Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory

Document Type: Research Paper

Authors

School of Mechanical Engineering, Shiraz University, Shiraz, Iran

Abstract

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried out. An analytical solution for static analysis of rectangular plates is obtained to solve the governing equations and boundary conditions. The suggested model is justified by a very good agreement between the results given by the present model and available data. Additionally, the effects of different parameters such as internal length scale parameter, length to thickness ratio and aspect ratio on the numerical results are also investigated. It is hoped that the present methodology lead to other models for static and dynamic analysis of rectangular nano structures with considering small scale effects.

Keywords


[1] E. Ghavanloo and S. A. Fazelzadeh, Free vibration analysis of orthotropic doubly-curved shallow shells based on the gradient elasticity. Composite: Part B, 45 (2013) 1448–1457.
[2] X. L. Gao and S. K. Park, Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem, International Journal of Solids and Structures, 44 (2007) 7486-7499.
 [3] S. Ramezani, A micro scale geometrically non-linear Timoshenko beam model based on strain gradient elasticity theory, International Journal of Non-Linear Mechanics, 47 (2012) 863-873.
 [4] F. Daneshmand, M. Rafiei, S. R. Mohebpour and M. Heshmati, Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory, Applied Mathematical Modelling 37 (2013) 7983-8003.
[5] A. Ashoori Movassagh and M. J. Mahmoodi, A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory, European Journal of Mechanics A/Solids, 40 (2013) 50-59.
[6] C. Polizzotto, A second strain gradient elasticity theory with second velocity gradient inertia – Part I: Constitutive equations and quasi-static behavior, International Journal of Solids and Structures 50 (2013) 3749-3765.
 [7] S. Sahmani and R. Ansari, On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Composite Structure 95 (2013) 430-442.
[8] B. Zhang, Y. He, D. Liu, Z. Gan and L. Shen, A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory, Composite Structure 106 (2013) 374-392.
 
[9] D. Yi, T. C. Wang and S. Chen, New strain gradient theory and analysis. Acta Mechanica Solida Sinica 22 (2009) 45-52.
 
 [10] B. Akgöz and O. Civalek, Application of strain gradient elasticity theory for buckling analysis of protein microtubules, Current Applied Physics 11 (2011) 1133-1138.
 
[11] E. C. Aifantis and H. Askes, Gradient elasticity and flexural wave dispersion in carbon nanotubes, Physics Review B, 80 (2009) 195412.
 
[12]S. Papargyri-Beskou and D. E. Beskos, Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates, Archive of Applied Mechanics 78 (2008) 625–635.
 
 [13]A. S. Sayyad and Y. M. Ghugal, Buckling analysis of thick isotropic plates by using exponential shear deformation theory, Applied Computer Mechanics 6 (2012) 185–196.
 [14]M. H. Sadd. Elasticity, Theory, Applications, and Numerics. Elsevier (2009).
 [15] K. A. Lazopoulos and A. K. Lazopoulos, Strain gradient elasticity and stress fibers, Archive of Applied Mechanics 83 (2013) 1371-1381.