Pre-buckling responses of Timoshenko nanobeams based on the integral and differential models of nonlocal elasticity: an isogeometric approach

Norouzzadeh, A.; Ansari, R.; Rouhi, H.

doi:10.1007/s00339-017-0887-4

Cited by 55 publications

(20 citation statements)

References 51 publications

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“…bending and vibration problems of cantilever beams. More information about paradoxical behaviour of the differential model can be found in [51][52][53][54].…”

Section: Review Of the Nonlocal Elasticity Theorymentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

317

112

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This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

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“…bending and vibration problems of cantilever beams. More information about paradoxical behaviour of the differential model can be found in [51][52][53][54].…”

Section: Review Of the Nonlocal Elasticity Theorymentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

317

112

View full text Add to dashboard Cite

show abstract

“…Norouzzadeh and Ansari [24] used integral form of nonlocal theory to study bending analysis of Timoshenko beam with the help of finite element method and concluded that the differential form of constitutive relation provides unexpected results for some boundary conditions. Some other interesting article of nanobeam and plates using the integral form of nonlocal theory can be found in [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Propagation of uncertainty in free vibration of Euler–Bernoulli nanobeam

Jena

Chakraverty

2019

J Braz. Soc. Mech. Sci. Eng.

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In this paper, Euler-Bernoulli nanobeam based on the framework of Eringen's nonlocal theory is modeled with material uncertainties where the uncertainties are associated with mass density and Young's modulus in terms of fuzzy numbers. A particular type of imprecisely defined number, namely triangular fuzzy number, is taken into consideration. In this regard, double parametric-based Rayleigh-Ritz method has been developed to handle the uncertainties. Vibration characteristics have been investigated, and the propagation of uncertainties in frequency parameters is analyzed. Material uncertainties are considered with respect to three cases, viz. (1) Young's modulus (2) mass density and (3) both Young's modulus and mass density, as imprecisely defined. Frequency parameters and mode shapes are computed and presented for Pined-Pined (P-P) and Clamped-Clamped (C-C) boundary conditions. Accuracy and efficiency of the models are verified by conducting the convergence study for all the three cases. Lower and upper bounds of frequency parameters are computed with the help of the double parameter, and graphical results are plotted as the triangular fuzzy number showing the sensitivity of the models. Obtained results for frequency parameters are compared with other well-known results found in previously published literature(s) in special cases (crisp cases) witnessing robust agreement. The uncertainty modeling and the bounds of frequency parameters may serve as an effective tool for the designing and optimal quality enhancement of engineering structures.

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“…For some boundary and loading conditions (especially for cantilever beams), inconsistent and illogical findings may be resulted by the differential model. [34][35][36][37] However, for MEMS modeled as cantilever beams, using an integral-based nonlocal elastic model, a solution identical to the classical local stress beam model without any small-scale effect is obtained. 38 On the other hand, Eringen 3 showed that the integral constitutive equation can be converted exactly into a corresponding differential form for some kernels.…”

Section: Introductionmentioning

confidence: 99%

Free vibration characteristics of functionally graded Mindlin nanoplates resting on variable elastic foundations using the nonlocal elasticity theory

Sari

Alrbai

Qawasmeh

2018

Advances in Mechanical Engineering

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In this research, free vibration behavior of thick functionally graded nanoplates is carried out using the Chebyshev spectral collocation method. It is assumed that the plates are resting on variable elastic foundations. Eringen's nonlocal elasticity theory is used to capture the size effect, and Mindlin's first-order shear deformation plate theory is employed to model the thick nanoplates. Hamilton's principle along with the differential form of Eringen's constitutive relations are utilized to obtain the governing partial differential equations of motion for the functionally graded nanoplates under consideration. A numerical solution is presented by applying the spectral collocation method and the natural frequencies are obtained. A parametric study is conducted to study the effects of several factors on the natural frequencies of the functionally graded nanoplates. It is found that the parameters of the variable elastic foundation (Winkler and shear moduli), thickness to length ratio, length to width ratio (aspect ratio), the nonlocal scale coefficient, the gradient index, the foundation type, and the boundary conditions have a remarkable influence on the free vibration characteristics of the functionally graded nanoplates.

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Pre-buckling responses of Timoshenko nanobeams based on the integral and differential models of nonlocal elasticity: an isogeometric approach

Cited by 55 publications

References 51 publications

A review of continuum mechanics models for size-dependent analysis of beams and plates

A review of continuum mechanics models for size-dependent analysis of beams and plates

Propagation of uncertainty in free vibration of Euler–Bernoulli nanobeam

Free vibration characteristics of functionally graded Mindlin nanoplates resting on variable elastic foundations using the nonlocal elasticity theory

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