A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

Based on the Reddy–Bickford beam theory (RBBT), a comprehensive study on high-order bending, buckling and free vibration of two-directional functionally graded (FG) nanobeams is presented. The variation of the material properties is assumed to obey arbitrary power-law form in both axial and thicknes...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Brazilian Society of Mechanical Sciences and Engineering 2019-07, Vol.41 (7), p.1-23, Article 303
Main Authors: Rezaiee-Pajand, M., Mokhtari, M.
Format: Article
Language:English
Subjects:
Beam theory (structures)
Boundary conditions
Computational fluid dynamics
Engineering
Equations of motion
Exact solutions
Finite element method
Fluid flow
Free vibration
Functionally gradient materials
Kernel functions
Material properties
Mechanical Engineering
Meshless methods
Modulus of elasticity
Nonlocal elasticity
Smooth particle hydrodynamics
Stiffness
Technical Paper
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Based on the Reddy–Bickford beam theory (RBBT), a comprehensive study on high-order bending, buckling and free vibration of two-directional functionally graded (FG) nanobeams is presented. The variation of the material properties is assumed to obey arbitrary power-law form in both axial and thickness directions. The equations of motion are derived using Hamilton’s principle, and small-scale effects are captured by nonlocal elasticity theory of Eringen. The RBBT formulation leads to complicated governing equations, and 2D FGM introduces additional stiffness terms. Accordingly, the governing equations cannot be solved by classical analytical schemes, and thus, symmetric smoothed particle hydrodynamics (SSPH) meshless method is adopted as an efficient numerical solution approach. The revised super-Gauss function is used as the kernel function. To validate the developed SSPH code, benchmark problems are studied and the results are compared to the analytical solutions. In this context, excellent agreement is observed. Several numerical examples are included to illustrate the effects of gradient indexes, boundary conditions, size scale parameters, aspect and elastic modulus ratios on static and dynamic responses of two-directional FG nanobeams.
ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-019-1799-3