A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law

Malikan, Mohammad; Nguyen, Van Bac

doi:10.1108/wje-11-2017-0357

Cited by 8 publications

(3 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They obtained exact solutions using the method. Malikan and Nguyen [35] used a single variable first-order shear deformation theory to solve biaxial stability problems of plates based on Eringen's nonlocal elasticity approach. Zhong and Qu [36] analyzed clamped rectangular thick plate bending problems but did not consider buckling.…”

Section: Introductionmentioning

confidence: 99%

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Ike

2023

ETJ

View full text Add to dashboard Cite

The double finite sine transform method was utilized to obtain exact buckling solutions for thick plate problems • The method simplified the problem to algebraic ones since the sinusoidal function satisfies the boundary conditions • The buckling solutions aligned with exact solutions for thick plates This paper derives buckling solutions for single variable thick plate buckling problems using the double finite sine transform method (DFSTM). The problem governing partial differential equation (GPDE), originally formulated by Shimpi and others, uses a refined plate theory (RPT) and accounts for transverse shear deformations, rendering it applicable to thick plates. The thick plate is simply supported and subjected to (i) uniform uniaxial compressive load in the x direction. (ii) uniform biaxial compressive load in the x and y axes. The DFSTM was applied to the GPDE, and the problem transformed into an algebraic equation, which was simpler in this case due to the Dirichlet boundary conditions satisfied by the sinusoidal kernel of the DFSTM. Analytical buckling solutions were determined for the two considered cases of uniaxial and biaxial compressive loads in terms of the buckling modes, Poisson's ratio (µ), and thickness (h) to least dimension (a) ratio. Critical buckling loads (Pcr) determined at the first buckling modes agreed with previously obtained Navier solutions for Mindlin, Reddy, and Refined plates. Pcr calculated for ratios of h/a equal to 0.01 converged to the solutions obtained using Kirchhoff-Love plate theory (KLPT), illustrating the applicability of the GPDE to thin and thin plate buckling.

show abstract

Section: Introductionmentioning

confidence: 99%

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Ike

2023

ETJ

View full text Add to dashboard Cite

show abstract

“…However, in nonlocal elasticity theory, introduced by Eringen (1983Eringen ( , 2004Eringen and Edelen (1972), stress at a given point is a function of strains in all points of the continuum (Rahimi et al, 2017). With the nonlocal theory for analyzing nanotubes (Aydogdu, 2012), mechanical behaviors of materials at small scales are more understandable (Malikan and Nguyen, 2018). Recently, nonlocal beam models have been widely used for determining static and vibration properties of single-or multi-walled CNTs (Murmu and Adhikari, 2012;Reddy, 2007;S ims ek, 2010).…”

Section: Introductionmentioning

confidence: 99%

Modified nonlocal theory for investigation the specific aspects of nonlinear behavior of carbon nanotube as a nano-resonator

ShayanMehr

Basiri

2020

WJE

View full text Add to dashboard Cite

Purpose In this paper, the important aspects of vibration analysis of carbon nanotubes (CNTs) as nano-resonators are studied. This study has covered the important nonlinear phenomena such as jump super-harmonic and chaotic behavior. CNT is modeled by using the modified nonlocal theory (MNT). Design/methodology/approach In previous research studies, the effects of CNT’s rotary inertia, stiffness and shear modulus of the medium were neglected. So by considering these terms in MNT, a comprehensive model of vibrational behavior of carbon nanotube as a nanosensor is presented. The nanotube is modeled as a nonlocal nonlinear beam. The first eigenmode of an undamped simply supported beam is used to extract the nonlinear equation of CNT. Harmonic balance method is used to solve the equation, while to study its super-harmonic behavior, higher-order harmonic terms were used. Findings In light of frequency response equation, jump phenomenon and chaotic behavior of the nanotube with respect to the amplitude of excitation are investigated. Also in each section of the study, the effects of elastic medium and nonlocal parameters on the vibration behavior of nanotube are investigated. Furthermore, parts of the results in linear and nonlinear cases were compared with results of other references. Originality/value The present modification of the nonlocal theory is so important and useful for accurate investigation of the vibrational behavior of nano structures such as a nano-resonator.

show abstract

“…1b [52]. A novel plate model is here proposed, which assumes the following displacement field [53][54][55][56][57][58][59] As far as the Hamilton's approach is concerned, the potential energy of the model, V, is defined as [60]  …”

Section: Introductionmentioning

confidence: 99%

Thermo-resonance analysis of an excited graphene sheet using a new approach

Malikan

Dimitri²,

Tornabene³

2018

International Journal of Engineering and Applied Sciences

Self Cite

View full text Add to dashboard Cite

This paper analyzes the thermo-vibration response of a graphene sheet excited with a uniform harmonic The problem is here tackled with a novel approach combined with a nonlocal strain gradient theory (NSGT), in order to include the size-dependence and the nonlocality effect on impacts. Simply-supported plates are here studied analytically, according to the Navier's method. Thus, the thermo-forced vibration equations of the problem are here written and solved numerically for graphene sheets. The accuracy of the proposed theory is checked by means of several comparative evaluations with respect to the available results from literature. Another key aspect of the works is the sensitivity of the thermo-mechanical response of the plate structures to different thermal and mechanical input parameters. This could be of great interest for design purposes for many engineering applications, including nanoelectromechanical systems (NEMS), biosensors, piezoelectric devices, biomechanical tissues, among others.

show abstract

A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law

Cited by 8 publications

References 54 publications

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Modified nonlocal theory for investigation the specific aspects of nonlinear behavior of carbon nanotube as a nano-resonator

Thermo-resonance analysis of an excited graphene sheet using a new approach

Contact Info

Product

Resources

About