Issue 70

H. Siguerdjidjene et alii, Frattura ed Integrità Strutturale, 70 (2024) 1-23; DOI: 10.3221/IGF-ESIS.70.01

(a)

(b)

(c)

(d) Figure 3: Reference geometry of the FGM and Gauss points. a) Graded surface b) Property variation along coordinate (z), c) homogeneous elements [45], d) The element SOLID-FGM and Gauss points. So, Eqn. 1 becomes:

 e h     g 1

z

(4)

g

g

2

n

z 1

    

  

  g

    

  m

g



 

 

P z

P z P z

P z

(5)

m

1

e

2

where

1 g g m n   represents the total number of integration points within the interval H , . g 1, 1 g m    is the position number of integration point in the interval H , g h must be carefully chosen to minimize the error in the numerical results, especially when the number of integration points is minimal. Where   P z g denotes the effective material property of the FGM. Note that   1 P z and   P z m are respectively the properties of the top and bottom faces of the interval H .

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