PSI - Issue 33

5

Derouiche Sami et al. / Procedia Structural Integrity 33 (2021) 996–1006 Author name / Structural Integrity Procedia 00 (2019) 000–000

1000

 1 1 2 1 2 6 1 1 2 1 2 6 1 1 2 1 3 1 1 2 1 4           



6

   



M

i

2



7

   



M

i

2



8

  

M

(5)

i

2



9

  

M i

i

2



1, 2

The nodal approximation of the displacement and stress fields is expressed by:                                       0 0 M B q where �B� is the strain-displacement transformation matrix. The element matrix �K � � is given by                       0 u e t u K K K K      

(6)

(7)

Here

  A K h M S M dA      T     e

e

(8)

and

  u A K h M B dA (9) where: h is the thickness, �S� is the compliance matrix, A � is the element area and T indicate the matrix transpose. For the goal to study the case of an orthotropic media, the compliance matrix will be taken as:     T    e e