On vibration of functionally graded sandwich nanoplates in the thermal environment

Daikh, Ahmed Amine; Draï, Ahmed; Bensaid, Ismail; Houari, Mohammed Sid Ahmed; Tounsi, Abdelouahed

doi:10.1177/1099636220909790

Cited by 52 publications

(15 citation statements)

References 43 publications

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“…Table 3 presents the convergence of the maximum values of non-dimensional displacements with various element discretization (ne ¼ 2, 4, 8, 12, 16, 24 and 32). These results are compared with the analytical solutions of Sims¸ek et al, 63 Vo et al 47 and Nguyen et al 7 and those obtained by Katili et al 59 using finite element model. As one can see in Table 3, for different values of volume fraction index (p) and various L/h ratios, the maximum deflection resulting from the present element is in excellent agreement with the reference results using in most of the cases four finite elements only.…”

Section: Convergence and Validation Studiesmentioning

confidence: 78%

“…3 Conventional sandwich structures consists of two thin, stiff, and strong face sheets connected by a thick, light and low-modulus core using adhesive joints. [4][5][6][7] However, a high mismatch in material and geometric properties between them leads to an interlaminar stress concentration at the face sheet-to-core interface when different materials are joined and, as a result, sandwich composites often suffer from premature failure caused by debonding from the core of the face sheet. Another significant factor is that there are no high service temperature capabilities for usual sandwich materials.…”

Section: Introductionmentioning

confidence: 99%

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Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Belarbi

Khechai

Bessaim

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

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Section: Convergence and Validation Studiesmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Belarbi

Khechai

Bessaim

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

View full text Add to dashboard Cite

show abstract

“…Nguyen et al [40] examined the vibration of functionally graded plates using HSDT. Moreover, nanoplates in the thermal environment were studied by Daikh et al [41]. Baghlani et al [42] investigated the free vibration of FGM cylindrical shells on elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

Javed

Mukahal

2021

International Journal of Aerospace Engineering

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This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.

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“…Nguyen et al [32] examined the vibration of functionally graded plates using HSDT. Moreover, nanoplates in the thermal environment were studied by Diakh et al [33]. Baghlani et al [34] investigated the free vibration of FGM cylindrical shells on elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory

Nuwairan

Javed

2021

Journal of Mathematics

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The focus of this study is to analyse the free vibration of cylindrical shells under third-order shear deformation theory (TSDT). The constitutive equations of the cylindrical shells are obtained using third-order shear deformation theory (TSDT). The surface and traverse displacements are expected to have cubic and quadratic variation. Spline approximation is used to approximate the displacements and transverse rotations. The resulting generalized eigenvalue problem is solved for the frequency parameter to get as many eigenfrequencies as required starting from the least. From the eigenvectors, the spline coefficients are computed from which the mode shapes are constructed. The frequency of cylindrical shells is analysed by varying circumferential node number, length dimension, layer number, and different materials. The authenticity of the present formulation is established by comparing with the available FEM results.

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On vibration of functionally graded sandwich nanoplates in the thermal environment

Cited by 52 publications

References 43 publications

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory

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