A simplified moment-curvature based approach for large deflection analysis of micro-beams using the consistent couple stress theory

Patel, Bhakti N.; Pandit, D.; Srinivasan, Sivakumar M.

doi:10.1016/j.euromechsol.2017.06.002

Cited by 15 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alavi et al 36 developed a CCST‐based Timoshenko beam theory (TBT) for static bending and dynamic response analyses of microbeams. Patel et al 37 used the CCST in conjunction with a simplified moment‐curvature relation to examine the large deflection behavior of microbeams. Ajri et al 38 conducted a nonlinear dynamic analysis of viscoelastic nanoplates using a CCST‐based classical shell theory.…”

Section: Introductionmentioning

confidence: 99%

An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

Lyu

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

Based on the three-dimensional (3D) consistent couple stress theory (CCST), we develop an asymptotic theory for the free vibration analysis of functionally graded (FG) microplates resting on an elastic medium. The material properties of the FG microplate are assumed to obey a power-law distribution of the volume fractions of the constituents in the thickness direction, for which the effective material properties are estimated using the rule of mixtures. The interactions between the FG microplate and its foundation medium are simulated using a Winkler-Pasternak foundation. Carrying out the asymptotic expansion method, we obtain recursive sets of motion equations for various order problems. The CCST-based classical plate theory is derived as a firstorder approximation of the 3D CCST. The asymptotic theory is shown to converge rapidly and to be in excellent agreement with the exact solutions for FG macroplates reported in the literature when the value of the material length scale parameter is assigned to be zero.

show abstract

Section: Introductionmentioning

confidence: 99%

An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

Lyu

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Patel et al . 23 proposed a model based on moment-curvature approach to analyze large deflection of nanobeams using the consistent couple stress theory (CCST). They reported on the large elastic deflection of nanobeams subjected to arbitrary inclined terminal load.…”

Section: Introductionmentioning

confidence: 99%

Efficient large amplitude primary resonance in in-extensional nanocapacitors: Nonlinear mean curvature component

Rahmanian

Hosseini-Hashemi

SoltanRezaee

2019

Sci Rep

View full text Add to dashboard Cite

In general, the impact of geometric nonlinearity, which arises from geometric relationships governing the motion of constituent particles of elastic mediums, becomes critically important while the system operates under large deformations. In this case, the influence of different physics governing the system dynamics might be coupled with the impact of geometric nonlinearity. Here, for the first time, the non-zero component of the mean curvature tensor is nonlinearly expressed in terms of the middle-axis curvature of a cantilevered beam. To this aim, the concept of local displacement field together with inextensibility condition are employed. A nanowire-based capacitor is assumed to be excited by the electrostatic load that is composed of both DC and AC voltages. The main concern is on the case, in which it is necessary to polarize the electrodes with large amplitude voltages. Other physics, including surface strain energy, size-dependency, and dispersion force are modeled to predict the system response more accurately. Hamilton’s principle is used to establish the motion equation, and the Galerkin method is applied to exploit a set of nonlinear ordinary differential equations (ODEs). Implementing a combination of shooting and arc-length continuation scheme, the frequency and force-displacement behaviors of the capacitor are captured near its primary resonance. The coupled effects of the nonlinear impact factor, surface elasticity and size parameters on the bifurcation point’s loci and dynamic pull-in instability are studied.

show abstract

A general dynamic model based on Mindlin’s high-frequency theory and the microstructure effect

Jin

2020

Acta Mech

View full text Add to dashboard Cite

A simplified moment-curvature based approach for large deflection analysis of micro-beams using the consistent couple stress theory

Cited by 15 publications

References 22 publications

An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

An asymptotic consistent couple stress theory for the three‐dimensional free vibration analysis of functionally graded microplates resting on an elastic medium

Efficient large amplitude primary resonance in in-extensional nanocapacitors: Nonlinear mean curvature component

A general dynamic model based on Mindlin’s high-frequency theory and the microstructure effect

Contact Info

Product

Resources

About