A review of size-dependent continuum mechanics models for micro-and nano-structures

MA Roudbari, TD Jorshari, C Lü, R Ansari… - Thin-Walled …, 2022 - Elsevier
Recently, the mechanical behavior of micro-/nano-structures has sparked an ongoing
debate, which leads to a fundamental question: what steps can be taken to investigate the …

A review of continuum mechanics models for size-dependent analysis of beams and plates

HT Thai, TP Vo, TK Nguyen, SE Kim - Composite Structures, 2017 - Elsevier
This paper presents a comprehensive review on the development of higher-order continuum
models for capturing size effects in small-scale structures. The review mainly focus on the …

Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material

L Li, Y Hu - International Journal of Engineering Science, 2016 - Elsevier
Abstract Size-dependent nonlinear Euler-Bernoulli and Timoshenko beam models, which
account for the through-thickness power-law variation of two-constituent functionally graded …

A review on the mechanics of functionally graded nanoscale and microscale structures

MH Ghayesh, A Farajpour - International Journal of Engineering Science, 2019 - Elsevier
This article reviews, for the first time, the mechanical behaviour of functionally graded
structures at small-scale levels. Functionally graded nanoscale and microscale structures …

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

D Chen, S Kitipornchai, J Yang - Thin-Walled Structures, 2016 - Elsevier
The nonlinear free vibration behavior of shear deformable sandwich porous beam is
investigated in this paper within the context of Timoshenko beam theory. The proposed …

Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory

X Li, L Li, Y Hu, Z Ding, W Deng - Composite Structures, 2017 - Elsevier
A size-dependent inhomogeneous beam model, which accounts for the through-length
power-law variation of a two-constituent axially functionally graded (FG) material, is deduced …

Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach

M Şimşek - International Journal of Engineering Science, 2016 - Elsevier
In this study, a novel size-dependent beam model is proposed for nonlinear free vibration of
a functionally graded (FG) nanobeam with immovable ends based on the nonlocal strain …

Microstructure-dependent couple stress theories of functionally graded beams

JN Reddy - Journal of the Mechanics and Physics of Solids, 2011 - Elsevier
A microstructure-dependent nonlinear Euler–Bernoulli and Timoshenko beam theories
which account for through-thickness power-law variation of a two-constituent material are …

Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures

F Ebrahimi, MR Barati, Ö Civalek - Engineering with Computers, 2020 - Springer
This research develops a nonlocal couple stress theory to investigate static stability and free
vibration characteristics of functionally graded (FG) nanobeams. The theory introduces two …

Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory

M Şimşek, JN Reddy - International Journal of Engineering Science, 2013 - Elsevier
Static bending and free vibration of functionally graded (FG) microbeams are examined in
this paper based on the modified couple stress theory (MCST) and various higher order …