Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory

Gholami, R.; Darvizeh, A.; Ansari, R.; Hosseinzadeh, M.

doi:10.1007/s11012-014-9944-7

Cited by 60 publications

(14 citation statements)

References 34 publications

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“…Based on the MST, a number of size-dependent models have been developed to predict the responses of microplates on the basis of various kinematic models, such as classical plate theory [33][34][35][36][37], first-order shear deformation theory [38][39][40][41][42][43] and higher-order shear deformation theories [44][45][46][47]. However, these aforementioned works are limited to analytical or semi-analytical methods, which are only applicable to simple problems with certain geometry and boundary and loading conditions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

Thai

et al. 2017

Engineering Structures

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The objective of this study is to develop an effective numerical model within the framework of an isogeometric analysis (IGA) to investigate the geometrically nonlinear responses of functionally graded (FG) microplates subjected to static and dynamic loadings. The size effect is captured based on the modified strain gradient theory with three length scale parameters. The third-order shear deformation plate theory is adopted to represent the kinematics of plates, while the geometric nonlinearity is accounted based on the von Kármán assumption. Moreover, the variations of material phrases through the plate thickness follow the rule of mixture. By using Hamilton's principle, the governing equation of motion is derived and then discretized based on the IGA technique, which tailors the non-uniform rational B-splines (NURBS) basis functions as interpolation functions to fulfil the C 2 −continuity requirement. The nonlinear equations are solved by the Newmark's time integration scheme with Newton-Raphson iterative procedure. Various examples are also presented to study the influences of size effect, material variations, boundary conditions and shear deformation on the nonlinear behaviour of FG microplates.

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Section: Introductionmentioning

confidence: 99%

Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

Thai

et al. 2017

Engineering Structures

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“…For example, Mehralian et al studied the buckling of FG piezoelectric nanoshell under pressure based on the new modified couple stress theory and the critical buckling pressure was shown significantly size dependent by increase in thickness and decrease in length [9]. Size-dependent first order shear deformable shell model on the basis of modified strain gradient theory was utilized by Gholami et al to study the axial buckling of functionally graded cylindrical shell [10]. The effect of material property gradient index was illustrated significant on the buckling load.…”

Section: Introductionmentioning

confidence: 99%

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Beni¹,

Mehralian²

2017

International Journal of Engineering &Amp; Applied Sciences

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In the current study, the size dependent free vibration of shear deformable functionally graded (FG) nanotubes is investigated. The nanotube is modeled as cylindrical shell which contains small scale effects by using the nonlocal strain gradient theory. Material properties of the FG nanotube are assumed to be variable along thickness direction according to power law distribution. The Hamilton's principle is implemented to derive the governing equations and boundary conditions. The numerical results are presented for simply supported FG nanotube and the influence of different parameters, such as nonlocal parameter, length scale parameter, length, thickness and power law index on frequency of FG nanotube are extensively studied. The results reveal that the frequency is significantly size dependent.

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“…Despite the significance of FG microstructures, several studies are devoted to explore the mechanical responses of these phenomenal structures [26][27][28][29][30][31][32][33][34][35][36]. In this direction, based upon the MSGT, Ansari et al [37] examined the nonlinear free vibration characteristics of FG Timoshenko microbeams.…”

Section: Introductionmentioning

confidence: 99%

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Ansari

Gholami

Shojaei

et al. 2016

Applied Mathematical Modelling

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1 Highlights  Development of a nonlinear first-order shear deformable small-scale beam model  Presenting formulation based on the most general Mindlin's strain gradient theory  Prediction of coupled free vibration of post-buckled micro-and nano-beams with various BCS  Study of the effects of ⁄ , ⁄ , and BCs on the postbuckling path and frequency  Comparing the results predicted by CT, MCST and MSGT Abstract Presented herein is a comprehensive study on the size-dependent coupled longitudinal-transverserotational free vibration behavior of post-buckled functionally graded (FG) micro-and nano-beams based on the most general Mindlin's strain gradient theory. The current model enables us to incorporate size effects via introducing material length scale parameters and is developed in the framework of the firstorder shear deformable beam model and the von Karman geometric nonlinearity. The FG micro-and nano-beams, whose volume fraction is expressed by using a power law function, are assumed to be made of a mixture of metals and ceramics. By using Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-and nano-beams in the postbuckling domain. Afterwards, the governing equations and boundary conditions are discretized using the generalized differential quadrature (GDQ) method in conjunction with a direct approach without linearization, before solving numerically by Newton's method. The effects of length scale parameter, length-to-thickness ratio, material gradient index and boundary conditions on the postbuckling path and frequency of FG micro-and nano-beams are carefully investigated. Finally, numerical results obtained from both the modified strain gradient theory (MSGT) and modified couple stress theory (MCST) are compared.Mindlin's strain gradient elasticity; Size-dependent first-order shear deformable beam model.

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Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory

Cited by 60 publications

References 34 publications

Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

A Nonlocal Strain Gradient Shell Model for Free Vibration Analysis of Functionally Graded Shear Deformable Nanotubes

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

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