PSI - Issue 12

Valerio G. Belardi et al. / Procedia Structural Integrity 12 (2018) 281–295 V.G. Belardi et al. / Structural Integrity Procedia 00 (2018) 000–000

290

10

being the theoretical sti ff ness terms defined as:

• K th Fn u the ratio of the resultant radial in-plane loads Fn 2 on the outer border of the circular sector having extension α 1 + α 2 and centered on θ = 0 − which is the maximum radial nodal loads − and the radial displacement at the nugget edge u 1 .

• K th Ft v the ratio between the resulting tangential in-plane loads Ft 2 on the outer border of the circular sector having extension α 1 + α 2 and centered on θ = π 2 − which is the maximum tangential nodal loads − and the tangential displacement at the rigid nugget edge v 1 for θ = π 2 ( v 1 = u 1 ).

N

mm

10 5

3 . 5 ·

3

A 11 ( θ ) A 16 ( θ ) A 26 ( θ )

A 12 ( θ ) A 22 ( θ ) A 66 ( θ )

2 . 5

2

1 . 5

1

0 . 5

0

− 1

− 0 . 5

0

0 . 5

1

θ

Fig. 4: Circumferential variation along the dimensionless angular coordinate θ of the A i j ( θ ) terms of the extensional sti ff nesses matrix.

Moreover, as regards the lay-up considered in the Results section, i.e. the quasi-isotropic one (details can be found in Section 5), even though the plate is made up of composite material, the in-plane sti ff ness terms A i j ( θ ) do not depend on the angular coordinate. Indeed, Fig. 4 outlines the dependence of the in-plane sti ff ness terms on the dimensionless angular coordinate θ , which shows a not appreciable circular variation. This aspect justifies the considerations regard ing the employment of the maximum values of Fn 2 and Ft 2 in order to define the sti ff ness functions K th Fn u and K th Ft v which, as a consequence (see Eq. (22)), do not depend on the angular coordinate θ .