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 …

Nonlocal theories for bending, buckling and vibration of beams

JN Reddy - International journal of engineering science, 2007 - Elsevier
Various available beam theories, including the Euler–Bernoulli, Timoshenko, Reddy, and
Levinson beam theories, are reformulated using the nonlocal differential constitutive …

An effective analytical method for buckling solutions of a restrained FGM nonlocal beam

Ö Civalek, B Uzun, MÖ Yaylı - Computational and Applied Mathematics, 2022 - Springer
This work studies the size-dependent stability analysis of restrained nanobeam with
functionally graded material via nonlocal Euler–Bernoulli beam theory using the Fourier …

A microstructure-dependent Timoshenko beam model based on a modified couple stress theory

HM Ma, XL Gao, JN Reddy - Journal of the Mechanics and Physics of Solids, 2008 - Elsevier
A microstructure-dependent Timoshenko beam model is developed using a variational
formulation. It is based on a modified couple stress theory and Hamilton's principle. The new …

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 …

[HTML][HTML] Bending of Euler–Bernoulli beams using Eringen's integral formulation: a paradox resolved

J Fernandez-Saez, R Zaera, JA Loya… - International Journal of …, 2016 - Elsevier
The Eringen nonlocal theory of elasticity formulated in differential form has been widely used
to address problems in which size effect cannot be disregarded in micro-and nano …

The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation

F Hou, S Wu, Z Moradi, N Shafiei - Engineering with Computers, 2022 - Springer
In this paper, the bending and buckling analysis of microbeam with the uniform and non-
uniform cylindrical cross-section was examined based on the classical beam theory and the …

Nonlocal continuum theories of beams for the analysis of carbon nanotubes

JN Reddy, SD Pang - Journal of applied physics, 2008 - pubs.aip.org
(1972)]. The equations of motion are then used to evaluate the static bending, vibration, and
buckling responses of beams with various boundary conditions. Numerical results are …

A nonlocal beam theory for bending, buckling, and vibration of nanobeams

HT Thai - International Journal of Engineering Science, 2012 - Elsevier
A nonlocal shear deformation beam theory is proposed for bending, buckling, and vibration
of nanobeams using the nonlocal differential constitutive relations of Eringen. The theory …