A new simple shear and normal deformations theory for functionally graded beams

Bourada, Mohamed; Kaci, Abdelhakim; Houari, Mohammed Sid Ahmed; Tounsi, Abdelouahed

doi:10.12989/scs.2015.18.2.409

Cited by 288 publications

(68 citation statements)

References 57 publications

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“…Vo et al (2014) presented static and free vibration analysis of functionally graded beams using refined shear deformation theory. Bourada et al (2015) developed a new trigonometric shear and normal deformation theory for bending and free vibration of functionally graded beams. Simsek (2016) presented buckling of bidirectional functionally graded Timoshenko beams with different boundary conditions using Ritz method.…”

Section: Latin American Journal Of Solids and Structures 14 (2017) 18mentioning

confidence: 99%

A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

Ghumare

Sayyad

2017

Lat. Am. j. solids struct.

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A new fifth-order shear and normal deformation theory (FOSNDT) is developed for the static bending and elastic buckling analysis of functionally graded beams. The properties of functionally graded material are assumed to vary through the thickness direction according to power-law distribution (P-FGM). The most important feature of the present theory is that it includes the effects of transverse shear and normal deformations. Axial and transverse displacements involve polynomial shape functions to include the effects of transverse shear and normal deformations. A polynomial shape function expanded up to fifth-order in terms of the thickness coordinate is used to account for the effects of transverse shear and normal deformations. The kinematics of the present theory is based on six independent field variables. The theory satisfies the traction free boundary conditions at top and bottom surfaces of the beam without using problem dependent shear correction factor. The closed-form solutions of simply supported FG beams are obtained using Navier's solution procedure and non-dimensional results are compared with those obtained by using classical beam theory, first order shear deformation theory and other higher order shear deformation theories. It is concluded that the present theory is accurate and efficient in predicting the bending and buckling responses of functionally graded beams.

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Section: Latin American Journal Of Solids and Structures 14 (2017) 18mentioning

confidence: 99%

A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

Ghumare

Sayyad

2017

Lat. Am. j. solids struct.

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“…In recent years, HSDT model has been used in many analytical research studies. [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61] In the present work, in order to count the shear effects, based on CNT thickness to radius ratio, FSDT model is used. The displacement field of FSDT model is defined as follows…”

Section: Couple Stress Theory For Anisotropic Cylindrical Shellmentioning

confidence: 99%

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Beni

Mehralian

Zeverdejani

2017

Journal of Low Frequency Noise, Vibration and Active Control

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In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.

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“…Ebrahimi and Barati [38] presented a nonlocal third-order beam theory for vibration analysis of size-dependent FG nanobeams. Bourada et al [39] presented a new simple shear and normal deformations theory for FG beams. Al-Basyouni et al [40] investigated size-dependent bending and vibration analysis of higher-order FG microbeams based on MCST and neutral surface position.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

Ebrahimi

Barati

2016

International Journal of Smart and Nano Materials

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In the present work, thermo-electro-mechanical buckling behavior of functionally graded piezoelectric (FGP) nanobeams is investigated based on higher-order shear deformation beam theory. The FGP nanobeam is subjected to four types of thermal loading including uniform, linear, and sinusoidal temperature rise as well as heat conduction through the beam thickness. Thermo-electromechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To consider the influences of small-scale sizes, Eringen's nonlocal elasticity theory is adopted. Applying Hamilton's principle, the nonlocal governing equations of an FGP nanobeam in thermal environments are obtained and are solved using Naviertype analytical solution. The significance of various parameters, such as thermal loadings, external electric voltage, power-law index, nonlocal parameter, and slenderness ratio on thermal buckling response of size-dependent FGP nanobeams is investigated. ARTICLE HISTORY

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A new simple shear and normal deformations theory for functionally graded beams

Cited by 288 publications

References 57 publications

A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

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