Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates based on nonlocal elasticity theory

Anjomshoa, Amin

doi:10.1007/s11012-012-9670-y

Cited by 37 publications

(24 citation statements)

References 33 publications

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“…Aydogdu [80] studied the buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions. Anjomshoa [81] presented a continuum model based on the nonlocal theory of elasticity for buckling analysis of embedded orthotropic circular and elliptical micro/nanoplates under uniform in-plane compression. Darvizeh et al [82] developed a mathematical modeling for generally laminated plates based on generalized differential quadrature rule and Rayleigh-Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closedform solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

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Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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“…Anjomshoa [152] and Anjomshoa et al [153] proposed nonlocal CPT models to examine the buckling [152] and free vibration [153] of orthotropic circular and elliptical SLGSs embedded in an elastic medium. The nonlocal CPT model was also developed by Mohammadi et al [154] to examine the shear buckling of orthotropic embedded SLGSs in thermal environment.…”

Section: Nonlocal Models Based On Hsdtsmentioning

confidence: 99%

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

Thai

Nguyen

et al. 2017

Composite Structures

326

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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“…The thickness variation in the radial direction is assumed to be linear, whereas in the circumferential directional the thickness varies according to cosine law. Anjomshoa (2013) developed a model based on non-local theory for buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates. The effects of non-local parameter, length of the nanoplate, change in material properties, aspect ratio and elastic foundation are studied using the Rayleigh–Ritz method.…”

Section: Platesmentioning

confidence: 99%

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Kumar¹

2017

Journal of Vibration and Control

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The Rayleigh–Ritz method is a classical method that has been widely used to investigate dynamic, static and buckling behavior, i.e., the natural frequencies, mode shapes, moments, stresses, critical buckling loads of vibrating structures and to solve boundary value problems. Different developments in the method have taken place from time to time. This paper presents a comprehensive literature review on the application of the Rayleigh–Ritz method to analyze vibration, static and buckling characteristics of beams, shells and plates using different theories.

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Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates based on nonlocal elasticity theory

Cited by 37 publications

References 33 publications

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

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

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

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