An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations

2016 ◽  
Vol 22 (3) ◽  
pp. 329-348 ◽  
Author(s):  
Salima Abdelbari ◽  
Abdelkader Fekrar ◽  
Houari Heireche ◽  
Hayat Said ◽  
Abdelouahed Tounsi ◽  
...  
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Simple Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elastic Foundations ◽  
Simple Shear Deformation

A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations

2014 ◽  
Vol 17 (2) ◽  
pp. 99-129 ◽  
Author(s):  
Fatima Zahra Taibi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Rabbab Bachir Bouiadjra ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Mechanical Behaviour ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Elastic Foundations ◽  
Simple Shear Deformation

A REFINED AND SIMPLE SHEAR DEFORMATION THEORY FOR THERMAL BUCKLING OF SOLAR FUNCTIONALLY GRADED PLATES ON ELASTIC FOUNDATION

2014 ◽  
Vol 11 (05) ◽  
pp. 1350077 ◽  
Author(s):  
YACINE KHALFI ◽  
MOHAMMED SID AHMED HOUARI ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plates ◽  
Neutral Surface Position ◽  
Simple Shear Deformation

A refined and simple shear deformation theory for thermal buckling of solar functionally graded plate (SFGP) resting on two-parameter Pasternak's foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. It is assumed that the material properties of the plate vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the present plate theory based on exact neutral surface position is employed to derive the governing stability equations. The nonlinear strain-displacement relations are also taken into consideration. The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. The effects of the foundation parameters, plate dimensions, and power law index are presented comprehensively for the thermal buckling of solar functionally graded plates.

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

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