Issue 64

M. A. Kenanda et alii, Frattura ed Integrità Strutturale, 64 (2023) 266-282; DOI: 10.3221/IGF-ESIS.64.18

In which

  0 β 1

(1d)

where ( η ) denotes the material properties, including the elastic modulus E , mass density  , and Poisson's ratio ν . P and β are the power law and porosity parameters, respectively.

T HEORY AND FORMULATION

A

ccording to high-order shear deformation theory, including the thickness stretching effect, the displacement field can be described as:



w

   

        









0

+ (z) θ x,y,t f

u x,y,t -z

x

0



x

 

 

    

 

u x,y,z,t



w









0

+ (z) θ x,y,t f

v x,y,z,t = v x,y,t -z

(2)

     

y

0



y





w x,y,z,t









w x,y,t +g(z) θ x,y,t

z

0

 

In which

d (z) dz f

g(z)=

In which t signifies the time, (x, y, z) are the Cartesian coordinates, 0 0

0 x y u , v , w , θ , θ and z θ are the mid-plane

displacement and rotation components along the x, y and z directions, respectively, f (z) is a shape function for describing the distribution of transverse shear stress. The most famous theories of high-order shear deformation are presented in Tab. 1 and Fig. 2.

  f z

Theories

Authors

Third-order shear deformation theory Trigonometric high order shear deformation theory Exponential high-order shear deformation theory arctangent exponential high-order shear deformation theory Hyperbolic high-order shear deformation theory

3 2

4z 3h

z

Reddy [1]

h π

      π z h

sin

Touratier [14]

          2 z h

zexp -2



Karama et al.[19]





   

   

             2 z h

-1

tan zexp -2

Vu et al. [34]

   z R h tanh tanh - 3 h h -       z       2

  

Present

-Rz;

R=1.62

  3sech 0.5 4

Table 1: The most famous high-order shear deformation theories.

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