A nonlinear Timoshenko beam formulation based on the modified couple stress theory

Asghari, Mohsen; Kahrobaiyan, M. H.; Ahmadian, Mohammad Taghi

doi:10.1016/j.ijengsci.2010.09.025

Cited by 369 publications

(114 citation statements)

References 32 publications

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“…Kahrobaiyan et al [12] used modi ed couple stress theory to obtain the dynamic characteristics of atomic force microscopes cantilevers. Asghari et al investigated the static and free vibration analyses of nonlinear Timoshenko beam based on the modi ed couple stress theory [13]. Akg oz and Civalek reported on the stability of axially loaded microbeams based on the strain gradient elasticity and modi ed couple stress theory [14].…”

Section: Introductionmentioning

confidence: 99%

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

et al. 2017

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KEYWORDSAbstract. In this paper, we study static bending and free vibration behaviors of Bernoulli-Euler microbeams with a single delamination using the modi ed couple stress theory. The delaminated beam is modeled by four interconnected sub-beams using the delamination zone as their boundaries. The free and constrained mode theories are utilized to model the interaction of delamination surfaces in the damaged area. The continuity as well as compatibility conditions are satis ed between the neighboring sub-beams. After veri cation of the results for some case studies with available solutions, the e ects of various parameters, such as spanwise and thicknesswise locations of the delamination, material length-scale parameter, and boundary conditions, on the static bending and free vibration characteristics of the size-dependent microbeam, have been investigated in detail.

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Section: Introductionmentioning

confidence: 99%

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

et al. 2017

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“…equilibrium equation of forces and moment of forces. Soon after that, the modi ed couple stress theory became a popular non-classical theory to develop microbeam and microplate models as well as to deal with the size-dependent problems in MEMS [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

2017

Self Cite

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Abstract. In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam a ected by an electric eld, including the fringing eld e ect, was obtained based on strain gradient elasticity, couple stress, and classical theory. In uences of di erent parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin's method via mode summation. The resulting non-linear di erential equation was also solved by using the Homotopy Analysis Method (HAM). The in uence of HAM parameters on accuracy was studied speci cally in the vicinity of the pull-in voltage. Comparison of the results of pull-in voltage indicated that low-voltage good agreement exists between numerical and semi-analytical methods, while HAM results deviated from those of numerical methods at high voltages. Findings indicate that strain gradient and couple stress e ects result in a sti er microbeam than with classical theory. E ects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at di erent voltages and orders of HAM approximation.

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“…A size-dependent nonlinear Euler-Bernoulli beam model was presented by Xia et al (2010). They studied nonlinear size-dependent static bending, postbuckling and the free vibration of beams, and Asghari et al (2010) developed their model for Timoshenko beam theory. Ke and Wang (2011) investigated dynamic stability of FGM Timoshenko microbeams and showed the significance of the size effect on dynamic stability.…”

Section: Introductionmentioning

confidence: 99%

A multi-spring model for buckling analysis of cracked Timoshenko nanobeams based on modified couple stress theory

Khorshidi

Shariati

2017

jtam

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This paper develops a cracked nanobeam model and presents buckling analysis of this developed model based on a modified couple stress theory. The Timoshenko beam theory and simply supported boundary conditions are considered. This nonclassical model contains a material length scale parameter and can interpret the size effect. The cracked nanobeam is modeled as two segments connected by two equivalent springs (longitudinal and rotational). This model promotes discontinuity in rotation of the beam and additionally considers discontinuity in longitudinal displacement due to presence of the crack. Therefore, this multi--spring model can consider coupled effects between the axial force and bending moment at the cracked section. The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations, boundary and continuity conditions. The influences of crack location, crack severity, material length scale parameter and flexibility constants of the presented spring model on the critical buckling load are studied.

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A nonlinear Timoshenko beam formulation based on the modified couple stress theory

Cited by 369 publications

References 32 publications

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

A multi-spring model for buckling analysis of cracked Timoshenko nanobeams based on modified couple stress theory

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