Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory

Malikan, Mohammad; Dastjerdi, Shahriar

doi:10.24107/ijeas.420838

Cited by 7 publications

(5 citation statements)

References 50 publications

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“…The total potential energy of distortion consists of three parts: distortion warping strain energy, distortion frame strain energy, and external load potential energy [ 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 ]. This derivation follows the principle of minimum potential energy.…”

Section: Total Potential Energy Variational Methodsmentioning

confidence: 99%

Distortion Effect on the UHPC Box Girder with Vertical Webs: Theoretical Analysis and Case Study

Wang,

Wu,

Zhang

et al. 2024

Materials

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Distortion deformation usually imposes a potential threat to bridge safety. In order to comprehensively understand the distortion effect on thin-walled ultra-high performance concrete (UHPC) box girders, an innovative approach encompassing the governing distortion differential equation is introduced in this study based on the general definition of distortion angle within the cross-section plane. The analytical results obtained from the proposed method are in accordance with those obtained from the energy method, and exhibit favorable agreement with experimental findings documented in the existing literature. Furthermore, a finite element model is developed on the ANSYS 2021 R1 software platform with the employment of a Shell 63 element. Numerical outcomes are also in good agreement with the experimental data, affirming the validity and reliability of the findings. In addition, parameter analysis results indicate that the distortion angle remains approximately constant at a location approximately 1/10 of the span from the mid-span cross-section of the box girder, regardless of changes in the span-to-depth ratio. Increasing the web thickness yields a notable reduction in the distortion effects, and decreasing the wall thickness can effectively mitigate the distortion-induced transverse bending moment. Compared with normal-strength concrete box girders, UHPC box girders can reduce the distortion angle within the span range, which is beneficial for maintaining the overall stability of the box girders. The outcomes obtained from this study yield engineers an enhanced understanding of distortion effect on the UHPC girder performance.

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Section: Total Potential Energy Variational Methodsmentioning

confidence: 99%

Distortion Effect on the UHPC Box Girder with Vertical Webs: Theoretical Analysis and Case Study

Wang,

Wu,

Zhang

et al. 2024

Materials

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“…Navier’s technique has been employed to find a closed-form solution for the Pined–Pined (P-P) boundary condition. As per the Navier’s technique, the transverse displacement (W) may be expressed as [23,24,25] W =true∑n=1∞Wn sin(nπX) eiωnt…”

Section: Solution Methodologymentioning

confidence: 99%

“…Here, unidirectional load is applied on the SWCNT. Buckling analysis of FG (Fanctionally Graded) nanobeam was studied in [23] analytically with the help of Navier’s method under the framework of first-order shear deformation beam theory. Malikan et al investigated the transient response [24] of nanotube for a simply supported boundary condition using Kelvin–Voigt viscoelasticity model with nonlocal strain gradient theory.…”

Section: Introductionmentioning

confidence: 99%

Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based Rayleigh-Ritz Method

Jena

Tornabene

2019

Nanomaterials

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In the present investigation, the buckling behavior of Euler–Bernoulli nanobeam, which is placed in an electro-magnetic field, is investigated in the framework of Eringen’s nonlocal theory. Critical buckling load for all the classical boundary conditions such as “Pined–Pined (P-P), Clamped–Pined (C-P), Clamped–Clamped (C-C), and Clamped-Free (C-F)” are obtained using shifted Chebyshev polynomials-based Rayleigh-Ritz method. The main advantage of the shifted Chebyshev polynomials is that it does not make the system ill-conditioning with the higher number of terms in the approximation due to the orthogonality of the functions. Validation and convergence studies of the model have been carried out for different cases. Also, a closed-form solution has been obtained for the “Pined–Pined (P-P)” boundary condition using Navier’s technique, and the numerical results obtained for the “Pined–Pined (P-P)” boundary condition are validated with a closed-form solution. Further, the effects of various scaling parameters on the critical buckling load have been explored, and new results are presented as Figures and Tables. Finally, buckling mode shapes are also plotted to show the sensitiveness of the critical buckling load.

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“…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

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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.

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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory

Cited by 7 publications

References 50 publications

Distortion Effect on the UHPC Box Girder with Vertical Webs: Theoretical Analysis and Case Study

Distortion Effect on the UHPC Box Girder with Vertical Webs: Theoretical Analysis and Case Study

Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based Rayleigh-Ritz Method

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

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