A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities

Zenkour, Ashraf M.

doi:10.1016/j.compstruct.2018.05.147

Cited by 124 publications

(30 citation statements)

References 62 publications

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“…16into Eq. (10), the governing algebraic equations of the FG plate using in PFEM for nonlinear analysis can be expressed in the following form (19) in which is the global stiffness matrix which can be computed as (20) in which , and are the global linear stiffness matrix, the global nonlinear stiffness matrix and the global geometric stiffness matrix, respectively. These global matrices are…”

Section: Construction Of Quadratic Serendipity Shape Functionmentioning

confidence: 99%

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Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Nguyen

Lee

et al. 2018

Advances in Engineering Software

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In this study, an efficient polygonal finite element method (PFEM) in combination with quadratic serendipity shape functions is proposed to study nonlinear static and dynamic responses of functionally graded (FG) plates with porosities. Two different porosity types including even and uneven distributions through the plate thickness are considered. The quadratic serendipity shape functions over arbitrary polygonal elements including triangular and quadrilateral ones, which are constructed based on a pairwise product of linear shape functions, are employed to interpolate the bending strains. Meanwhile, the shear strains are defined according to the Wachspress coordinates. By using the Timoshenko's beam to interpolate the assumption of the strain field along the edges of polygonal element, the shear locking phenomenon can be naturally eliminated. Furthermore, the C 0-type higher-order shear deformation theory (C 0-HSDT), in which two additional variables are included in the displacement field, significantly improves the accuracy of numerical results. The nonlinear equations of static and dynamic problems are solved by Newton-Raphson iterative procedure and by Newmark's integration scheme in association with the Picard methods, respectively. Through various numerical examples in which complex geometries and different boundary conditions are involved, the proposed approach yields more stable and accurate results than those generated using other existing approaches.

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Section: Construction Of Quadratic Serendipity Shape Functionmentioning

confidence: 99%

“…Additionally, the buckling problems of porous FG beams and plates have also been discussed [18,19]. Based on the quasi-3D shear deformation theory, Zenkour [20] investigated the bending responses of porous FG single-layered and sandwich plates which are graded using two types of exponential or polynomial laws.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Nguyen

Lee

et al. 2018

Advances in Engineering Software

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“…e same schemes are used for free vibration analysis of piezoelectric nanobeams [45,46]. Recent studies have investigated the vibration analysis of composite plate resting on elastic foundations, using DSCDQM [47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Ragb

Salah

Matbuly

et al. 2020

Mathematical Problems in Engineering

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In this work, free vibration of the piezoelectric composite plate resting on nonlinear elastic foundations is examined. The three-dimensionality of elasticity theory and piezoelectricity is used to derive the governing equation of motion. By implementing two differential quadrature schemes and applying different boundary conditions, the problem is converted to a nonlinear eigenvalue problem. The perturbation method and iterative quadrature formula are used to solve the obtained equation. Numerical analysis of the proposed schemes is introduced to demonstrate the accuracy and efficiency of the obtained results. The obtained results are compared with available results in the literature, showing excellent agreement. Additionally, the proposed schemes have higher efficiency than previous schemes. Furthermore, a parametric study is introduced to investigate the effect of elastic foundation parameters, different materials of sensors and actuators, and elastic and geometric characteristics of the composite plate on the natural frequencies and mode shapes.

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“…Many investigations on the mechanical behavior of FGM structures subjected to static and dynamic loads have been reported in the literature, contributions that are most relevant to the present work are briefly discussed herein. Zenkour and his co-workers [1][2][3][4] adopted classical and shear deformation plate theories in their static bending, free vibration, stability and thermal stability analyses of FGSW plates with or without 78 porosities. The results obtained in these studies show that the material distribution plays an important role on the behavior of the plates.…”

Section: Introductionmentioning

confidence: 99%

Static Bending of Two-Directional Functionally Graded Sandwich Plates Using a Third-Order Shear Deformation Finite Element Model

Chính

2020

JST

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In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

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A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities

Cited by 124 publications

References 62 publications

Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates

Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

Static Bending of Two-Directional Functionally Graded Sandwich Plates Using a Third-Order Shear Deformation Finite Element Model

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