A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Cross-Ply Laminated Plates

Benhenni, M. A.; Adim, Belkacem; Daouadji, Tahar Hassaine; Abbès, Boussad; Abbès, Fazilay; Li, Y.; Bouzidane, Ahmed

doi:10.1007/s11029-019-09803-2

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…Although it keeps increasing the n>15, it causes constant NDNF values at various BCs. However, Benhenni et al [482] employed the HSDT associated with 3D-FEA to investigate the NF of hybrid carbon/glass cross-ply LCPs, and the HP has been utilized to define the EOM. Besides, the NvS has been used to determine the closed-form solutions.…”

Section: Mixed Solution With Considering the Sdementioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

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Section: Mixed Solution With Considering the Sdementioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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“…The influence of different ply orientation in square and rectangular laminated plates was studied for different cases of dynamic loading. In [8][9][10], free vibrations of laminated plates under different boundary conditions were studied. The propagation of elastic waves in laminated composite with special emphasis on Lamb waves was also analyzed [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Finite element modelling of laminated composite: Effects of different ply orientations

Čukanović¹,

Bogdanović²,

Radaković³

2022

Engineering Today

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The subject of analysis in this paper are laminated composites as an always popular topic in the field of composite materials. The introductory part of the paper presents a brief overview of the current state of research in this area and points out further directions of research related to this very interesting topic. The classification of laminated composite plates from the aspect of different criteria are described in detail. As the subject of the paper is stress-strain analysis of laminated composite, the expression for the generalized Hooke's law of orthotropic class of material symmetry is given. The terms of the constitutive matrix are expressed through engineering constants. At the end, the bending analysis of the rigidly supported laminated plate under a sinusoidal load was performed. The mentioned analysis was conducted using software based on the finite element method. A comparative analysis of the plate with the different ply orientation (0°/90°/90°/0° and -45°/45°/45°/-45°) was done. The obtained results were analyzed and appropriate conclusions were made.

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“…Daouadji et al [35], Chergui et al [29], Rabahi et al [78] presented the numerical and experimental results to study the flexural behaviour of steel and RC beams strengthened by laminates. Benhenni et al [18][19][20][21], Benferhat [15], Bensattalah et al [22,23], Hadji et al [51], Adim et al [7] reported the free vibration response for the FG, laminated beams and plates. Adim et al [5,6], Bensattalah et al [24], Khalifa [57] examined the buckling response of FG and laminated composite plate using refined HSDTs.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for the hygro-thermo-mechanical bending of FG beams using a new fifth order shear and normal deformation theory

Ghumare

Sayyad

2020

ACM

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A new analytical solution is presented for functionally graded (FG) beams to investigate the bending behaviour under the hygro-thermo-mechanical loading using a new fifth order shear and normal deformation theory (FOSNDT). The material properties of the FG beam are varied along the thickness direction according to the power law index. In the present theory, a polynomial shape function is expanded up to fifth-order in terms of thickness coordinate to consider the effects of transverse shear and normal deformations. The present theory is free from the shear correction factor. Using the Navier's solution technique the closed-form solution is obtained for simply supported FG beams. All the results are presented in non-dimensional form and validated it by developing the classical beam theory (CBT), first order shear deformation theory (FSDT by Mindlin) and third order shear deformation theory (TSDT by Reddy) considering the hygro-thermo-mechanical loading effects which is mostly missing in the literature. It is noticed that the presented FOSNDT is very simple and accurate to predict the bending behaviour of FG beams under linear and non-linear hygro-thermo-mechanical loadings.

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A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Cross-Ply Laminated Plates

Cited by 10 publications

References 12 publications

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Finite element modelling of laminated composite: Effects of different ply orientations

Analytical solutions for the hygro-thermo-mechanical bending of FG beams using a new fifth order shear and normal deformation theory

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