PSI - Issue 8

V.G. Belardi et al. / Procedia Structural Integrity 8 (2018) 368–378 V.G. Belardi t l. / Structural Integrity Procedia 00 (2017) 0 0–000

377

10

ρ

ρ

0

0 . 2

0 . 4

0 . 6

0 . 8

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1

0

0

0 . 2

0 . 2

0 . 4

0 . 4

w FEA ( β )

w FEA ( β )

w ( ρ )

w ( ρ )

0 . 6

0 . 6

t a = 0 . 02

t a = 0 . 03

0 . 8

0 . 8

Galerkin FEA

Galerkin FEA

1

1

β 1 β 2 β 3

β 1 β 2 β 3

ρ

ρ

0

0 . 2

0 . 4

0 . 6

0 . 8

0

0 . 2

0 . 4

0 . 6

0 . 8

1

1

0

0

0 . 2

0 . 2

0 . 4

0 . 4

w FEA ( β )

w FEA ( β )

w ( ρ )

w ( ρ )

0 . 6

0 . 6

t a = 0 . 04

t a = 0 . 05

0 . 8

0 . 8

Galerkin FEA

Galerkin FEA

1

1

β 1 β 2 β 3

β 1 β 2 β 3

Fig. 2: Variation of the dimensionless mid-surface deflection along the dimensionless radius for di ff erent ratios t

a and for β 1 = 0 . 05, β 2 = 0 . 1 and

β 3 = 0 . 2.

6. Conclusions

An original approach to the solution of transversally loaded quasi-isotropic rectilinear orthotropic composite annu lar plate was presented. Following the analytical derivation from the equilibrium equations and the stress resultants strains relations of the governing equation in the cylindrical coordinate system, which is a third order di ff erential equation in terms of mid-surface deflection, the polynomial approximation functions compliant with both essential and natural boundary conditions were derived in order to properly apply Galerkin method. This work is an initial approach towards the realization of a Spot Joint Element, enhancement of the one described in Vivio (2009), able of providing a complete sti ff ness evaluation of composite bolted joints with a limited computa tional cost. Because of this objective, a suitable theoretical reference model of the composite bolted joints has been defined, i.e. a rectilinear orthotropic composite annular plate with a rigid inner core and clamped at the outer radius.