PSI - Issue 19

Giovanni M. Teixeira et al. / Procedia Structural Integrity 19 (2019) 175–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

178

4

Fig. 2. Structural Stresses from nodal forces and moments.

Equation 4 needs to be evaluated six times, replacing the F’s and f’s for the forces and moments at the three orthogonal directions x, y and z. From the local forces and moments Equations 1-3 provides the three structural stresses that are used to compose the effective structural stress range according to Equation 5.

l

l

  

 

0 0 0 0

1

1

1 1 2 l l l  3 6

1          2    f f f 3 n           M M f

1       2       F F F

l

M M

0

2

6 3 6

(4)

2 3 3 l l l 

l

0

       

3

2



n   F         M M

6 3 6

      

M M

O M

n 1 n 1 6 3   O M l

l

0 0 0 0





2 s e 3            2 s 2 z

(5)

The recommendation (Hong et al. (2014)) is that if the shear structural stress ranges are smaller than 1/3 of the normal structural stress ranges they can be ignored, which yields in the Equation 6 below:

s e     

(6)

At this point a fracture mechanics based equivalent structural stress parameter can be presented by normalizing the above structural stress range Δ σ s , taking the plate thickness t and r ratio into account:

t I r  

  

s S

(7)



  s

2 m 1 2m m

The I(r) 1/m parameter is a dimensionless function of the ratio r and is presented in two expressions, depending on the loading conditions i.e., whether the structure is under load-controlled or displacement controlled conditions. Under load-controlled conditions I(r) 1/m becomes: