DOI QR코드

DOI QR Code

Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium

  • 투고 : 2015.03.11
  • 심사 : 2015.07.31
  • 발행 : 2015.09.10

초록

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

키워드

참고문헌

  1. Ameur, M., Tounsi, A., Mechab, I. and El Bedia, A.A., (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15, 1405-1414. https://doi.org/10.1007/s12205-011-1361-z
  2. Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H. and Adda Bedia, E.A., (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46, 425-434. https://doi.org/10.1007/s11029-010-9159-5
  3. Della Croce, L. and Venini, P. (2004), "Finite elements for functionally graded Reissner-Mindlin plates", Comput. Meth. Appl. Mech. Eng., 193, 705-725. https://doi.org/10.1016/j.cma.2003.09.014
  4. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  5. Fares, M.E., Elmarghany, M.K. and Atta, D. (2009), "An efficient and simple refined theory for bending and vibration of functionally graded plates", Compos. Struct., 91, 296-305. https://doi.org/10.1016/j.compstruct.2009.05.008
  6. Javaheri, R. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82, 277-283.
  7. 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", Int. J. Solids Struct., 40, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  8. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  9. Merdaci, S., Tounsi, A., Houari, M., Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81, 1507-1522. https://doi.org/10.1007/s00419-010-0497-5
  10. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib. 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  11. Reddy J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  12. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34, 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034
  13. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2011), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. Tech., 24, 563-572.
  14. Xiao, J.R., Batra, R.C., Gilhooley, D.F., Gillespie, J.W. and McCarthy, M.A. (2007), "Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions", Comput. Meth. Appl. Mech. Eng., 196, 979-987. https://doi.org/10.1016/j.cma.2006.08.002
  15. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solid. Struct., 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  16. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93, 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022

피인용 문헌

  1. Nanotechnology, smartness and orthotropic nonhomogeneous elastic medium effects on buckling of piezoelectric pipes vol.58, pp.5, 2016, https://doi.org/10.12989/sem.2016.58.5.931
  2. Buckling analysis of embedded concrete columns armed with carbon nanotubes vol.17, pp.5, 2016, https://doi.org/10.12989/cac.2016.17.5.567
  3. A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations 2017, https://doi.org/10.1177/1099636217727577
  4. Nonlinear higher order Reddy theory for temperature-dependent vibration and instability of embedded functionally graded pipes conveying fluid-nanoparticle mixture vol.59, pp.1, 2016, https://doi.org/10.12989/sem.2016.59.1.153
  5. Vibration of size-dependent functionally graded sandwich microbeams with different boundary conditions based on the modified couple stress theory 2017, https://doi.org/10.1177/1099636217738909
  6. A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods vol.66, 2017, https://doi.org/10.1016/j.ast.2017.03.016
  7. Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.963
  8. Vibration analysis of concrete foundations retrofit with NFRP layer resting on soil medium using sinusoidal shear deformation theory vol.103, 2017, https://doi.org/10.1016/j.soildyn.2017.09.018
  9. Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP) vol.18, pp.5, 2016, https://doi.org/10.12989/cac.2016.18.5.1053
  10. Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method vol.90, pp.1, 2017, https://doi.org/10.1007/s11071-017-3676-x
  11. Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations vol.55, pp.1661-9897, 2018, https://doi.org/10.4028/www.scientific.net/JNanoR.55.42
  12. Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory pp.1435-5663, 2018, https://doi.org/10.1007/s00366-018-0609-3
  13. Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory vol.62, pp.3, 2017, https://doi.org/10.12989/sem.2017.62.3.311
  14. Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials vol.63, pp.2, 2015, https://doi.org/10.12989/sem.2017.63.2.161
  15. Theoretical and experimental analysis of wave propagation in concrete blocks subjected to impact load considering the effect of nanoparticles vol.20, pp.6, 2015, https://doi.org/10.12989/cac.2017.20.6.711
  16. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2015, https://doi.org/10.12989/sss.2018.21.4.397
  17. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2015, https://doi.org/10.12989/scs.2018.27.5.599
  18. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2015, https://doi.org/10.12989/scs.2018.28.1.013
  19. Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory vol.15, pp.4, 2018, https://doi.org/10.12989/eas.2018.15.4.369
  20. Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel vol.16, pp.1, 2015, https://doi.org/10.12989/eas.2019.16.1.055
  21. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2015, https://doi.org/10.12989/was.2019.28.1.019
  22. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2015, https://doi.org/10.12989/sem.2019.69.6.637
  23. Three-dimensional modelling of functionally graded beams using Saint-Venant's beam theory vol.72, pp.2, 2015, https://doi.org/10.12989/sem.2019.72.2.257
  24. A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes vol.60, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.60.21
  25. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2015, https://doi.org/10.12989/eas.2019.17.5.447
  26. Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates vol.8, pp.2, 2015, https://doi.org/10.12989/anr.2020.8.2.115
  27. Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis vol.25, pp.2, 2015, https://doi.org/10.12989/cac.2020.25.2.133
  28. Experimental and numerical bending deflection of cenosphere filled hybrid (Glass/Cenosphere/Epoxy) composite vol.73, pp.6, 2015, https://doi.org/10.12989/sem.2020.73.6.715
  29. Buckling response of functionally graded nanoplates under combined thermal and mechanical loadings vol.22, pp.4, 2020, https://doi.org/10.1007/s11051-020-04815-9
  30. Eringen's nonlocal model sandwich with Kelvin's theory for vibration of DWCNT vol.25, pp.4, 2015, https://doi.org/10.12989/cac.2020.25.4.343
  31. Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.237
  32. Nonlinear deflection responses of layered composite structure using uncertain fuzzified elastic properties vol.35, pp.6, 2015, https://doi.org/10.12989/scs.2020.35.6.753
  33. A novel hyperbolic plate theory including stretching effect for free vibration analysis of advanced composite plates in thermal environments vol.75, pp.2, 2020, https://doi.org/10.12989/sem.2020.75.2.193
  34. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2015, https://doi.org/10.12989/sem.2021.77.1.057
  35. Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam vol.78, pp.2, 2021, https://doi.org/10.12989/sem.2021.78.2.117