Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T19:11:25.832Z Has data issue: false hasContentIssue false
  • English
  • Français

Small-Scale Effects on the Buckling of Skew Nanoplates Based on Non-Local Elasticity and Second-Order Strain Gradient Theory

Published online by Cambridge University Press:  22 February 2017

B. Shahriari  and
S. Shirvani
B. Shahriari*
Affiliation:
Department of Mechanical and Aerospace EngineeringMalek Ashtar University of TechnologyIsfahan, Iran
S. Shirvani
Affiliation:
Department of Mechanical EngineeringSirjan University of TechnologySirjan, Iran
*
*Corresponding author ([email protected])
Get access

Abstract

In recent years, nanostructures have been used in a vast number of applications, making the study of the mechanical behaviour of such structures important. In this paper, two different constitutive equations including first-order strain gradient and simplified differential non-local are employed to model the buckling behaviour of skew nanoplates. The Galerkin method is used for solving the equations in order to obtain buckling load. Using this method, the influence of different parameters consisting of non-classical properties, boundary conditions, and geometrical parameters such as length and angle on the buckling load, are studied. The results showed that small-scale effects are very important in skew graphene sheets and their inclusion results in smaller buckling loads.

Keywords

Skew nanoplateNon-localStrain gradientGalerkin method
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 443 - 452
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Aksencer, T. and Aydogdu, M., “Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory,” Physica E: Lowdimensional Systems and Nanostructures, 43, pp. 954–959 (2011).Google Scholar
2. Eringen, A. C., Nonlocal Continuum Field Theories, Springer-Verlag, New York (2002).Google Scholar
3. Mindlin, R. D. and Eshel, N. N., “On first straingradient theories in linear elasticity,” International Journal of Solids and Structures, 4, pp. 109–124 (1968).Google Scholar
4. Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J. and Tong, P., “Experiments and theory strain gradient elasticity,” Journal of the Mechanics and Physics of Solids, 51, pp. 1477–1508 (2003).Google Scholar
5. Hadjesfandiari, A. R. and Dargush, G. F., “Couple stress theory for solids,” International Journal of Solids and Structures, 48, pp. 2496–2510 (2011).Google Scholar
6. Aifantis, E. C., “Update on a class of gradient theories,” Mechanics of Materials, 35, pp. 259–280 (2003).Google Scholar
7. Aifantis, E. C., “On the gradient approach – Relation to Eringen's nonlocal theory,” International Journal of Engineering Science, 49, pp. 1367–1377 (2011).Google Scholar
8. Dingreville, R. M., Qu, J. and Cherkaoui, M., “Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films,” Journal of the Mechanics and Physics of Solids, 53, pp. 1827–1854 (2005).Google Scholar
9. Lu, P., He, L., Lee, H. and Lu, C., “Thin plate theory including surface effects,” International Journal of Solids and Structures, 43, pp. 4631–4647 (2006).Google Scholar
10. Sakhaee-Pour, A., “Elastic buckling of single-layered graphene sheet,” Computational Materials Science, 45, pp. 266–270 (2009).Google Scholar
11. Pradhan, S. and Murmu, T., “Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics,” Computational Materials Science, 47, pp. 268–274 (2009).Google Scholar
12. Murmu, T. and Pradhan, S., “Buckling of biaxially compressed orthotropic plates at small scales,” Mechanics Research Communications, 36, pp. 933–938 (2009).Google Scholar
13. Sheng, H., Li, H., Lu, P. and Xu, H., “Free vibration analysis for micro-structures used in MEMS considering surface effects,” Journal of Sound and Vibration, 329, pp. 236–246 (2010).Google Scholar
14. Babaei, H. and Shahidi, A. R., “Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method,” Archive of Applied Mechanics, 81, pp. 1051–1062 (2011).Google Scholar
15. Malekzadeh, P., Setoodeh, A. and Alibeygi Beni, A., “Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium,” Composite Structures, 93, pp. 2083–2089 (2011).Google Scholar
16. Narendar, S., “Buckling analysis of micro-/nanoscale plates based on two-variable refined plate theory incorporating nonlocal scale effects,” Composite Structures, 93, pp. 3093–3103 (2011).Google Scholar
17. Arash, B., Wang, Q. and Liew, K. M., “Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation,” Computer Methods in Applied Mechanics and Engineering, 223, pp. 1–9 (2012).Google Scholar
18. Murmu, T., Sienz, J., Adhikari, S. and Arnold, C., “Nonlocal buckling of double-nanoplate-systems under biaxial compression,” Composites Part B: Engineering, 44, pp. 84–94 (2013).Google Scholar
19. Aksencer, T. and Aydogdu, M., “Levy type solution method for vibration and buckling of nano plates using non local elasticity theory,” Physica E, 43, pp. 954–959 (2011).Google Scholar
20. Narendar, S. and Gopalakrishnan, S., “Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory,” Acta Mech, DOI:10.1007/s00707-011-0560-5 (2011).Google Scholar
21. Narendar, S., “Buckling analysis of micro-/nanoscale plates based on two-variable refined plate theory incorporating nonlocal scale effects,” Composite Structures, 93, pp. 3093–3103 (2011).Google Scholar
22. Babaei, H. and Shahidi, A. R., “Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method,” Archive of Applied Mechanics, 81, pp. 1051–1062 (2011).Google Scholar
23. Malekzadeh, P., Setoodeh, A. and Alibeygi, Beni, “Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium,” Composite Structures, 93, pp. 2083–2089 (2011).Google Scholar
24. Movassagh, A. A. and Mahmoodi, M. J., “A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory,” European Journal of Mechanics A/Solids, 40, pp. 50–59 (2013).Google Scholar
25. Ghorbanpour Arani, A., Shiravand, A., Rahi, M. and Kolahchi, R., “Nonlocal vibration of coupled DLGS systems embedded on Visco-Pasternak foundation,” Physica B: Condensed Matter, 407, pp. 4123–4131 (2012).Google Scholar