Buckling and free vibrations behaviour through differential quadrature method for foamed composites

Duryodhana, Dasari; Waddar, Sunil; Bonthu, Dileep; Pitchaimani, Jeyaraj; Powar, Satvasheel; Doddamani, Mrityunjay

doi:10.1016/j.rineng.2023.100894

Cited by 9 publications

(4 citation statements)

References 26 publications

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“…DQM is a powerful numerical method that has been used in many papers [ 43 , 44 ]. The basic goal of this technique is to apply Lagrange interpolation polynomials to field coefficients and to solve the equations at discrete grid points.…”

Section: Introductionmentioning

confidence: 99%

“…Ghorbani et al [42] studied surface effects on the natural frequency of a functionally graded cylindrical nanoshell using the nonlocal strain gradient theory via generalized DQM. DQM is a powerful numerical method that has been used in many papers [43,44]. The basic goal of this technique is to apply Lagrange interpolation polynomials to field coefficients and to solve the equations at discrete grid points.…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate

2023

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A nonlinear static analysis of a circular/annular nanoplate on the Winkler–Pasternak elastic foundation based on the nonlocal strain gradient theory is presented in the paper. The governing equations of the graphene plate are derived using first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) with nonlinear von Karman strains. The article analyses a bilayer circular/annular nanoplate on the Winkler–Pasternak elastic foundation. HSDT while providing a suitable distribution of shear stress along the thickness of the FSDT plate, eliminating the defects of the FSDT and providing good accuracy without using a shear correction factor. To solve the governing equations of the present study, the differential quadratic method (DQM) has been used. Moreover, to validate numerical solutions, the results were compared with the results from other papers. Finally, the effect of the nonlocal coefficient, strain gradient parameter, geometric dimensions, boundary conditions, and foundation elasticity on maximum non-dimensional deflection are investigated. In addition, the deflection results obtained by HSDT have been compared with the results of FSDT, and the importance of using higher-order models has been investigated. From the results, it can be observed that both strain gradient and nonlocal parameters have significant effects on reducing or increasing the dimensionless maximum deflection of the nanoplate. In addition, it is observed that by increasing load values, the importance of considering both strain gradient and nonlocal coefficients in the bending analysis of nanoplates is highlighted. Furthermore, replacing a bilayer nanoplate (considering van der Waals forces between layers) with a single-layer nanoplate (which has the same equivalent thickness as the bilayer nanoplate) is not possible when attempting to obtain exact deflection results, especially when reducing the stiffness of elastic foundations (or in higher bending loads). In addition, the single-layer nanoplate underestimates the deflection results compared to the bilayer nanoplate. Because performing the experiment at the nanoscale is difficult and molecular dynamics simulation is also time-consuming, the potential application of the present study can be expected for the analysis, design, and development of nanoscale devices, such as circular gate transistors, etc.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate

2023

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“…DQM is one of the numerical methods that has been employed by many authors [ 36 , 37 ]. The initial purpose of this procedure is to employ Lagrange interpolation polynomials to field constants and to solve the equations at discrete grid nodes.…”

Section: Introductionmentioning

confidence: 99%

“…With the aid of DQM, Han et al [ 38 ] studied one-electrode microresonators on the basis of a generalized 1DOF principle. Duryodhana et al [ 37 ] employed DQM to study the buckling (and free vibrations) of foamed composites. By means of DQM, Ren et al [ 39 ] investigated the thermal and mechanical buckling behavior of heated rectangular plates considering the characteristics of the temperature-dependent material.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Thermal/Mechanical Buckling of Orthotropic Annular/Circular Nanoplate with the Nonlocal Strain Gradient Model

Sadeghian,

Palevicius,

Janusas

2023

Micromachines

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This article presents the nonlinear investigation of the thermal and mechanical buckling of orthotropic annular/circular single-layer/bilayer nanoplate with the Pasternak and Winkler elastic foundations based on the nonlocal strain gradient theory. The stability equations of the graphene plate are derived using higher-order shear deformation theory (HSDT) and first-order shear deformation theory (FSDT) considering nonlinear von Karman strains. Furthermore, this paper analyses the nonlinear thermal and mechanical buckling of the orthotropic bilayer annular/circular nanoplate. HSDT provides an appropriate distribution for shear stress in the thickness direction, removes the limitation of the FSDT, and provides proper precision without using a shear correction coefficient. To solve the stability equations, the differential quadratic method (DQM) is employed. Additionally, for validation, the results are checked with available papers. The effects of strain gradient coefficient, nonlocal parameter, boundary conditions, elastic foundations, and geometric dimensions are studied on the results of the nondimensional buckling loads. Finally, an equation is proposed in which the thermal buckling results can be obtained from mechanical results (or vice versa).

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Predicting the indentation load of FRP facesheet / foam core sandwiches

Çetin,

Uzay,

Tütüncü

et al. 2024

Structures

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Buckling and free vibrations behaviour through differential quadrature method for foamed composites

Cited by 9 publications

References 26 publications

Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate

Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate

Nonlinear Thermal/Mechanical Buckling of Orthotropic Annular/Circular Nanoplate with the Nonlocal Strain Gradient Model

Predicting the indentation load of FRP facesheet / foam core sandwiches

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