JOUR AU - Nguyen Thai Dung AU - Le Minh Thai AU - Tran Van Ke AU - Truong Thi Huong Huyen AU - Phung Van Minh TI - Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory JO - Comptes Rendus. Mécanique PY - 2022 SP - 121 EP - 141 VL - 350 PB - Académie des sciences, Paris DO - 10.5802/crmeca.105 LA - en ID - CRMECA_2022__350_G1_121_0 ER -
%0 Journal Article %A Nguyen Thai Dung %A Le Minh Thai %A Tran Van Ke %A Truong Thi Huong Huyen %A Phung Van Minh %T Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory %J Comptes Rendus. Mécanique %D 2022 %P 121-141 %V 350 %I Académie des sciences, Paris %R 10.5802/crmeca.105 %G en %F CRMECA_2022__350_G1_121_0
Nguyen Thai Dung; Le Minh Thai; Tran Van Ke; Truong Thi Huong Huyen; Phung Van Minh. Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 121-141. doi : 10.5802/crmeca.105. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.105/
[1] Micro- and nano-fibers by electrospinning technology: processing, properties, and applications, Micromanufacturing Engineering and Technology, William Andrew, Oxford, UK, 2015, pp. 513-548 | DOI
[2] Application of micro- and nanotechnology in photovoltaics, Compr. Renew. Energy, Volume 1 (2012), pp. 515-531 | DOI
[3] New micro- and nanotechnologies for electrochemical biosensor development, Advanced Biosensors for Health Care Applications, Elsevier, Amsterdam, Netherlands, 2019, pp. 279-313 | DOI
[4] Biomedical optics and lasers, Introduction to Biomedical Engineering, Academic Press, Cambridge, MA, USA, 2011, pp. 1111-1173
[5] Types of nanostructures, Interface Sci. Technol., Volume 28 (2019), pp. 29-80 | DOI
[6] Strain gradient plasticity: Theory and experiment, Acta Metall. Mater., Volume 42 (1994) no. 2, pp. 475-487 | DOI
[7] Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids, Volume 51 (2003) no. 8, pp. 1477-1508 | DOI | Zbl
[8] Finite Element Method for Plates/Shells BT — Engineering Computation of Structures: The Finite Element Method (M. A. Neto; A. Amaro; L. Roseiro; J. Cirne; R. Leal, eds.), Springer International Publishing, Cham, 2015, pp. 195-232 | DOI
[9] Nonlocal theories for bending, buckling and vibration of beams, Int. J. Eng. Sci., Volume 45 (2007) no. 2, pp. 288-307 | DOI | Zbl
[10] Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., Volume 39 (2002) no. 10, pp. 2731-2743 | DOI | Zbl
[11] Nonlocal theories in continuum mechanics, Acta Polytech., Volume 44 (2004), pp. 16-34 | DOI
[12] A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids, Volume 78 (2015), pp. 298-313 | DOI | MR | Zbl
[13] The modified couple stress functionally graded Timoshenko beam formulation, Mater. Des., Volume 32 (2011) no. 3, pp. 1435-1443 | DOI
[14] Modified couple stress theory applied to dynamic analysis of composite laminated beams by considering different beam theories, Int. J. Eng. Sci., Volume 87 (2015), pp. 83-102 | DOI
[15] Dynamic response of thin strain gradient elastic beams, Int. J. Mech. Sci., Volume 58 (2012) no. 1, pp. 27-33 | DOI
[16] A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, J. Mech. Phys. Solids, Volume 56 (2008) no. 12, pp. 3379-3391 | DOI | MR | Zbl
[17] Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory, Int. J. Mech. Sci., Volume 57 (2012) no. 1, pp. 63-73 | DOI
[18] Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory, J. Sound Vib., Volume 331 (2012) no. 1, pp. 94-106 | DOI
[19] Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory, Compos. Struct., Volume 95 (2013), pp. 142-153 | DOI
[20] A size-dependent model for bi-layered Kirchhoff micro-plate based on strain gradient elasticity theory, Compos. Struct., Volume 113 (2014) no. 1, pp. 272-280 | DOI
[21] Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory, Eur. J. Mech. A/Solids, Volume 49 (2015), pp. 251-267 | DOI | MR | Zbl
[22] On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Compos. Struct., Volume 95 (2013), pp. 430-442 | DOI
[23] Modelling of the flexoelectric effect on rotating nanobeams with geometrical imperfection, J. Braz. Soc. Mech. Sci. Eng., Volume 43 (2021) no. 11, 510 | DOI
[24] A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory, Comput. Methods Appl. Mech. Eng., Volume 313 (2017), pp. 904-940 | DOI | MR | Zbl
[25] The size-dependent analysis of microplates via a newly developed shear deformation theory, Acta Mech., Volume 230 (2019) no. 1, pp. 49-65 | DOI | MR | Zbl
[26] Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory, Int. J. Eng. Sci., Volume 97 (2015), pp. 40-59 | DOI | MR | Zbl
[27] Finite element analyses of the modified strain gradient theory based Kirchhoff microplates, Surfaces, Volume 4 (2021) no. 2, pp. 115-156 | DOI
[28] Nonlinear dynamics of a microscale beam based on the modified couple stress theory, Compos. B: Eng., Volume 50 (2013), pp. 318-324 | DOI
[29] Geometrically nonlinear micro-plate formulation based on the modified couple stress theory, Int. J. Eng. Sci., Volume 51 (2012), pp. 292-309 | DOI | MR | Zbl
[30] Nonlinear bending of size-dependent circular microplates based on the modified couple stress theory, Arch. Appl. Mech., Volume 84 (2014) no. 3, pp. 391-400 | DOI | Zbl
[31] Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory, Int. J. Mech. Sci., Volume 87 (2014), pp. 150-162 | DOI
[32] Nonlinear static and dynamic buckling analyses of imperfect fgp cylindrical shells resting on nonlinear elastic foundation under axial compression, Int. J. Struct. Stab. Dyn., Volume 20 (2020) no. 7, 2071005 | DOI | MR
[33] An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation, Appl. Math. Model., Volume 39 (2015) no. 13, pp. 3814-3845 | DOI | MR | Zbl
[34] Buckling of piezoelectric sandwich microplates with arbitrary in-plane BCs rested on foundation: effect of hygro-thermo-electro-elastic field, Eur. Phys. J. Plus, Volume 135 (2020) no. 1, 61 | DOI
[35] Static bending and free vibration of organic solar cell resting on Winkler–Pasternak elastic foundation through the modified strain gradient theory, Eur. J. Mech. - A/Solids, Volume 78 (2019), 103852 | MR | Zbl
[36] Static and stability characteristics of geometrically imperfect FGM plates resting on pasternak elastic foundation with microstructural defect, Arab. J. Sci. Eng., Volume 43 (2018) no. 9, pp. 4931-4947 | DOI
[37] Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory, Steel Compos. Struct., Volume 27 (2018) no. 3, pp. 311-325
[38] Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects, Arch. Appl. Mech., Volume 92 (2022) no. 1, pp. 163-182 | DOI
[39] Buckling and post-buckling of symmetric functionally graded microplate lying on nonlinear elastic foundation based on modified couple stress theory, Int. J. Struct. Stab. Dyn., Volume 18 (2018) no. 09, 1850110 | MR
[40] A comprehensive study on the size-dependent hygrothermal analysis of exponentially graded microplates on elastic foundations, Mech. Adv. Mater. Struct., Volume 27 (2020) no. 10, pp. 816-830 | DOI
[41] Size-dependent instability of organic solar cell resting on Winkler–Pasternak elastic foundation based on the modified strain gradient theory, Int. J. Mech. Sci., Volume 177 (2020), 105306 | DOI
[42] A finite element formulation and nonlocal theory for the static and free vibration analysis of the sandwich functionally graded nanoplates resting on elastic foundation, J. Nanomater., Volume 2020 (2020), 8786373 | DOI
[43] Forced vibration analysis of laminated composite shells reinforced with graphene nanoplatelets using finite element method, Adv. Civ. Eng., Volume 2020 (2020), 1471037 | DOI
[44] High frequency modes meshfree analysis of Reissner–Mindlin plates, J. Sci. Adv. Mater. Devices, Volume 1 (2016) no. 3, pp. 400-412 | DOI
[45] Numerical investigation on static bending and free vibration responses of two-layer variable thickness plates with shear connectors, Iran. J. Sci. Technol. - Trans. Mech. Eng. (2022) | DOI
[46] An improved treatment of transverse shear in the mindlin-type four-node quadrilateral element, Comput. Methods Appl. Mech. Eng., Volume 39 (1983) no. 3, pp. 311-335 | DOI | Zbl
[47] Historical development of the Newton–Raphson method, SIAM Rev., Volume 37 (1995) no. 4, pp. 531-551 | DOI | MR | Zbl
[48] Nonlinear static bending and free vibration analysis of bidirectional functionally graded material plates, Int. J. Aerosp. Eng., Volume 2020 (2020), 8831366 | DOI
Cité par Sources :
Commentaires - Politique