• Title/Summary/Keyword: Winkler-Pasternak elastic foundation

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A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations

  • Nebab, Mokhtar;Benguediab, Soumia;Atmane, Hassen Ait;Bernard, Fabrice
    • Geomechanics and Engineering
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    • v.22 no.5
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    • pp.415-431
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    • 2020
  • In this study, dynamics responses of advanced composite plates resting variable elastic foundations via a quasi-3D theory are developed using an analytical approach. This higher shear deformation theory (HSDT) is included the shear deformation theory and effect stretching that has five unknowns, which is even inferior to normal deformation theories found literature and other theories. The quasi-three-dimensional (quasi-3D) theory accounts for a parabolic distribution of the transverse shear deformation and satisfies the zero traction boundary conditions on the surfaces of the advanced composite plate without needing shear correction factors. The plates assumed to be rest on two-parameter elastic foundations, the Winkler parameter is supposed to be constant but the Pasternak parameter varies along the long side of the plate with three distributions (linear, parabolic and sinusoidal). The material properties of the advanced composite plates gradually vary through the thickness according to two distribution models (power law and Mori-Tanaka). Governing differential equations and associated boundary conditions for dynamics responses of the advanced composite plates are derived using the Hamilton principle and are solved by using an analytical solution of Navier's technique. The present results and validations of our modal with literature are presented that permitted to demonstrate the accuracy of the present quasi-3D theory to predict the effect of variables elastic foundation on dynamics responses of advanced composite plates.

A cylindrical shell model for nonlocal buckling behavior of CNTs embedded in an elastic foundation under the simultaneous effects of magnetic field, temperature change, and number of walls

  • Timesli, Abdelaziz
    • Advances in nano research
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    • v.11 no.6
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    • pp.581-593
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    • 2021
  • This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory

  • Bousahla, Abdelmoumen Anis;Bourada, Fouad;Mahmoud, S.R.;Tounsi, Abdeldjebbar;Algarni, Ali;Bedia, E.A. Adda;Tounsi, Abdelouahed
    • Computers and Concrete
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    • v.25 no.2
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    • pp.155-166
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    • 2020
  • In this work, the buckling and vibrational behavior of the composite beam armed with single-walled carbon nanotubes (SW-CNT) resting on Winkler-Pasternak elastic foundation are investigated. The CNT-RC beam is modeled by a novel integral first order shear deformation theory. The current theory contains three variables and uses the shear correction factors. The equivalent properties of the CNT-RC beam are computed using the mixture rule. The equations of motion are derived and resolved by Applying the Hamilton's principle and Navier solution on the current model. The accuracy of the current model is verified by comparison studies with others models found in the literature. Also, several parametric studies and their discussions are presented.

Size-dependent free vibration of coated functionally graded graphene reinforced nanoplates rested on viscoelastic medium

  • Ali Alnujaie;Ahmed A. Daikh;Mofareh H. Ghazwani;Amr E. Assie;Mohamed A Eltaher
    • Advances in nano research
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    • v.17 no.2
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    • pp.181-195
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    • 2024
  • This study introduces a novel functionally graded material model, termed the "Coated Functionally Graded Graphene-Reinforced Composite (FG GRC)" model, for investigating the free vibration response of plates, highlighting its potential to advance the understanding and application of material property variations in structural engineering. Two types of coated FG GRC plates are examined: Hardcore and Softcore, and five distribution patterns are proposed, namely FG-A, FG-B, FG-C, FG-D, and FG-E. A modified displacement field is proposed based on the higher-order shear deformation theory, effectively reducing the number of variables from five to four while accurately accounting for shear deformation effects. To solve the equations of motion, an analytical solution based on the Galerkin approach was developed for FG GRC plates resting on a viscoelastic Winkler/Pasternak foundation, applicable to various boundary conditions. A comprehensive parametric analysis elucidates the impact of multiple factors on the fundamental frequencies. These factors encompass the types and distribution patterns of the coated FG GRC plates, gradient material distribution, porosities, nonlocal length scale parameter, gradient material scale parameter, nanoplate geometry, and variations in the elastic foundation. Our theoretical research aims to overcome the inherent challenges in modeling structures, providing a robust alternative to experimental analyses of the mechanical behavior of complex structures.

Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates

  • Esmaeilzadeh, Mostafa;Golmakani, Mohammad Esmaeil;Kadkhodayan, Mehran;Amoozgar, Mohammadreza;Bodaghi, Mahdi
    • Advances in nano research
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    • v.10 no.2
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    • pp.151-163
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    • 2021
  • The main target of this study is to investigate nonlinear transient responses of moving polymer nano-size plates fortified by means of Graphene Platelets (GPLs) and resting on a Winkler-Pasternak foundation under a transverse pressure force and a temperature variation. Two graphene spreading forms dispersed through the plate thickness are studied, and the Halpin-Tsai micro-mechanics model is used to obtain the effective Young's modulus. Furthermore, the rule of mixture is employed to calculate the effective mass density and Poisson's ratio. In accordance with the first order shear deformation and von Karman theory for nonlinear systems, the kinematic equations are derived, and then nonlocal strain gradient scheme is used to reflect the effects of nonlocal and strain gradient parameters on small-size objects. Afterwards, a combined approach, kinetic dynamic relaxation method accompanied by Newmark technique, is hired for solving the time-varying equation sets, and Fortran program is developed to generate the numerical results. The accuracy of the current model is verified by comparative studies with available results in the literature. Finally, a parametric study is carried out to explore the effects of GPL's weight fractions and dispersion patterns, edge conditions, softening and hardening factors, the temperature change, the velocity of moving nanoplate and elastic foundation stiffness on the dynamic response of the structure. The result illustrates that the effects of nonlocality and strain gradient parameters are more remarkable in the higher magnitudes of the nanoplate speed.

Theoretical buckling analysis of inhomogeneous plates under various thermal gradients and boundary conditions

  • Laid Lekouara;Belgacem Mamen;Abdelhakim Bouhadra;Abderahmane Menasria;Kouider Halim Benrahou;Abdelouahed Tounsi;Mohammed A. Al-Osta
    • Structural Engineering and Mechanics
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    • v.86 no.4
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    • pp.443-459
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    • 2023
  • This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

Bending analysis of nano-Fe2O3 reinforced concrete slabs exposed to temperature fields and supported by viscoelastic foundation

  • Zouaoui R. Harrat;Mohammed Chatbi;Baghdad Krour;Sofiane Amziane;Mohamed Bachir Bouiadjra;Marijana Hadzima-Nyarko;Dorin Radu;Ercan Isik
    • Advances in concrete construction
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    • v.17 no.2
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    • pp.111-126
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    • 2024
  • During the clinkering stages of cement production, the chemical composition of fine raw materials such as limestone and clay, which include iron oxide (Fe2O3), silicon dioxide (SiO2) and aluminum oxide (Al2O3), significantly influences the quality of the final product. Specifically, the chemical interaction of Fe2O3 with CaO, SiO2 and Al2O3 during clinkerisation plays a key role in determining the chemical reactivity and overall quality of the final cement, shaping the properties of the concrete produced. As an extension, this study aims to investigate the physical effects of incorporating nanosized Fe2O3 particles as fillers in concrete matrices, and their impact on concrete structures, namely slabs. To accurately model the reinforced concrete (RC) slabs, a refined trigonometric shear deformation theory (RTSDT) is used. Additionally, the stochastic Eshelby's homogenization approach is employed to determine the thermoelastic properties of nano-Fe2O3 infused concrete slabs. To ensure comprehensive coverage in the study, the RC slabs undergo various mechanical loads and are exposed to temperature fields to assess their thermo-mechanical performance. Furthermore, the slabs are assumed to rest on a three-parameter viscoelastic foundation, comprising the Winkler elastic springs, Pasternak shear layer and a damping parameter. The equilibrium governing equations of the system are derived using the principle of virtual work and subsequently solved using Navier's technique. The findings indicate that while ferric oxide nanoparticles enhance the mechanical properties of concrete against mechanical loading, they have less favorable effects on its performance against thermal exposure. However, the viscoelastic foundation contributes to mitigating these effects, improving the concrete's overall performance in both scenarios. These results highlight the trade-offs between mechanical and thermal performance when using Fe2O3 nanoparticles in concrete and underscore the importance of optimizing nanoparticle content and loading conditions to improve the structural performance of concrete structures.