A continuum shell element in layerwise models for free vibration analysis of FGM sandwich panels

Burlayenko, Vyacheslav N.

doi:10.1007/s00161-021-00981-w

Cited by 11 publications

(2 citation statements)

References 67 publications

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“…A compromising choice between the simplicity of ESL theories and the accuracy of complicated 3D elasticity solutions, stems from the use of layerwise (LW) models [69][70][71]. In these models, each single layer is treated as a plate itself and the kinematic model is linked to specific layers [72][73][74]. Liu et al [71] studied the free vibration analysis of FG sandwich plates by using a refined higher-order LW model and finite elements.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.

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Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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“…The graded elements are superior than conventional elements for simulation of the FGMs (Kim and Paulino, 2002; Santare et al ., 2003). In ABAQUS/Standard owing to simulate the continuous distribution of material properties, the user-defined material model has been implemented by employing the user subroutine UMAT (Burlayenko, 2021). The volume fraction terms and the effective value of elasticity modulus have been calculated, and the stiffness matrix has been exported based on the rule of mixture with appropriate formulation.…”

Section: Problem Formulationmentioning

confidence: 99%

Three-dimensional natural frequency investigation of bidirectional FG truncated thick hollow cone

Najibi

Kianifar²,

Ghazifard³

2022

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PurposeThe authors examined the numerical natural frequency analysis of a 2D functionally graded (FG) truncated thick hollow cone using 3D elasticity theory.Design/methodology/approachThe material properties of the 2D-FGM (two dimensional-functionally graded materials) cone are graded along the radial and axial axes of the cone using a power–law distribution. The eigenvalue problem was solved using finite element analysis (FEA) employing graded hexahedral elements, and the verification of the finite element approach was assessed by comparing the current solution to earlier experimental studies.FindingsThe effects of semivertex angle, material distribution and the cone configuration on the natural frequencies have been analyzed. For various semivertex angles, thickness, length and power law exponents, many results in the form of natural frequencies and mode shapes are presented for the 2D-FGM cone. As a result, the effects of the given parameters were addressed, and the results were compared, demonstrating the direct efficiency of raising the power–law exponents and cone thickness on the rise of natural frequencies.Originality/valueFor the first time, the numerical natural frequency analysis of a 2D-FG truncated thick hollow truncated cone based on 3D equations of elasticity has been investigated. The material properties of the truncated cone have been distributed along two directions, which has not been considered before in any research for the truncated thick cone. The reason for using these innovative volume fraction functions is the lack of accurate coverage by functions that are available in the literature (Asemi et al., 2011; Babaei et al. 2021).

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