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Bending and free vibration analysis of porous functionally graded sandwich plate with various porosity distributions using an extended layerwise theory

Belarbi Mohamed-Ouejdi, Daikh Ahmed Amine, Garg Aman, Hirane Hicham, Houari Mohammed Sid Ahmed, Civalek Ömer, Chalak H. D.

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e15, 2023

EN

In this paper, for the first time, the bending and free vibration analysis of porous functionally graded sandwich plates with various porosity distributions is investigated using an efficient layerwise model. The present model, proposed recently by the authors, supposes a first-order displacement field for the two face sheets and a higher-order displacement field for the core, thereby ensuring the displacement continuity at the layer's interface. Unlike the conventional layerwise models, the number of degrees of freedom is fixed and does not increase when increasing the number of layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Three different types of porosity distribution including even, logarithmic-uneven, and linear-uneven porosities are considered. The material properties of the FGM sandwich porous plate are graded continuously through the thickness direction according to a power-law function. The numerical analysis is carried out by using an efficient C0 continuous eight-node quadrilateral isoparametric element developed for this purpose. The governing equations are derived according to Hamilton’s principle and solved by employing the finite element method. The robustness and accuracy of the proposed formulation are ascertained by comparing its results with those available by other researchers in the existing literature. Further, a comprehensive parametric study is examined in detail to show the effects of material distribution, aspect ratios, porosity coefficient, side-to-thickness ratio, porosity distribution, core-to-face thickness ratio, boundary conditions, volume fraction index, modes shapes on the bending and free vibration behaviors of symmetric and non-symmetric FGM porous sandwich plate. The numerical results show that these parameters play significant roles in the bending and free vibration behaviors of the FGM sandwich porous plates. Many new results are also reported, which will serve as a benchmark for future analysis of FGM sandwich plates with porosity.

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Stress and failure analysis of composite plates with circular hole subjected to shear loading. Part 1, Analytical and finite element formulation

Khechai Abdelhak, Tati Abdelouahab, Belarbi Mohamed-Ouejdi, Rekbi Fares Mohammed Laid

Composites Theory and Practice

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2022

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R. 22, nr 4

205--210

EN

This current paper, which is the first part of two parts of a complete article, presents the theoretical and finite element formulation developed and proposed by the authors to obtain the stress concentration factors (SCFs) and the first ply failure (FPF) loads of composite laminated plates. The numerical studies are performed using a quadrilateral finite element of four nodes with thirty-two degrees of freedom. The present finite element was previously developed by the authors to study the bending and buckling of composite plates. The present finite element is a combination of two finite elements. The first one is a linear isoparametric membrane element, and the second one is a high-precision rectangular Hermitian element. In the second part of the paper, several examples will be considered to demonstrate and affirm the accuracy and the performance of the present element, as well as highlight the effect of some parameters on the stress distribution. The FPF strengths and their locations in laminated plates with and without holes are calculated by adapting the Hashin-Rotem, Tsai-Hill, and Tsai-Wu failure theories.

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Stress and failure analysis of composite plates with a circular hole subjected to shear loading. Part 2, Results and discussions

Khechai Abdelhak, Tati Abdelouahab, Belarbi Mohamed-Ouejdi, Rekbi Fares Mohammed Laid

Composites Theory and Practice

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2022

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R. 22, nr 4

225--232

EN

This paper, the second part of two parts of a complete paper, presents the analytical and numerical results of stresses around circular cutouts in anisotropic and isotropic plates under shear loading. The main aim of this study is to understand the effect of the presence of cutouts on the stress concentration and failure mechanisms in composite laminates. The numerical investigations are performed by means of the quadrilateral finite element of four nodes with thirty-two degrees of freedom. The present finite element is a combination of two finite elements. The first one is a simple linear isoparametric membrane element and the second one is a high-precision rectangular Hermitian element. The analytical and finite element formulations were presented in the first part of the paper. Several new examples are considered to demonstrate and affirm the accuracy and the performance of the present element and to highlight the effect of some parameters on the stress distributions. The numerically obtained results are found to be in good agreement with the analytical findings. On the other hand, first ply failure (FPF) strengths in laminates with and without holes are calculated by adapting the Hashin-Rotem, Tsai-Hill, and Tsai-Wu failure theories. Finally, the numbers of the figures are obtained, using various E1/E2 ratio values, for the maximum positive and negative stresses values located in the vicinity of the cutout versus the angular location of points, and for various fiber orientation angles.