### Tóm tắt

The quasi-3D shear deformation theory, which includes the thickness stretching effect into consideration, is employed to develop a Q4 plate element for buckling analysis of two-directional functionally graded sandwich (2D-FGSW) plates. The plates are considered to be formed from three layers, a homogeneous core and two functionally graded face layers with material properties varying in both the thickness and length directions by power gradation laws. The plate element with nine degrees of freedom per node is derived using Lagrange interpolation functions and employed in computing the buckling loads. The accuracy of the element is confirmed by comparing the result obtained in the present work with published data. A parametric study is carried out to illustrate the effect of the material gradation and the layer thickness ratio on the buckling loads. The influence of the length to thickness ratio on the buckling loads of the plates is also examined and discussed.

### Từ khoá

2D-FGSW plate; Power gradation law; Quasi-3D theory; Q4 element; Buckling analysis.

### Tài liệu tham khảo

A.M. Zenkour.A comprehensive analysis of functionally graded sandwich plates: Part 1 - Deflection and stresses. International Journal of Solids and Structures,42, (2005), pp. 5224–5242.

A.M. Zenkour.A comprehensive analysis of functionally graded sandwich plates: Part 2 - Buckling and free vibration. International Journal of Solids and Structures,42, (2005), pp. 5243–5258.

A.M. Zenkour, M. Sobhy. Thermal buckling of various types of FGM sandwich plates. Composite Structures,93, (2010), pp. 93-102.

Ashraf M. Zenkour. A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities.Composite Structures,201, (2018), pp. 38-48.

M. Bateni, Y. Kiani, M.R. Eslami, A comprehensive study on stability of FGM plates. International Journal of Mechanical Sciences, 75, (2013), pp.134-144.

A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Composite Structures,94, (2012), pp. 1814–1825.

A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Composites Part B, 43, (2012), pp. 711–725.

A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Composites Part B, 44, (2013), pp. 657–674.

J. N. Reddy, Analysis of functionally graded plates. International Journal for numerical methodsin engineering, 47 (2000), pp. 663-684.

Huu-Tai Thai, Seung-Eock Kim. A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates.Composite Structures,99, (2013), pp. 172–180.

Huu-Tai Thai, Trung-Kien Nguyen, Thuc P. Vo, Jaehong Lee. Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics A/Solids, 45, (2014),pp. 211 – 225.

S. Amir Farzam-Rad, Behrooz Hassani, Abbas Karamodin. Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface.Composites Part B, 108, (2017), pp. 174 - 189.

Zahra Vafakhah, Bahram Navayi Neya. An exact three dimensional solution for bending of thick rectangular FGM plate. Composites Part B, 156, (2019), pp. 72 - 87.

A.M. Zenkour.A comprehensive analysis of functionally graded sandwich plates: Part 2 - Buckling and free vibration. International Journal of Solids and Structures,42, (2005), pp. 5243–5258.

A.M. Zenkour, M. Sobhy. Thermal buckling of various types of FGM sandwich plates. Composite Structures,93, (2010), pp. 93-102.

Ashraf M. Zenkour. A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities.Composite Structures,201, (2018), pp. 38-48.

M. Bateni, Y. Kiani, M.R. Eslami, A comprehensive study on stability of FGM plates. International Journal of Mechanical Sciences, 75, (2013), pp.134-144.

A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Composite Structures,94, (2012), pp. 1814–1825.

A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares. A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Composites Part B, 43, (2012), pp. 711–725.

A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Composites Part B, 44, (2013), pp. 657–674.

J. N. Reddy, Analysis of functionally graded plates. International Journal for numerical methodsin engineering, 47 (2000), pp. 663-684.

Huu-Tai Thai, Seung-Eock Kim. A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates.Composite Structures,99, (2013), pp. 172–180.

Huu-Tai Thai, Trung-Kien Nguyen, Thuc P. Vo, Jaehong Lee. Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics A/Solids, 45, (2014),pp. 211 – 225.

S. Amir Farzam-Rad, Behrooz Hassani, Abbas Karamodin. Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface.Composites Part B, 108, (2017), pp. 174 - 189.

Zahra Vafakhah, Bahram Navayi Neya. An exact three dimensional solution for bending of thick rectangular FGM plate. Composites Part B, 156, (2019), pp. 72 - 87.