Ismail Mechab - Academia.edu (original) (raw)

Papers by Ismail Mechab

Computational Materials Science, 2009

In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded materia... more In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded material (S-FGM) beam of thick thickness subjected to uniformly distributed transverse loading has been investigated. The S-FGM system consists of ceramic (Al 2 O 3) and metal (Al) phases varying through the thickness of beam. Major classes of representative theories such as classical laminate beam theory (CLBT), first-order shear deformation theory (FSDT) and high-order theories (HOTs) have been considered and a unified kinematic formulation is then proposed. The Poisson's ratio of the thick S-FGM beam is assumed to be constant, but their Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by sigmoid function. The numerical illustrations concern bending response of S-FGM rectangular beams. Qualitative and quantitative assessments of displacement and stress fields have been presented and discussed.

Computational Materials Science, Dec 1, 2008

Journal of The Brazilian Society of Mechanical Sciences and Engineering, Feb 1, 2016

engineering design and manufacture. FGMs have continuous variation of material properties in one ... more engineering design and manufacture. FGMs have continuous variation of material properties in one or more directions. Typically, FGMs are made from a mixture of ceramics and metals with the variation of the volume fraction according to a power law through thickness [1, 2]. FGMs have received wide applications as structural components in modern industries such as mechanical, aerospace, nuclear reactors, and civil engineering. In the process of FGMs fabrication, the existence of porosities and micro-voids inside the materials possiblyoccurs due to technical problems, especially at the ceramic zone. The impact of this failure has been the subject of much attention, as evidenced by the large number of studies on this subject. For porous plates and shells, Magnucka-Blandzi [3] studied the dynamic stability for a circular porous plate to determine the critical loads. The influence of unstable regions for the Mathieu equation was described. She [4, 5] also examined the nonlinear dynamic stability and axi-symmetrical deflection and buckling of circular porous plates. Belica and Magnucki [6, 7] investigated the dynamic stability of a porous cylindrical shell under different loading. Wattanasakulpong and Ungbhakor [8] investigate linear and nonlinear vibration problems of FGMs beams having porosities. Wattanasakulpong et al. and Ebrahimi [9, 10] presented a work on porosities happening inside FGMs samples fabricated by a multi-step sequential infiltration technique. FGMs may possess a number of advantages such as high resistance to temperature gradients, significant reduction in residual and thermal stresses, and high wear resistance. Composite structures on elastic foundations have wide applications in modern engineering and pose great technical problems in structural design. In the vast majority of the classical mechanics, plates on an elastic foundation are Abstract This paper presents a free vibration analysis of functionally graded materials nano-plate resting on Winkler-Pasternak elastic foundations based on two-variable refined plate theories including the porosities effect. The small-scale effects are introduced using the nonlocal elasticity theory with a new shear deformation function. The governing equations are obtained through the Hamilton's principle. The effect of material property, porosities, various boundary conditions and elastic foundation stiffnesses on free vibration functionally graded materials nanoplate are also presented and discussed in detail. The present solutions are compared with those obtained by other researchers. The results are in a good agreement with those in the literature.

Journal of Mathematical Analysis and Applications, Oct 1, 2008

High-order flexural theories for short laminated composite beams subjected to mechanical and ther... more High-order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented. The formulation allows for warping of the cross-section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories. Based on higher-order shear deformation theories, the governing equations are obtained using the principle of virtual work (PVW). The justification for use of higherorder shear deformation theories is established for short and composite beams where cross-sectional warping is predominant.

International Journal of Mechanics and Materials in Design, Feb 3, 2010

Free vibration analysis of simply supported functionally graded plates (FGP) resting on a Winkler... more Free vibration analysis of simply supported functionally graded plates (FGP) resting on a Winkler–Pasternak elastic foundation are examined by a new higher shear deformation theory in this paper. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The material properties change continuously through the thickness of the plate, which can vary according to

Composites Part B-engineering, Feb 1, 2013

ABSTRACT

Résumé Cette investigation modifiée du modèle de Shear-Lag [1], tient compte de la contrainte de ... more Résumé Cette investigation modifiée du modèle de Shear-Lag [1], tient compte de la contrainte de cisaillement interlaminaire et la couche adhésive pour calculer les contraintes en présence des fissures transversales avec l'apparition du délaminage au bord libre du stratifié ainsi que les réductions de rigidité pour les différents stratifiés croisés de type [ ] s m n 90 , 0 en matériaux composites, glass/epoxy, graphite/epoxy et hybride. Le but est de montrer la contribution de la couche adhésive interlaminaire entre deux plis adjacents avec une bonne transition de l'effort de cisaillement interlaminaire et l'effort normal à travers cette couche. La distribution des contraintes résolue par le modèle utilisé satisfait les conditions d'équilibres, les conditions de frontières, la continuité de déplacement et la continuité de traction aux interfaces entre les couches. Ces considérations ont données une bonne corrélation pour, les fonctions de déplacements, les contrainte...

Applied Mathematics and Mechanics, 2009

Periodica Polytechnica Civil Engineering, 2020

The present article aims essentially to present an analytical and numerical method which makes it... more The present article aims essentially to present an analytical and numerical method which makes it possible to study the damped vibrations of viscoelastic FGM nanoplates resting on viscoelastic foundations. A new model for the higher-order shear deformation plate theory is coupled with the internal Kelvin - Voigt viscoelastic model and the three-parameter viscoelastic foundation model for the purpose of reducing and minimizing the vibration response of the system. It is widely admitted that the mechanical properties of these new functionally gradient materials (FGMs) vary according to the thickness of the plate and depend on its volume fraction. The use of FGM plates seems to be an ideal solution for the study of free vibrations because of their multifunctionality that is fully integrated with the nonlocal Eringen effect. The dynamic response of such a complex system has been investigated by varying the aspect ratio of the plate, the mechanical characteristics of the material used, t...

Mechanics Based Design of Structures and Machines

Proceedings of the Third International Symposium on Materials and Sustainable Development, 2018

This study presents a mechanical model to predict the effective damped viscoelastic behavior of a... more This study presents a mechanical model to predict the effective damped viscoelastic behavior of a functional grading material (FGM). A detailed parametric study is carried out to elucidate the dynamic response of an Euler-Bernoulli beam with finite length on the basis of the non-local Eringen theory which reveal the influence of the material proprieties, nonlocal parameter and the viscoelastic parameter on the vibratory frequency of the system, we obtain the analytical solutions for the vibratory frequency of the system with boundary conditions. The applicability and the effectiveness of the model presented are demonstrated in canonical numerical examples.

MATEC Web of Conferences, 2018

Knowing what occurs above anchor plates is certainly instructive. In this general vision of the i... more Knowing what occurs above anchor plates is certainly instructive. In this general vision of the interaction soil-anchor plates that our work was directed. An experimental study which required the design and implantation of a model containing plastic granules powder to similate a natural environment, is presented. The latter is subjected to the removal of anchor paltes. For each test, digital photographs are taken to materialize different deformed configurations during the pullout process. These photos processed in couples by the 7D software (image correlation) giving the evolution of the displacement field and plane strain analogical environment. Particular attention is paid to the discussion of the interference of rupture zones of contiguous anchors by reducing the distance between plates.

International Journal of Structural Stability and Dynamics, 2019

This paper presents a two-variable refined plate theory for free vibration of functionally graded... more This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.

Composites Part B: Engineering, 2017

Steel & Composite structures, 2011

ABSTRACT

Applied Mathematical Modelling, 2016

Abstract A free vibration of FGM nanoplate resting on Winkler–Pasternak elastic foundations is in... more Abstract A free vibration of FGM nanoplate resting on Winkler–Pasternak elastic foundations is investigated based on two variable refined plate theory. The small scale effects are introduced using the nonlocal elasticity theory. The effect of material property, porosities, geometry and elastic foundation stiffnesses are presented, the present solutions are compared with those obtained by other researchers. The results are in a good agreement with those in the literature. The Monte Carlo method is used to predict the distribution function of the vibration response. According to the obtained results, we note that the porosities parameter are important factors influencing on the distribution function of ω ¯ . The uncertainty in the porosities parameter, have a significant effect on increasing the probability of failure of plate and reduced of durability of structure.

Materials & Design, 2009

In application, many thin structural components such as beams, plates and shells experience a thr... more In application, many thin structural components such as beams, plates and shells experience a throughthickness temperature variation. This temperature variation can produce both an in-plane expansion and an out-of-plane (bending) curvature. Given that these thin components interact with or connect to other components, we often wish to minimize the thermal deformation or match the thermal deformation of another component. This is accomplished by using a composite whose fibers have a negative axial thermal expansion coefficient. By varying the fiber volume fraction within a symmetric laminated beam to create a functionally graded material (FGM), certain thermal deformations can be controlled or tailored. Specifically, a beam can be designed which does not curve under a steady-state through-thickness temperature variation. Continuous gradation of the fiber volume fraction in the FGM layer is modelled in the form of a mth power polynomial of the coordinate axis in thickness direction of the beam. The beam results are independent of the actual temperature values, within the limitations of steady-state heat transfer and constant material properties. The influence of volume fiber fraction distributions are studied to match or eliminate an in-plane expansion coefficient, or to match a desired axial stiffness. Combining two fiber types to create a hybrid FGM can offer desirable increase in axial and bending stiffness while still retaining the useful thermal deformation behavior.

Mechanics of Composite Materials, 2010

The static response of simply supported functionally graded plates (FGP) subjected to a transvers... more The static response of simply supported functionally graded plates (FGP) subjected to a transverse uniform load (UL) or a sinusoidally distributed load (SL) and resting on an elastic foundation is examined by using a new hyperbolic displacement model. The present theory exactly satisfies the stress boundary conditions on the top and bottom surfaces of the plate. No transverse shear correction factors are needed, because a correct representation of the transverse shear strain is given. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second parameter is zero. The equilibrium equations of a functionally graded plate are given based on the hyperbolic shear deformation theory of plates presented. The effects of stiffness and gradient index of the foundation on the mechanical responses of the plates are discussed. It is established that the elastic foundations significantly affect the mechanical behavior of thick functionally graded plates. The numerical results presented in the paper can serve as benchmarks for future analyses of thick functionally graded plates on elastic foundations.

Materials & Design, 2010

An analytical model is developed for prediction of thermal residual stresses, arising from the fa... more An analytical model is developed for prediction of thermal residual stresses, arising from the fabrication of exponential functionally graded material (simply called E-FGM) systems. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small.

Computational Materials Science, 2009

In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded materia... more In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded material (S-FGM) beam of thick thickness subjected to uniformly distributed transverse loading has been investigated. The S-FGM system consists of ceramic (Al 2 O 3) and metal (Al) phases varying through the thickness of beam. Major classes of representative theories such as classical laminate beam theory (CLBT), first-order shear deformation theory (FSDT) and high-order theories (HOTs) have been considered and a unified kinematic formulation is then proposed. The Poisson's ratio of the thick S-FGM beam is assumed to be constant, but their Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by sigmoid function. The numerical illustrations concern bending response of S-FGM rectangular beams. Qualitative and quantitative assessments of displacement and stress fields have been presented and discussed.

Computational Materials Science, Dec 1, 2008

Journal of The Brazilian Society of Mechanical Sciences and Engineering, Feb 1, 2016

engineering design and manufacture. FGMs have continuous variation of material properties in one ... more engineering design and manufacture. FGMs have continuous variation of material properties in one or more directions. Typically, FGMs are made from a mixture of ceramics and metals with the variation of the volume fraction according to a power law through thickness [1, 2]. FGMs have received wide applications as structural components in modern industries such as mechanical, aerospace, nuclear reactors, and civil engineering. In the process of FGMs fabrication, the existence of porosities and micro-voids inside the materials possiblyoccurs due to technical problems, especially at the ceramic zone. The impact of this failure has been the subject of much attention, as evidenced by the large number of studies on this subject. For porous plates and shells, Magnucka-Blandzi [3] studied the dynamic stability for a circular porous plate to determine the critical loads. The influence of unstable regions for the Mathieu equation was described. She [4, 5] also examined the nonlinear dynamic stability and axi-symmetrical deflection and buckling of circular porous plates. Belica and Magnucki [6, 7] investigated the dynamic stability of a porous cylindrical shell under different loading. Wattanasakulpong and Ungbhakor [8] investigate linear and nonlinear vibration problems of FGMs beams having porosities. Wattanasakulpong et al. and Ebrahimi [9, 10] presented a work on porosities happening inside FGMs samples fabricated by a multi-step sequential infiltration technique. FGMs may possess a number of advantages such as high resistance to temperature gradients, significant reduction in residual and thermal stresses, and high wear resistance. Composite structures on elastic foundations have wide applications in modern engineering and pose great technical problems in structural design. In the vast majority of the classical mechanics, plates on an elastic foundation are Abstract This paper presents a free vibration analysis of functionally graded materials nano-plate resting on Winkler-Pasternak elastic foundations based on two-variable refined plate theories including the porosities effect. The small-scale effects are introduced using the nonlocal elasticity theory with a new shear deformation function. The governing equations are obtained through the Hamilton's principle. The effect of material property, porosities, various boundary conditions and elastic foundation stiffnesses on free vibration functionally graded materials nanoplate are also presented and discussed in detail. The present solutions are compared with those obtained by other researchers. The results are in a good agreement with those in the literature.

Journal of Mathematical Analysis and Applications, Oct 1, 2008

High-order flexural theories for short laminated composite beams subjected to mechanical and ther... more High-order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented. The formulation allows for warping of the cross-section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories. Based on higher-order shear deformation theories, the governing equations are obtained using the principle of virtual work (PVW). The justification for use of higherorder shear deformation theories is established for short and composite beams where cross-sectional warping is predominant.

International Journal of Mechanics and Materials in Design, Feb 3, 2010

Free vibration analysis of simply supported functionally graded plates (FGP) resting on a Winkler... more Free vibration analysis of simply supported functionally graded plates (FGP) resting on a Winkler–Pasternak elastic foundation are examined by a new higher shear deformation theory in this paper. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The material properties change continuously through the thickness of the plate, which can vary according to

Composites Part B-engineering, Feb 1, 2013

ABSTRACT

Résumé Cette investigation modifiée du modèle de Shear-Lag [1], tient compte de la contrainte de ... more Résumé Cette investigation modifiée du modèle de Shear-Lag [1], tient compte de la contrainte de cisaillement interlaminaire et la couche adhésive pour calculer les contraintes en présence des fissures transversales avec l'apparition du délaminage au bord libre du stratifié ainsi que les réductions de rigidité pour les différents stratifiés croisés de type [ ] s m n 90 , 0 en matériaux composites, glass/epoxy, graphite/epoxy et hybride. Le but est de montrer la contribution de la couche adhésive interlaminaire entre deux plis adjacents avec une bonne transition de l'effort de cisaillement interlaminaire et l'effort normal à travers cette couche. La distribution des contraintes résolue par le modèle utilisé satisfait les conditions d'équilibres, les conditions de frontières, la continuité de déplacement et la continuité de traction aux interfaces entre les couches. Ces considérations ont données une bonne corrélation pour, les fonctions de déplacements, les contrainte...

Applied Mathematics and Mechanics, 2009

Periodica Polytechnica Civil Engineering, 2020

The present article aims essentially to present an analytical and numerical method which makes it... more The present article aims essentially to present an analytical and numerical method which makes it possible to study the damped vibrations of viscoelastic FGM nanoplates resting on viscoelastic foundations. A new model for the higher-order shear deformation plate theory is coupled with the internal Kelvin - Voigt viscoelastic model and the three-parameter viscoelastic foundation model for the purpose of reducing and minimizing the vibration response of the system. It is widely admitted that the mechanical properties of these new functionally gradient materials (FGMs) vary according to the thickness of the plate and depend on its volume fraction. The use of FGM plates seems to be an ideal solution for the study of free vibrations because of their multifunctionality that is fully integrated with the nonlocal Eringen effect. The dynamic response of such a complex system has been investigated by varying the aspect ratio of the plate, the mechanical characteristics of the material used, t...

Mechanics Based Design of Structures and Machines

Proceedings of the Third International Symposium on Materials and Sustainable Development, 2018

This study presents a mechanical model to predict the effective damped viscoelastic behavior of a... more This study presents a mechanical model to predict the effective damped viscoelastic behavior of a functional grading material (FGM). A detailed parametric study is carried out to elucidate the dynamic response of an Euler-Bernoulli beam with finite length on the basis of the non-local Eringen theory which reveal the influence of the material proprieties, nonlocal parameter and the viscoelastic parameter on the vibratory frequency of the system, we obtain the analytical solutions for the vibratory frequency of the system with boundary conditions. The applicability and the effectiveness of the model presented are demonstrated in canonical numerical examples.

MATEC Web of Conferences, 2018

Knowing what occurs above anchor plates is certainly instructive. In this general vision of the i... more Knowing what occurs above anchor plates is certainly instructive. In this general vision of the interaction soil-anchor plates that our work was directed. An experimental study which required the design and implantation of a model containing plastic granules powder to similate a natural environment, is presented. The latter is subjected to the removal of anchor paltes. For each test, digital photographs are taken to materialize different deformed configurations during the pullout process. These photos processed in couples by the 7D software (image correlation) giving the evolution of the displacement field and plane strain analogical environment. Particular attention is paid to the discussion of the interference of rupture zones of contiguous anchors by reducing the distance between plates.

International Journal of Structural Stability and Dynamics, 2019

This paper presents a two-variable refined plate theory for free vibration of functionally graded... more This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.

Composites Part B: Engineering, 2017

Steel & Composite structures, 2011

ABSTRACT

Applied Mathematical Modelling, 2016

Abstract A free vibration of FGM nanoplate resting on Winkler–Pasternak elastic foundations is in... more Abstract A free vibration of FGM nanoplate resting on Winkler–Pasternak elastic foundations is investigated based on two variable refined plate theory. The small scale effects are introduced using the nonlocal elasticity theory. The effect of material property, porosities, geometry and elastic foundation stiffnesses are presented, the present solutions are compared with those obtained by other researchers. The results are in a good agreement with those in the literature. The Monte Carlo method is used to predict the distribution function of the vibration response. According to the obtained results, we note that the porosities parameter are important factors influencing on the distribution function of ω ¯ . The uncertainty in the porosities parameter, have a significant effect on increasing the probability of failure of plate and reduced of durability of structure.

Materials & Design, 2009

In application, many thin structural components such as beams, plates and shells experience a thr... more In application, many thin structural components such as beams, plates and shells experience a throughthickness temperature variation. This temperature variation can produce both an in-plane expansion and an out-of-plane (bending) curvature. Given that these thin components interact with or connect to other components, we often wish to minimize the thermal deformation or match the thermal deformation of another component. This is accomplished by using a composite whose fibers have a negative axial thermal expansion coefficient. By varying the fiber volume fraction within a symmetric laminated beam to create a functionally graded material (FGM), certain thermal deformations can be controlled or tailored. Specifically, a beam can be designed which does not curve under a steady-state through-thickness temperature variation. Continuous gradation of the fiber volume fraction in the FGM layer is modelled in the form of a mth power polynomial of the coordinate axis in thickness direction of the beam. The beam results are independent of the actual temperature values, within the limitations of steady-state heat transfer and constant material properties. The influence of volume fiber fraction distributions are studied to match or eliminate an in-plane expansion coefficient, or to match a desired axial stiffness. Combining two fiber types to create a hybrid FGM can offer desirable increase in axial and bending stiffness while still retaining the useful thermal deformation behavior.

Mechanics of Composite Materials, 2010

The static response of simply supported functionally graded plates (FGP) subjected to a transvers... more The static response of simply supported functionally graded plates (FGP) subjected to a transverse uniform load (UL) or a sinusoidally distributed load (SL) and resting on an elastic foundation is examined by using a new hyperbolic displacement model. The present theory exactly satisfies the stress boundary conditions on the top and bottom surfaces of the plate. No transverse shear correction factors are needed, because a correct representation of the transverse shear strain is given. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second parameter is zero. The equilibrium equations of a functionally graded plate are given based on the hyperbolic shear deformation theory of plates presented. The effects of stiffness and gradient index of the foundation on the mechanical responses of the plates are discussed. It is established that the elastic foundations significantly affect the mechanical behavior of thick functionally graded plates. The numerical results presented in the paper can serve as benchmarks for future analyses of thick functionally graded plates on elastic foundations.

Materials & Design, 2010

An analytical model is developed for prediction of thermal residual stresses, arising from the fa... more An analytical model is developed for prediction of thermal residual stresses, arising from the fabrication of exponential functionally graded material (simply called E-FGM) systems. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small.