Issue 57

S. Derouiche et alii, Frattura ed Integrità Strutturale, 57 (2021) 359-372; DOI: 10.3221/IGF-ESIS.57.26

 1 1 1 2 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 2                       2

    

N

1

    

N

2

   

N

(3)

3

   

N

4





N

5

The stress field in any point is written          M

(4) where ሾMሿ is the matrix of interpolation functions for stresses and { τ } vector of nodal stresses. In the configuration of Fig. 1, the shape functions used to estimate ଵଵ are given by:                                 8 11 9 11 10 11 11 11 1 1 2 1 2 4 1 1 2 1 2 4 1 1 2 1 2 4 1 1 2 1 2 4 M M M M (5) The shape functions used to calculate ଵଶ and ଶଶ is given as follows :                                  6 2 7 2 8 2 9 2 1 1 2 1 2 6 1 1 2 1 2 6 1 1 2 1 3 1 1 2 1 4 1, 2 i i i i M M M M i (6)

The nodal estimation of the displacement and stress fields is expressed by:

        0 0 M

                 

              

  

(7)

B q

where [B] is the strain-displacement transformation matrix.

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