Static analysis of rectangular nano-plate using three-dimensional theory of elasticity

Applied Mathematical Modelling

Volumn 37, Issue 10-11, 2013, Pages 7016-7026

  Alibeigloo, A ^a   Pasha Zanoosi, A A ^b  

^a TARBIAT MODARES UNIVERSITY   (Iran)

^b IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Elasticity; Nano plate; State space; Static analysis; Three dimensional

Indexed keywords

CLOSED FORM SOLUTIONS; CONSTITUTIVE RELATIONS; DISPLACEMENT AND STRESS FIELDS; DISPLACEMENT COMPONENTS; NANO-PLATE; RECTANGULAR COORDINATES; STATE SPACE; THREE-DIMENSIONAL THEORY OF ELASTICITY;

ASPECT RATIO; CONTINUUM MECHANICS; ELASTICITY; FOURIER SERIES; GRAPHENE; NANOSTRUCTURES; STATIC ANALYSIS; THREE DIMENSIONAL;

EQUATIONS OF STATE;

EID: 84878197540     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.02.041     Document Type: Article

References (16)

1. Wong E.W., Sheehan P.E., Lieber C.M. Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotube. Science 1997, 277:1971-1975.
2. Sorop T.G., Delong L.J. Size-dependent anisotropic diamagnetic screening in super conducting Sn nanowires. Phys. Rev. B 2007, 75:014510.
3. Sun C.T., Zhang H.T. Size dependent elastic moduli of plate like nanomaterials. J. Appl. Phys. 2003, 93:1212-1218.
4. Zhu R., Pan E., Roy A.K. Molecular dynamic study of the stress-strain behavior of carbon nanotube reinforced Epon 862 composites. Mater. Sci. Eng. 2007, A 447:51-57.
5. Liang Y.C., Dou J.H., Bai Q.S. Molecular dynamic simulation study of AFM single-wall carbon nanotube tip-surface interactions. Mater. Sci. Eng. 2007, 339:206-210.
6. Eringen A.C. On nonlocal elasticity. Int. J. Eng. Sci. 1972, 10:233-248.
7. Eringen A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 1983, 54:4703-4710.
8. Eringen A.C. Nonlocal Continuum Field Theories 2002, Springer, New York.
9. Lu H., Sun H., Mao A., Yang H., Wang H., Nu X. Preparation of plate-like nano α-AL2O3 using nano-aluminum seeds by wet-chemical methods. Mater. Sci. Eng. A 2005, 406:19-23.
10. Sumitomo T., Kakisawa H., Owaki H., Kagawa Y. Structure of natural nano-laminar composites. Mater. Sci. Eng 2007, 561-565(PART1):713-716.
11. Aghababaei R., Reddy J.N. Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J. Sound Vibration 2009, 326:277-289.
12. Duan W.H., Wang C.M. Exact solution for axisymmetric loading of micro/nanoscale circular plates based on nonlocal plate theory. Nanotechnology 2007, 18:385704.
13. Pradhan S.C., Kumar A. Nonlocal theories for bending, buckling and vibration of beams. J. Eng. Sci. 2007, 45:288-307.
14. Alibeigloo A. Free vibration analysis of nano-plate using three-dimensional theory of elasticity. Acta Mech. 2011, 222:149-159.
15. Alibeigloo A. Three-dimensional free vibration analysis of multi-layered graphene sheets embedded in elastic matrix. J. Vib. Control 2012, 10.1177/1077546312456056.
16. Pradhan S.C., Kumar A. Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method. Comput. Mater. Sci. 2010, 50:239-245.