An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation

2014 ◽  
Vol 108 ◽  
pp. 667-676 ◽  
Author(s):  
S.S. Akavci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Plates On Elastic Foundation

A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation

2017 ◽  
Vol 12 (1) ◽  
pp. 9-34 ◽  
Author(s):  
Abdelkarim Benahmed ◽  
Mohammed Sid Ahmed Houari ◽  
Samir Benyoucef ◽  
Khalil Belakhdar ◽  
Abdelouahed Tounsi
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Plates On Elastic Foundation

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

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