PSI - Issue 18

Yaroslav Dubyk et al. / Procedia Structural Integrity 18 (2019) 622–629 Yaroslav Dubyk and Iryna Seliverstova / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 5. Influence of relative depth of dent / h  on bending stresses: R=400mm,h =10mm, l=120 мм

σ bx ;

σ b φ

a – axial force, b – pressure load.

Beside the dent curvature:

2              2 2 2 x  



w

xx   

(21)



We can easily account for the additional curvature  we need only to modify the third static equation (14):



2 2 2 x w      , resulting from the shell deformation, 2 / /



   



Q N

N

2

2

Q  

1









2 x R R D x R               x x N

w w  

(22)

2 2







Then, using the analogous procedure as described by the Eqs. (12)-(20), we obtain only slightly complicated solutions in the form of a solution of the algebraic equation. The nonlinearity (22) influence is shown in Table. 1, analysis of which shows, that the effect of this additional curvature is negligible and can be neglected in calculations.

Table. 1. The impact of deformation component on stress concentration for the periodic dent: E=70GPa, µ=0.3, R/h=500, σ φ =1MPa

0.05 h  

0.5 h  

5 h  

50 h  

Def

No def -0.015 0.985 -0.014 -0.014

%

Def

No def -0.146 0.854 -0.143 -0.143

%

Def

No def -1.463 -0.462 -1.431 -1.426

%

Def

No def -14.632 -13.625 -14.306 -14.261

%

-0.015 0.985 -0.014 -0.014

0.829 0.012 0.829 0.829

-0.145 0.855 -0.142 -0.141

0.829 0.142 0.829 0.829

-1.451 -0.450 -1.419 -1.414

0.829 2.622 0.829 0.829

-14.511 -13.503 -14.187 -14.143

0.829 0.890 0.829 0.829