Issue 57

E. Sgambitterra et alii, Frattura ed Integrità Strutturale, 57 (2021) 300-320; DOI: 10.3221/IGF-ESIS.57.22

2

    

  x D y    2 / 2



r

(17)

2

The theoretical displacement fields, calculated from Eqn. (12), are illustrated in Fig. 2 in the form of contour maps.

Figure 2: Schematic depiction of a Brazilian disk subjected to a compression load P, together with the corresponding displacements along the x and y axis. Case study 3: displacement field of an axisymmetric component subjected to pressure and thermal load The displacement field of an axisymmetric component subjected to an external pressure P e , see Fig. 3, can be written as follows [56]:





T

    11 21

  

  





v

v

1

1

       ψ u U

12





 P E E e

(18)

P

e

22

where

 

 



2

r

  

      2 2 e e i r r r



 

cos

11

  

  

 r r r r r r  2 2 2 2 2 i i

1 cos

       12 e e 

  



(19)



 

 

  

  

e



  r

sin

     

21

   2 2 e i r r r r r r r          2 2 2 2 e i e i

1 sin

  



 



22

where r e and r i are the external and inner radius, respectively, r and  , are the polar coordinates referred to the axis of the component ( x 0 , y 0 ), see Fig. 3.

305