Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations

Zenkour, Ashraf M.; Allam, M. N. M.; Sobhy, Mohammed

doi:10.1007/s00707-009-0252-6

Cited by 77 publications

(23 citation statements)

References 42 publications

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“…The latter one is a simple higher-order theory that takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. All of the HSDT are not contain the normal deformation effect, thus refined higher-order shear and normal deformation theories are arisen [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment

Zenkour

Sobhy

2015

Physica E: Low-dimensional Systems and Nanostructures

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Section: Introductionmentioning

confidence: 99%

“…However, the number of the unknown functions contained in the refined higher-order shear and normal deformation beam theory [23,24] is four functions. Consequently, it gives four governing equations.…”

Section: Introductionmentioning

confidence: 99%

A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment

Zenkour

Sobhy

2015

Physica E: Low-dimensional Systems and Nanostructures

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“…Frostig et al [25] studied the behavior of sandwich beams based on the high-order theory. The investigation of bending response for functionally graded viscoelastic sandwich beam with elastic core resting on Pasternak's elastic foundations was presented by Zenkour [26]. Arikoglu [27] dealt with the vibration of a three-layered composite beam with a viscoelastic core by using the differential transform method.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Deformations for Two‐Layer Timoshenko Beams Glued by a Viscoelastic Interlayer

Pei

Wang

et al. 2019

Mathematical Problems in Engineering

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An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a viscoelastic interlayer under uniform transverse load is presented. The standard linear solid model is employed to simulate the viscoelastic characteristics of the interlayer, in which the memory effect of strains is considered. The mechanical behavior of each layer is described by the first-order shear deformation theory (FSDT). By means of the principle of minimum potential energy, a group of equations for displacements and rotation angles are derived out. The final solution is obtained by conducting the Laplace transform and the inversion of Laplace transform to the equation group. Numerical comparison shows that the present solutions and the finite element results are in good agreement. It is shown that the present results are more accurate than those obtained from the Euler-Bernoulli beam theory, especially for thick beams. And the present solutions can accurately describe the variation of stresses and deformations of the beam with the time, compared with those ignoring the memory effect of strains. Finally, the effects of the geometric parameters and material properties of the interlayer on stresses and deformations of the beam are studied in detail.

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“…Applying the sinusoidal shear deformation plate theory in conjunction with the first-order, the third-order, and the classical plate bending theories, Zenkour and Alghamdi [17,18] studied the flexural behaviors of functionally graded sandwich plates subjected to mechanical and thermal loads. Based on the sinusoidal shear deformation plate models, Zenkour et al [19] studied the bending behaviors of a simply-supported functionally graded viscoelastic sandwich beam resting on Pasternak's elastic foundation. Zenkour and Sobhy [20] further employed the sinusoidal shear deformation plate model and the third-order model to evaluate the static response of simply-supported FGM viscoelastic sandwich plates under transverse uniform loads.…”

Section: Introductionmentioning

confidence: 99%

“…It is seen from the literature that the generalized shear deformation models with five displacement parameters are widely used to study the hygrothermal behaviors of the FGM structures [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. However, the transverse normal strain has been neglected in these models.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Functionally Graded Plates Subjected to Hygrothermomechanical Loads

Ren

et al. 2016

AIAA Journal

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Analytical solution taking into account the transverse normal strain is developed for the analysis of the mechanical and hygrothermal behaviors of functionally graded material (FGM) plates. In order to include the transverse normal deformation, the hygrothermal deformation through the thickness due to thermal and moisture loads is introduced in the transverse displacement field. Employing the bounding surface free traction condition, effects of transverse normal hygrothermal deformation can be incorporated in the in-plane displacement field. Moreover, there are only five displacement variables in the proposed model as transverse normal deformations due to hygrothermal loads are absorbed in the generalized force vector.By analyzing the hygrothermal behaviors of FGM plates, the accuracy and efficiency of the proposed model are assessed. Moreover, the effects of temperature, moisture concentration, transverse normal strain, volume fraction distributions and side-to-thickness ratios on the displacements and the stresses of FGM plates have all been studied.

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Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations

Cited by 77 publications

References 42 publications

A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment

A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment

Analytical Solution of Deformations for Two‐Layer Timoshenko Beams Glued by a Viscoelastic Interlayer

Analysis of Functionally Graded Plates Subjected to Hygrothermomechanical Loads

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