FINITE DIFFERENCE METHOD FOR SIXTH-ORDER DERIVATIVES OF DIFFERENTIAL EQUATIONS IN BUCKLING OF NANOPLATES DUE TO COUPLED SURFACE ENERGY AND NON-LOCAL ELASTICITY THEORIES

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KARIMI M.; SHAHIDI A.R.

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Journal Paper

Paper Information

Journal: International Journal of Nano Dimension Year:2015 | Volume:6 | Issue:5 (SPECIAL ISSUE FOR NCNC) Page(s): 525-537

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Title

FINITE DIFFERENCE METHOD FOR SIXTH-ORDER DERIVATIVES OF DIFFERENTIAL EQUATIONS IN BUCKLING OF NANOPLATES DUE TO COUPLED SURFACE ENERGY AND NON-LOCAL ELASTICITY THEORIES

Author(s)

KARIMI M. | SHAHIDI A.R. | Issue Writer Certificate

Keywords

BUCKLING ANALYSIS

FINITE DIFFERENCE METHOD

NANOPLATE

NON-LOCAL ELASTICITY THEORY

SURFACE ENERGY THEORY

Abstract

In this article, FINITE DIFFERENCE METHOD (FDM) is used to solve sixth-order derivatives of differential equations in BUCKLING ANALYSIS of NANOPLATEs due to coupled surface energy and non-local elasticity theories. The uniform temperature change is used to study thermal effect. The small scale and surface energy effects are added into the governing equations using Eringen’s non-local elasticity and Gurtin-Murdoch’s theories, respectively. Two different boundary conditions including simply-supported and clamped boundary conditions are investigated. The numerical results are presented to demonstrate the difference between buckling obtained by considering the surface energy effects and that obtained without the consideration of surface properties. The results show that the FINITE DIFFERENCE METHOD can be used as a powerful method to determine the mechanical behavior of NANOPLATEs. In addition, this method can be used to solve higher-order derivatives of differential equations with different types of boundary condition with little computational effort. Moreover, it is observed that the effects of surface properties tend to increase in thinner and larger NANOPLATEs; and vice versa.

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APA: Copy

KARIMI, M., & SHAHIDI, A.R.. (2015). FINITE DIFFERENCE METHOD FOR SIXTH-ORDER DERIVATIVES OF DIFFERENTIAL EQUATIONS IN BUCKLING OF NANOPLATES DUE TO COUPLED SURFACE ENERGY AND NON-LOCAL ELASTICITY THEORIES. INTERNATIONAL JOURNAL OF NANO DIMENSION (IJND), 6(5 (SPECIAL ISSUE FOR NCNC)), 525-537. SID. https://sid.ir/paper/322291/en

Vancouver: Copy

KARIMI M., SHAHIDI A.R.. FINITE DIFFERENCE METHOD FOR SIXTH-ORDER DERIVATIVES OF DIFFERENTIAL EQUATIONS IN BUCKLING OF NANOPLATES DUE TO COUPLED SURFACE ENERGY AND NON-LOCAL ELASTICITY THEORIES. INTERNATIONAL JOURNAL OF NANO DIMENSION (IJND)[Internet]. 2015;6(5 (SPECIAL ISSUE FOR NCNC)):525-537. Available from: https://sid.ir/paper/322291/en

IEEE: Copy

M. KARIMI, and A.R. SHAHIDI, “FINITE DIFFERENCE METHOD FOR SIXTH-ORDER DERIVATIVES OF DIFFERENTIAL EQUATIONS IN BUCKLING OF NANOPLATES DUE TO COUPLED SURFACE ENERGY AND NON-LOCAL ELASTICITY THEORIES,” INTERNATIONAL JOURNAL OF NANO DIMENSION (IJND), vol. 6, no. 5 (SPECIAL ISSUE FOR NCNC), pp. 525–537, 2015, [Online]. Available: https://sid.ir/paper/322291/en

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