Element free galerkin method for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory

被引：7

作者：

Naderi, A. ^{[1
]}

Baradaran, G.H. ^{[1
]}

机构：

[1] Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman

来源：

International Journal of Engineering, Transactions A: Basics | 2013年 / 26卷 / 07期

关键词：

Element free Galerkin method; Graphene sheet; Micro/nanoscale plates; Nonlocal theory;

D O I：

10.5829/idosi.ije.2013.26.07a.14

中图分类号：

学科分类号：

摘要：

In this article, element free Galerkin method is used for static analysis of thin orthotropic micro/nanoscale plates based on the nonlocal plate theory. Equilibrium equation is obtained based on the nonlocal Kirchoff plate theory. Weak form of the equilibrium equation is discretized based on the moving least square (MLS) approximation functions. Since MLS approximation functions do not satisfy the Kronecker's delta property, the penalty method is used to impose the essential boundary conditions. Discrete form of the weak form is then solved and the plate deflection is obtained. Numerical results show that the number of nodes scattered in the plate domain, support domain radius and the number of Gauss quadrature points affect the results. Therefore, before presentation of the final results, the method is calibrated using some exact results. Finally, the plate deflection is obtained for various boundary conditions and the small scale effect is studied. In addition, as an example bending problem of nano graphene sheets is solved for different boundary conditions.

引用

页码：795 / 806

页数：11

共 33 条

[1]

Sorop T., De Jongh L., Size-dependent anisotropic diamagnetic screening in superconducting sn nanowires, Physical Review B, 75, 1, (2007)

[2]

Wong E.W., Sheehan P.E., Lieber C.M., Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes, Science, 277, 5334, pp. 1971-1975, (1997)

[3]

Zhou S., Li Z., Length scales in the static and dynamic torsion of a circular cylindrical micro-bar, Journal of Shandong University of Technology, 31, 5, pp. 401-407, (2001)

[4]

Fleck N., Hutchinson J., Strain gradient plasticity, Advances in Applied Mechanics, 33, pp. 295-361, (1997)

[5]

Eringen A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 9, pp. 4703-4710, (1983)

[6]

Lu P., Zhang P., Lee H., Wang C., Reddy J., Non-local elastic plate theories, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 463, 2088, pp. 3225-3240, (2007)

[7]

Murmu T., Pradhan S., Buckling of biaxially compressed orthotropic plates at small scales, Mechanics Research Communications, 36, 8, pp. 933-938, (2009)

[8]

Pradhan S., Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory, Physics Letters A, 373, 45, pp. 4182-4188, (2009)

[9]

Pradhan S., Phadikar J., Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A, 373, 11, pp. 1062-1069, (2009)

[10]

Aghababaei R., Reddy J., Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration, 326, 1, pp. 277-289, (2009)

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