A nonlinear Timoshenko beam formulation based on strain gradient theory

Ansari, R.; Gholami, R.; Darabi, Mohammad Ali

doi:10.2140/jomms.2012.7.195

Cited by 42 publications

(16 citation statements)

References 41 publications

(54 reference statements)

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“…Herein, the GDQ method [Shu 2000] is utilized to discretize the stability equations and boundary conditions. This technique has exhibited a great potential in solving large partial differential equations [Ansari et al 2012a;2012b]. In this work, for sake of briefness, we avoid presenting the discretized counterparts of stability equations and corresponding boundary conditions.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…In another work, , based on the MSGT, proposed a nonlinear size-dependent Euler-Bernoulli beam model and studied the nonlinear size-dependent static bending of a hinged-hinged microbeam. In a recent study, based on the MSGT, Ansari et al [2012a] developed a nonlinear size-dependent Timoshenko microbeam model and examined the influences of geometric parameters, Poisson's ratio and material length scale parameters on the vibrational behavior of microbeams.…”

Section: Introductionmentioning

confidence: 99%

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2012

J. Mech. Mater. Struct.

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Most theoretical studies of mechanical indention, going back to Boussinesq, Hertz, and later Sneddon, address the relations between indenter pressure, indention size, and stress components. However, the relationship between indention and residual stress is also interesting. Here we use the Dorris and NematNasser method to derive a relation between the indention and the residual stress components for an axisymmetric load.

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Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Untitled

2012

J. Mech. Mater. Struct.

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“…(2011) did the static bending, instability and free vibration problems of an all edges simply supported rectangular micro-plate based on a size-dependent Kirchhoff micro-plate model. A comprehensive geometrically nonlinear size-dependent Timoshenko beam model was developed by Ansari et al (2012) based on strain gradient and von Kármán theories. They applied the model and described the nonlinear free vibration of simply supported microbeam.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

Ansari

Hasrati

Shojaei

et al. 2016

Lat. Am. j. solids struct.

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In this paper, a size-dependent microscale plate model is developed to describe the bending, buckling and free vibration behaviors of microplates made of functionally graded materials (FGMs). The size effects are captured based on the modified strain gradient theory (MSGT), and the formulation of the paper is on the basis of Mindlin plate theory. The presented model accommodates the models based upon the classical theory (CT) and the modified couple stress theory (MCST) if all or two scale parameters are set to zero, respectively. By using Hamilton's principle, the governing equations and related boundary conditions are derived. The bending, buckling and free vibration problems are considered and are solved through the generalized differential quadrature (GDQ) method. A detailed parametric and comparative study is conducted to evaluate the effects of length scale parameter, material gradient index and aspect ratio predicted by the CT, MCST and MSGT on the deflection, critical buckling load and first natural frequency of the microplate. The numerical results indicate that the model developed herein is significantly sizedependent when the thickness of the microplate is on the order of the material scale parameters.

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“…Different modified continuum theories capable of considering scale dependency are developed, such as the strain gradient elasticity, couplestress elasticity, nonlocal elasticity and surface elasticity theories [21][22][23]. These non-classical theories have been efficiently employed to capture the size effect on the mechanical behavior of micro-and nanostructures [24][25][26][27][28].…”

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confidence: 99%

Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

et al. 2015

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Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes. To this end, the nanoscale pipe is modeled as a Timoshenko nanobeam. The equations of motion of the nanoscale pipe are obtained based on Hamilton's principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect. Afterwards, the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions. To what extent important parameters such as the thickness, material and surface stress modulus, residual surface stress, surface density, and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.

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A nonlinear Timoshenko beam formulation based on strain gradient theory

Cited by 42 publications

References 41 publications

Untitled

Untitled

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

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