Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

doi:10.1016/J.COMPSTRUCT.2012.10.038

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Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

Journal Article•DOI•

Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

Mesut Şimşek¹, H.H. Yurtcu¹•Institutions (1)

Yıldız Technical University¹

01 Mar 2013-Composite Structures (COMPOSITE STRUCTURES)-Vol. 97, Iss: 97, pp 378-386

TL;DR: In this paper, a non-classical (non-local) nanobeam model incorporating the length scale parameter (nonlocal parameter) which can capture the small scale effect is proposed.

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About: This article is published in Composite Structures.The article was published on 2013-03-01. It has received 336 citations till now. The article focuses on the topics: Timoshenko beam theory & Buckling.

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Journal Article•DOI•

Free vibration analysis of nonlocal strain gradient beams made of functionally graded material

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Li Li¹, Xiaobai Li¹, Yujin Hu¹•Institutions (1)

Huazhong University of Science and Technology¹

01 May 2016-International Journal of Engineering Science

TL;DR: In this article, a size-dependent Timoshenko beam model, which accounts for through-thickness power-law variation of a two-constituent functionally graded (FG) material, is derived in the framework of the nonlocal strain gradient theory.

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349 citations

Journal Article•DOI•

Elastic buckling and static bending of shear deformable functionally graded porous beam

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Da Chen¹, Jie Yang², Sritawat Kitipornchai¹•Institutions (2)

University of Queensland¹, RMIT University²

01 Dec 2015-Composite Structures

TL;DR: In this paper, the elastic buckling and static bending analysis of shear deformable functionally graded (FG) porous beams based on the Timoshenko beam theory is presented, where the elasticity moduli and mass density of porous composites are assumed to be graded in the thickness direction according to two different distribution patterns.

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345 citations

Cites methods from "Analytical solutions for bending an..."

...Simsek and Yurtcu [24] used the nonlocal Timoshenko and Euler-Bernoulli beam theory to examine the analytical solutions for the static bending and buckling of a FG nanobeam....
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Journal Article•DOI•

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

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Mesut Şimşek¹•Institutions (1)

Yıldız Technical University¹

01 Aug 2016-International Journal of Engineering Science

TL;DR: In this paper, a size-dependent beam model is proposed for nonlinear free vibration of a functionally graded (FG) nanobeam with immovable ends based on the nonlocal strain gradient theory (NLSGT) and Euler-Bernoulli beam theory in conjunction with the von-Karman's geometric nonlinearity.

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313 citations

Journal Article•DOI•

Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs)

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Chuang Feng¹, Sritawat Kitipornchai², Jie Yang¹•Institutions (2)

RMIT University¹, University of Queensland²

01 Feb 2017-Composites Part B-engineering

TL;DR: In this paper, the nonlinear bending behavior of a novel class of multi-layer polymer nanocomposite beams reinforced with graphene platelets (GPLs) that are non-uniformly distributed along the thickness direction was investigated.

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Abstract: This paper studies the nonlinear bending behavior of a novel class of multi-layer polymer nanocomposite beams reinforced with graphene platelets (GPLs) that are non-uniformly distributed along the thickness direction. Nonlinear governing equation is established based on Timoshenko beam theory and von Karman nonlinear strain-displacement relationship. The effective Young's modulus of the nanocomposites is determined by modified Halpin-Tsai micromechanics model. Ritz method is employed to reduce the governing differential equation into an algebraic system from which the static bending solutions can be obtained. A comprehensive parametric study is then conducted, with a particular focus on the influences of distribution pattern, weight fraction, geometry and size of GPLs together with the total number of layers on the linear and nonlinear bending performances of the beams. Numerical results demonstrate the significantly improved bending performance through the addition of a very small amount of GPLs into polymer matrix as reinforcements. It is found that dispersing more GPLs that are in square shape with fewer single graphene layers near the top and bottom surfaces of the beam is the most effective way to reduce bending deflections. Beams with a higher weight fraction of GPLs that are symmetrically distributed in such a way are also less sensitive to the nonlinear deformation.

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300 citations

Journal Article•DOI•

Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory

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Omid Rahmani¹, O. Pedram¹•Institutions (1)

University of Zanjan¹

01 Apr 2014-International Journal of Engineering Science

TL;DR: In this article, the effects of the gradient index, length scale parameter and length-to-thickness ratio on the vibration of functionally graded material (FGM) nanobeams were examined.

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282 citations

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References

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Journal Article•DOI•

On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves

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A. Cemal Eringen

01 Sep 1983-Journal of Applied Physics

TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.

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Abstract: Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.

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3,929 citations

"Analytical solutions for bending an..." refers background in this paper

...Nanotechnology is able to create many new materials and devices with a vast range of applications, such as in medicine, electronics, biomaterials and energy production....
[...]
...…constants, such as the modified couple stress theory [1], the strain gradient theory [2], the micropolar theory [3], the nonlocal elasticity theory [4], and the surface elasticity [5], have been developed to characterize the size effect in micro, nano-scale structures by introducing an intrinsic…...
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...The material properties of the FG nanobeam are assumed to vary in the thickness direction....
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Journal Article•DOI•

Couple stress based strain gradient theory for elasticity

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Fan Yang¹, Fan Yang², Arthur C.M. Chong¹, David Chuen Chun Lam¹, Pin Tong¹ - Show less +1 more•Institutions (2)

Hong Kong University of Science and Technology¹, Southwest Jiaotong University²

01 May 2002-International Journal of Solids and Structures

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.

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2,725 citations

"Analytical solutions for bending an..." refers methods in this paper

...Please cite this article in press as: S ims ek M, Y nonlocal Timoshenko beam theory....
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Journal Article•DOI•

Nonlocal polar elastic continua

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A. Cemal Eringen¹•Institutions (1)

Princeton University¹

01 Jan 1972-International Journal of Engineering Science

TL;DR: In this article, a continuum theory of non-local polar bodies is developed for nonlinear micromorphic elastic solids, and the balance laws and jump conditions are given.

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1,788 citations

"Analytical solutions for bending an..." refers methods in this paper

...Compos Str a b s t r a c t In this paper, static bending and buckling of a functionally graded (FG) nanobeam are examined based on the nonlocal Timoshenko and Euler–Bernoulli beam theory....
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Journal Article•DOI•

Nonlocal theories for bending, buckling and vibration of beams

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J. N. Reddy¹, J. N. Reddy²•Institutions (2)

National University of Singapore¹, Texas A&M University²

01 Feb 2007-International Journal of Engineering Science

TL;DR: In this article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.

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1,519 citations

Additional excerpts

Journal Article•DOI•

Application of nonlocal continuum models to nanotechnology

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John Peddieson¹, George R. Buchanan¹, Richard P. McNitt²•Institutions (2)

Tennessee Technological University¹, Pennsylvania State University²

01 Mar 2003-International Journal of Engineering Science

TL;DR: In this paper, a nonlocal elasticity theory is employed to develop a non-local Benoulli/Euler beam model and some representative problems are solved to illustrate the magnitude of predicted nonlocal effects.

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1,171 citations

"Analytical solutions for bending an..." refers methods in this paper

...The Navier-type solution is developed for simply-supported boundary conditions, and exact formulas are proposed for the deflections and the buckling load....
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