PSI - Issue 1

Salem Cherif Sadek et al. / Procedia Structural Integrity 1 (2016) 234–241 Salem cherif sadek/ Structural Integrity Procedia 00 (2016) 000 – 000

240

7

1,17

Mode 3

1,14

1,11

1,08

1,05



1,02

0,99

0,96

0,93

0

10

20

30

40

50

60

70

80

90



Fig 8. Evolution of the report ψ according to the crack inclinations angle for 2a / w = 0.5. From these graphs, it is noticed that some ψ values exceed the unit value ( ψ> 1) for angles superior at 30 ° and 40° depending on the mode. Accordingly, from these inclinations of the crack, it is found improved resistance to buckling phenomenon panel. Comparing the result of our calculations with those Roberto Brighenti [2], in terms of growth ratio ψ as a function of the angle of inclination θ , shows the same aspect by considering a fixed length 2a / w and taking complementary angle of the author (θ B = π/2 – θ).

Fig 9. Evolution of the report  - according to the crack inclinations angle, Brighenti reference.

A trend curves representing the ψ function was determined in the polynomial form of fourth order for the three modes.

(b)

(a)

ψ = 7.10 -09 θ 4 – 2.10 -06 θ 3 0,921 R² = 0,999

ψ = 5.10 -10 θ 4 – 1.10 -07 θ 3 + 8.10 -06 θ 2 – 3.10 -05 θ + 0,998 R² = 0,999

0.9975 0.999 1.0005 1.002 1.0035 1.005 1.0065 

1.015



0.965

0.915

0 10 20 30 40 50 60 70 80 90 θ °

0 10 20 30 40 50 60 70 80 90 

0.93 0.96 0.99 1.02 1.05 1.08 1.11 1.14 1.17 

(c)

ψ = -8.10 -09 θ 4 + 6.10 -07 θ 3 + 4.10 -05 θ 2 + 0,937 R² = 0,999

Fig 10. Trend curves ; (a) mode 1 ; (b) mode 2 ; (c) mode 3. 0 10 20 30 40 50 60 70 80 90 θ °