Journal ArticleDOI
The size-dependent natural frequency of Bernoulli-Euler micro-beams
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TLDR
In this article, the dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of modified couple stress theory and Hamilton's principle, and the difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio.About:
This article is published in International Journal of Engineering Science.The article was published on 2008-05-01. It has received 560 citations till now. The article focuses on the topics: Boundary value problem & Beam (structure).read more
Citations
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Static and dynamic analysis of micro beams based on strain gradient elasticity theory
TL;DR: In this paper, the static and dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of strain gradient elasticity theory due to Lam et al.
Journal ArticleDOI
Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory
Mesut Şimşek,J. N. Reddy +1 more
TL;DR: In this article, a non-classical microbeam model incorporating the material length scale parameter was proposed to capture the size effect of the FG microbeams and the governing equations and the related boundary conditions were derived using Hamilton's principle.
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A new Kirchhoff plate model based on a modified couple stress theory
TL;DR: In this article, a modified couple stress model is proposed for the static analysis of isotropic micro-plates with arbitrary shape based on the Kirchhoff plate model, which is capable of handling plates with complex geometries and boundary conditions.
Journal ArticleDOI
A nonlinear Timoshenko beam formulation based on the modified couple stress theory
TL;DR: In this article, a nonlinear size-dependent Timoshenko beam model based on modified couple stress theory is presented, a non-classical continuum theory capable of capturing the size effects.
Journal ArticleDOI
A micro scale Timoshenko beam model based on strain gradient elasticity theory
TL;DR: In this article, a micro scale Timoshenko beam model based on strain gradient elasticity theory was developed and the governing equations, initial conditions and boundary conditions were derived simultaneously by using Hamilton's principle.
References
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Journal ArticleDOI
Strain gradient plasticity: Theory and experiment
TL;DR: In this paper, a deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening, which is a non-linear generalization of Cosserat couple stress theory.
Journal ArticleDOI
Couple stress based strain gradient theory for elasticity
TL;DR: In this paper, an equilibrium relation is developed to govern the behavior of the couples, which constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system.
Journal ArticleDOI
Elastic materials with couple-stresses
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
Journal ArticleDOI
Experiments and theory in strain gradient elasticity
TL;DR: In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors in small-scale structures and a strain gradient elastic bending theory for plane-strain beams is developed.
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A microstructure-dependent Timoshenko beam model based on a modified couple stress theory
H. M. Ma,Xin-Lin Gao,J. N. Reddy +2 more