Eur. Phys. J. Plus (2019) 134: 336
https://doi.org/10.1140/epjp/i2019-12724-9

Regular Article

h-p finite element vibration analysis of side cracked rectangular nano-plates based on nonlocal elasticity theory

Laboratory of Computational Mechanics, Department of Mechanical Engineering, Faculty of Technology, University of Tlemcen, Tlemcen, Algeria

^* e-mail: wassak40@gmail.com

Received: 3 February 2019
Accepted: 1 May 2019
Published online: 17 July 2019

Abstract

The h-p version of the finite element method based on a quadrilateral p-element is applied to free vibration analysis of side cracked nano plates. The h-p version of the finite element method marries both the concepts of the conventional h-version and the p-version. The accuracy of the solution is sought by simultaneously refining the mesh and increasing the polynomial order in each element. The formulation takes into account shear deformation, rotary inertia, and non-local elasticity theory. The proposed model is compared to various analytical, numerical and experimental results to validate it’s accuracy and efficiency, computationally expensive preprocessing tasks are avoided due to hierarchic refining strategy that requires no re-meshing when changing crack parameters. The effects of plate aspect ratio, side-to-thickness ratio, non-local parameter, boundary conditions, crack length and crack angle on the free vibration analysis of side cracked nano plates is discussed and presented for the first time.