Modified porosity model in analysis of functionally graded porous nanobeams

Eltaher, Mohamed A.; Fouda, Noha; El-Midany, T. T.; Sadoun, A.M.

doi:10.1007/s40430-018-1065-0

Cited by 53 publications

(23 citation statements)

References 35 publications

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“…where ''r''s are the unknown coefficients of the polynomials that obtained with six thermal boundary conditions in Eqs. (11) and (12).…”

Section: Fundamental Equationsmentioning

confidence: 99%

“…They considered porosity volume fraction in the mixture rule to model the material properties. Eltaher et al [12] studied the bending and vibration of FG nanobeams by considering porosity effect to model the material properties. Rahmani et al [13] investigated the vibration behavior porous FG circular sandwich plate based on a modified high-order sandwich plate theory.…”

Section: Introductionmentioning

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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“…where ''r''s are the unknown coefficients of the polynomials that obtained with six thermal boundary conditions in Eqs. (11) and (12).…”

Section: Fundamental Equationsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…In order to calculate the weighting coefficients, a set of test functions should be inserted in Eq. (24). By using the Lagrange polynomials, Shu and Richards [46] developed explicit formulation for the weighting coefficients [36] and these formulas are used in this work:…”

Section: Solution Proceduresmentioning

confidence: 99%

Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads

Heydarpour

Malekzadeh

2019

J Braz. Soc. Mech. Sci. Eng.

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The dynamic stability of cylindrical nanoshells subjected to combined static and time-dependent periodic axial forces is studied by employing the two-dimensional nonlocal elasticity theory together with the first-order shear deformation theory of shells. The differential quadrature method as an efficient and accurate numerical technique is applied to discretize the equations of motion under different boundary conditions in the spatial domain and transform them into a system of coupled Mathieu-Hill-type equations in time domain. Subsequently, the Bolotin's first approximation method is employed to extract the dynamic instability regions of the cylindrical nanoshells. The approach is validated by showing its fast convergence rate and carrying out comparison studies with existing results in the limit cases. Afterward, the effects of the nonlocal parameter, length and thickness-to-mean radius ratios together with different boundary conditions on the principal dynamic instability regions of the cylindrical nanoshells are studied in detail.

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“…Fazzorali studied vibration and elastic stability behavior of FG sandwich beams in three‐dimensional with ceramic in top skin and metal in bottom skin and upside down, which is rested on Winkler‐Pasternak foundation by two different types of porosities. Eltaher et al . analyzed the vibration and bending of Euler‐Bernoulli modified FG porous nanobeam.…”

Section: Introductionmentioning

confidence: 99%

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

2019

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In this study, free vibration of the sandwich microbeam with porous core and FG carbon nanotubes reinforced composite face sheets which is rested on Winkler‐Pasternak substrate is investigated. It is assumed the beam is in thermal environment and is subjected to thermal load and the displacement components are described based on sinusoidal shear deformation beam theory. The small scale effects are taken into account according to the modified couple stress theory. The core and face sheets properties are diffused through the thickness. The motion equations are derived and solved using Hamilton's principle and Navier's method, respectively. Effect of different parameters such as porosity coefficient and distributions, different types of CNTs distribution, small scale and geometrical size of the beam is considered. The results show by enhancing the porosity, the frequency decreased. The findings of the current study can be used to design prominent role in modern engineering applications.

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Modified porosity model in analysis of functionally graded porous nanobeams

Cited by 53 publications

References 35 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

Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

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