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

Ma, Hongmei; Gao, X.-L.; Reddy, J. N.

doi:10.1016/j.jmps.2008.09.007

Cited by 1,030 publications

(407 citation statements)

References 40 publications

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“…6, for increasing values of the internal length l. It is quite interesting to point out that the stiffening effects shown in Fig. 7, for L/ h = cost, b/h = cost, and decreasing h are predicted by other non-local theories [25] and are generally considered in agreement with experimental evidence on small-size stiffening effects in several materials [12,13].…”

Section: Simply-supported Beamsupporting

confidence: 82%

“…They can be explained based upon the same reasoning and, for this, further comments are omitted for brevity. It is only worth remarking that similar behaviors are predicted by alternative non-local theories [25,27] and are generally considered in agreement with small-size stiffening effects in many materials [12,13]. …”

Section: Cantilever Beamsupporting

confidence: 78%

“…For instance, non-local EB beam models have been built by Kong et al [22] based on a modified couple stress theory, by Zhang et al [23] based on a so-called hybrid approach, which involves a strain energy functional depending on local and nonlocal curvatures. A non-local TM beam model has been built by Wang et al [24] in conjunction with the gradient elasticity theory presented by Lam et al [12], and by Ma et al [25] based on a modified couple stress theory. In all these studies, the motion equations have been derived by Hamilton's principle.…”

Section: Introductionmentioning

confidence: 99%

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A new displacement-based framework for non-local Timoshenko beams

2015

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In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of nonadjacent beam segments, and separately accounting for pure axial, pure bending and pure shear deformation modes. The variational consistency of the proposed non-local beam model is demonstrated by minimization of an appropriate total potential energy functional. Numerical results concerning the static behavior for different boundary and loading conditions are presented. It is shown that the proposed nonlocal beam model is able to capture experimental data on the static deflection of micro-beams, available in the literature.

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Section: Simply-supported Beamsupporting

confidence: 82%

Section: Cantilever Beamsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

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A new displacement-based framework for non-local Timoshenko beams

2015

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“…First equation and system of the rest two equations can be solved independently. We have to mention that system (68) coincide with the one presented in [47,50,51] up to notation. Therefore analysis and verification presented in [47,50] take place in considered here case.…”

Section: Timoshenko's Couple Stress Theory Of the Curved Rodsmentioning

confidence: 81%

“…In most publications the considered models are based on Euler-Bernoulli and Timoshenko's hypothesis. Among the many articles on couple stress theories of beams based on Euler-Bernoulli hypothesis we mention here [43][44][45][46] and on Timoshenko's hypothesis we mention here [46][47][48][49][50][51][52], curved rods along with others have been considered in [4,16,42,[53][54][55], for more information see the extensive review paper [56].…”

Section: Introductionmentioning

confidence: 99%

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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New models for plane curved rods based on linear couple stress theory of elasticity have been developed. 2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and EulerBernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

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2012

Carbon Nanotubes and Nanosensors

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

Cited by 1,030 publications

References 40 publications

A new displacement-based framework for non-local Timoshenko beams

A new displacement-based framework for non-local Timoshenko beams

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

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