A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities, resting on elastic foundations

Boutahar, Lhoucine; Bikri, Khalid El; Benamar, Rhali

doi:10.1016/j.asej.2015.11.016

Cited by 18 publications

(7 citation statements)

References 73 publications

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“…By considering two kinds of porosity distribution, even and uneven, which appear in the manufacturing process, the power law rule is modified to approach an accurate prediction of material properties. Even porosity distribution that modifies the power law rule for type-I is presented as follows [31]:…”

Section: Fundamental Equationsmentioning

confidence: 99%

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Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings

Rahmani

Mohammadi

Kakavand

2020

J Braz. Soc. Mech. Sci. Eng.

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For the first time, by applying a modified high-order sandwich shells theory, buckling behavior of two types of porous FG conical sandwich shells are investigated. In the first type, the face sheets and in the second one the core are made of FGM modeled by power law rule that is modified by considering two types of porosity distributions. All materials are temperature dependent and uniform; linear and nonlinear temperature distributions are used to model the effect of the temperature changing in the sandwiches. Governing equations are obtained by a variation principle and solved by Galerkin method. To verify the results, they are compared with FEM results obtained by Abaqus software and for special cases with the results in literatures. Keywords Conical sandwich shell Á Porosity Á FGM Á Temperature dependent Á Buckling List of symbols R 1 , R 2 Small and large radius (m) T Temperature (K) T Time (s) u 0j , v 0j , w 0j Displacements of mid-plane of layers m, n Wave numbers Greek symbols q Density (kg m-3) v, w Curve-linear coordination component c Semi-angle vertex of the cone u v , u w Rotation of normal to mid-plane vector t Poisson ratio e v , e w , e z Normal strains in face sheets and core c vw , c wz , c vz Shear strains in face sheets and core f Porosity volume fraction k v , k w , k z Lagrange multipliers Superscripts T Related to thermal resultant Subscripts j = i, o, c Related to inner and outer face sheets and core

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Section: Fundamental Equationsmentioning

confidence: 99%

“…And, in the second approximation, it is considered that the porosities are distributed in the middle area of the FG layers, and by approaching to the edges, they decrease and tend to the zero. Therefore, in the type-I, the equation of the material properties in the uneven case modified as follows [31]:…”

Section: Fundamental Equationsmentioning

confidence: 99%

Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings

Rahmani

Mohammadi

Kakavand

2020

J Braz. Soc. Mech. Sci. Eng.

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“…If the porosity distribution is assumed to be uniform, the rule of mixture is modi ed as follows [52]:…”

Section: Mechanical Properties Of P-fgbmentioning

confidence: 99%

“…e studies on the vibration response of porous FG are still limited in number. For porous plates, the nonlinear free vibrations analysis of FG porous annular plates resting on elastic foundations have been presented by Boutahar et al [52]. ey concluded that porosity volume fraction and type of porosity distribution have a significant influence on the geometrically nonlinear free vibration response of the FG annular plates at large amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Ibnorachid

Boutahar

Bikri

et al. 2019

Advances in Acoustics and Vibration

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In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

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“…Recently, Mechab et al (2016) developed a nonlocal elasticity model for free vibration of FG porous nanoplates resting on elastic foundations. Boutahar and Benamar (2016) presented a semi analytical method for non-linear vibration analysis of FGM porous annular plates resting on elastic foundations. Recently, it is well understood that classic plate theory (CPT) is not appropriate for thick beams and higher modes of vibration.…”

Section: Introductionmentioning

confidence: 99%

Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory

Ebrahimi¹,

Jafari²

2016

Advances in materials Research

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Present disquisition proposes an analytical solution method for exploring the buckling characteristics of porous magneto-electro-elastic functionally graded (MEE-FG) plates with various boundary conditions for the first time. Magneto electro mechanical properties of FGM plate are supposed to change through the thickness direction of plate. The rule of power-law is modified to consider influence of porosity according to two types of distribution namely even and uneven. Pores possibly occur inside FGMs due the result of technical problems that lead to creation of micro-voids in these materials. The variation of pores along the thickness direction influences the mechanical and physical properties. Four-variable tangential-exponential refined theory is employed to derive the governing equations and boundary conditions of porous FGM plate under magneto-electrical field via Hamilton's principle. An analytical solution procedure is exploited to achieve the non-dimensional buckling load of porous FG plate exposed to magneto-electrical field with various boundary condition. A parametric study is led to assess the efficacy of material graduation exponent, coefficient of porosity, porosity distribution, magnetic potential, electric voltage, boundary conditions, aspect ratio and side-tothickness ratio on the non-dimensional buckling load of the plate made of magneto electro elastic FG materials with porosities. It is concluded that these parameters play remarkable roles on the dynamic behavior of porous MEE-FG plates. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

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A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities, resting on elastic foundations

Cited by 18 publications

References 73 publications

Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings

Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory

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