PSI - Issue 18

Yaroslav Dubyk et al. / Procedia Structural Integrity 18 (2019) 630–638

635

6

Yaroslav Dubyk et al. / Structural Integrity Procedia 00 (2019) 000–000

0 obl u  , thus

It obvious, that

is a boundary condition for

3 n  together with

-(1 / 2

1 / 2 ) long

str

long

u

w

v tg 





0 4 n  will be disregarded because the small values of resultant forces. For a combined pressure and bending loading , we can just sum results obtained separately for a pressure and bending loading. The obtained results for local forces and moments allow us to find expressions for circular and axial stresses: 0  . Solution for long x L 

2 6 N M h h 

2 N M h h 6 x



   

(20)

sin      

x

x

m

The components (20) are described by the corresponding expressions of forces and moments and their sum at different values n . The developed approach was tested for connection with half angle of the sector bend - 2º, to which the bending moment 5647 kip • in (Fig. 2 - Fig. 4) and the internal pressure of 3.8 MPa were applied. A comparison with the FEM with calculation and experimental data by Feier et al. (2010) and its own numerical solution is also presented, it is evident that the results have a fairly good convergence.

Fig. 2. Pressure (a) Outer diameter; (b) Inner diameter.

Fig. 3. Bending (a) Outer diameter; (b) Inner diameter.