journal article·2015-12

A comprehensive study on FGM nanoplates embedded in an elastic medium

Mohammed Sobhy

Publisher page

Abstract

Abstract This work is devoted to investigate the bending response, free vibration, mechanical buckling and thermal buckling of functionally graded material (FGM) nanoplates embedded in an elastic medium. According to a new mixture law, the material properties of the FGM nanoplate are graded only in the thickness direction. The elastic medium is modeled as Pasternak’s two-parameter elastic foundations. The four-unknown shear deformation theory incorporated in Eringen’s nonlocal elasticity theory is employed to deduce the equations of motion from the Hamilton’s principle. The solutions of simply supported FGM nanoplates are obtained and the results are compared with those available in the literature. Detailed numerical studies are performed to demonstrate the influences of inhomogeneity parameter, nonlocal parameter, elastic foundation stiffness, plate aspect ratio and side-to-thickness ratio on the behavior of FGM nanoplates.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Numerical methods in engineering

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (85)

Show source-provided references
1. New ferromagnetic and functionally grade shape memory alloys
2. Functionally graded TiN/TiNi shape memory alloy films10.1016/S0167-577X(02)01419-2 ↗
3. TiNi-based thin films in MEMS applications: a review10.1016/j.sna.2004.02.019 ↗
4. The use of functionally graded poly-SiGe layers for MEMS applications10.4028/www.scientific.net/MSF.492-493.255 ↗
5. Metallic NEMS components fabricated from nanocomposite Al–Mo films10.1088/0957-4484/17/12/042 ↗
6. Torsion and bending of micron-scaled structures10.1557/JMR.2001.0146 ↗
7. Strain gradient plasticity: theory and experiment10.1016/0956-7151(94)90502-9 ↗
8. Size dependent hardness of silver single crystals10.1557/JMR.1995.0853 ↗
9. Couple stress based strain gradient theory for elasticity10.1016/S0020-7683(02)00152-X ↗
10. Strain gradient interpretation of size effects10.1023/A:1018625006804 ↗
11. Strain gradient elasticity solution for functionally graded micro-cylinders10.1016/j.ijengsci.2011.09.006 ↗
12. Theory of micropolar plates10.1007/BF01593891 ↗
13. Nonlocal polar elastic continua10.1016/0020-7225(72)90070-5 ↗
14. The general theory of curved deformable interfaces in solids at equilibrium10.1080/01418619808239977 ↗
15. On nonlocal elasticity10.1016/0020-7225(72)90039-0 ↗
16. ON differential-equations of nonlocal elasticity and solutions of screw dislocation and surface-waves10.1063/1.332803 ↗
17. Eringen · 2002
18. Nonlocal theories for bending, buckling and vibration of beams10.1016/j.ijengsci.2007.04.004 ↗
19. Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes10.1007/s00707-006-0417-5 ↗
20. Nonlocal continuum theories of beams for the analysis of carbon nanotubes10.1063/1.2833431 ↗
21. Vibration of multi-walled carbon nanotubes by generalized shear deformation theory10.1016/j.ijmecsci.2007.10.003 ↗
22. Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates10.1016/j.jsv.2009.04.044 ↗
23. Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field10.1016/j.apm.2010.03.029 ↗
24. Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory10.1016/j.physe.2010.11.024 ↗
25. Buckling analysis of multi-walled carbon nanotubes with consideration of small scale effects10.1166/jctn.2011.1946 ↗
26. Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory10.1016/j.physe.2011.03.012 ↗
27. Forced transverse vibration of nanoplates using nonlocal elasticity10.1016/j.physe.2011.12.004 ↗
28. A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams10.1016/j.ijengsci.2012.01.009 ↗
29. Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium10.1016/j.physe.2013.04.022 ↗
30. Small scale effect on hygro-thermo-mechanical bending of nanoplates embedded in an elastic medium
31. Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory10.1007/s10409-014-0072-3 ↗
32. Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium10.1016/j.physe.2013.10.017 ↗
33. Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions10.1007/s00707-014-1093-5 ↗
34. Natural frequency and buckling of orthotropic nanoplates resting on two-parameter elastic foundations with various boundary conditions10.1017/jmech.2014.46 ↗
35. Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory10.1016/j.ijmecsci.2014.11.014 ↗
36. Hygrothermal deformation of orthotropic nanoplates based on the state-space concept10.1016/j.compositesb.2015.04.042 ↗
37. Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods10.1016/j.commatsci.2012.04.001 ↗
38. Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory10.1016/j.compstruct.2012.10.038 ↗
39. Size-dependent free flexural vibration behavior of functionally graded nanoplates10.1016/j.commatsci.2012.06.031 ↗
40. Free vibration analysis of functionally graded size-dependent nanobeams10.1016/j.amc.2011.12.090 ↗
41. An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity10.1016/j.compstruct.2013.02.022 ↗
42. Nonlocal nonlinear free vibration of functionally graded nanobeams10.1016/j.compstruct.2013.12.006 ↗
43. Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity10.1016/j.apm.2013.11.068 ↗
44. Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity10.1007/s00707-013-1014-z ↗
45. Influence of rotatory inertia and shear in flexural motion of isotropic elastic plates10.1115/1.4010217 ↗
46. A refined nonlinear theory of plates with transverse shear deformation10.1016/0020-7683(84)90056-8 ↗
48. An efficient standard plate theory10.1016/0020-7225(91)90165-Y ↗
49. A transverse shear deformation theory for homogeneous monoclinic plates10.1007/BF01176650 ↗
50. Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity10.1016/S0020-7683(02)00647-9 ↗
51. Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading10.1016/j.compstruct.2003.11.012 ↗
52. Elastic foundation analysis of uniformly loaded functionally graded viscoelastic sandwich plates10.1017/jmech.2012.53 ↗
53. Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations10.1016/j.ast.2013.01.003 ↗
54. Refined plate theory and its variants10.2514/2.1622 ↗
55. Free vibrations of plate using two variable refined plate theory10.1016/j.jsv.2006.03.030 ↗
56. A nonlocal beam theory for bending, buckling, and vibration of nanobeams10.1016/j.ijengsci.2011.11.011 ↗
57. Free vibration of nanoplates based on a nonlocal two-variable refined plate theory10.1016/j.compstruct.2012.07.006 ↗
58. Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects10.1016/j.compstruct.2011.06.028 ↗
59. Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory10.1007/s00707-011-0560-5 ↗
60. A two variable refined plate theory for the bending analysis of functionally graded plates10.1007/s10409-010-0372-1 ↗
61. A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient10.1016/j.compositesb.2011.05.032 ↗
62. A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate10.1016/j.ijmecsci.2011.01.004 ↗
63. A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates10.1177/1099636211426386 ↗
64. A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates10.1016/j.ast.2011.11.009 ↗
65. An efficient and simple refined theory for buckling analysis of functionally graded plates10.1016/j.apm.2011.07.062 ↗
66. A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates10.1016/j.apm.2012.08.008 ↗
67. A comprehensive analysis of functionally graded sandwich plates: Part 2 – Buckling and free vibration10.1016/j.ijsolstr.2005.02.015 ↗
68. Thermoelastic buckling and vibration behavior of functionally graded sandwich beam with constrained viscoelastic core10.1016/j.jsv.2006.01.026 ↗
69. Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties10.1016/j.ijmecsci.2006.09.011 ↗
70. Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties10.1016/j.compositesb.2007.01.004 ↗
71. Thermal buckling of various types of FGM sandwich plates10.1016/j.compstruct.2010.06.012 ↗
72. The buckling and post-buckling behaviour of composite plates under biaxial loading10.1016/0020-7403(75)90052-1 ↗
73. Bifurcation buckling of unsymmetrically laminated plates10.1016/0961-9526(94)90026-4 ↗
74. Conditions for laminated plates to remain flat under in-plane loading10.1016/0263-8223(86)90022-X ↗
75. Buckling or transverse deflections of unsymmetrically laminated plates subjected to in-plane loads10.2514/3.11336 ↗
76. Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading10.1016/S0020-7683(03)00096-9 ↗
77. Thermal post-buckling of laminated plates comprising functionally graded materials with temperature-dependent properties10.1115/1.1795220 ↗
78. Nonlinear analysis of functionally graded plates under transverse and in-plane loads10.1016/S0020-7462(01)00070-1 ↗
79. Flexural wave propagation in single-walled carbon nanotubes10.1103/PhysRevB.71.195412 ↗
80. Transverse vibrations of double-walled carbon nanotubes under compressive axial load10.1016/j.physleta.2005.03.064 ↗
81. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes10.1088/0957-4484/18/7/075702 ↗
82. Variable kinematic model for the analysis of functionally graded material plates10.2514/1.32490 ↗
83. Generalized shear deformation theory for bending analysis of functionally graded plates10.1016/j.apm.2005.03.009 ↗
84. A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations10.1007/s12205-011-1361-z ↗
85. Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation10.1016/j.compstruct.2011.01.020 ↗