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

283

3

The stress-strain relation, defined in the cylindrical coordinate system ( r , θ, z ), in plane stress and strain conditions of the k th rectilinear orthotropic layer composing the laminate circular plate is:

=    

    k

   ε r ε θ γ r θ

   k

   k

   ε r ε θ γ r θ

   k

   σ r σ θ τ r θ

Q 11 ( θ ) Q 12 ( θ ) Q 16 ( θ )

= Q ( θ ) k

(1)

Q 12 ( θ ) Q 22 ( θ ) Q 26 ( θ )

Q 16 ( θ ) Q 26 ( θ ) Q 66 ( θ )

where:

Q ( θ )

= T ( θ ) Q

k

T ( θ )

T

(2)

k

is the transformed reduced sti ff ness matrix in the cylindrical coordinate system of the k th rectilinear orthotropic layer, Q k denotes the analogous sti ff ness matrix in the Cartesian coordinate system ( x , y , z ) and T ( θ ) is the coordinate system transformation matrix:

   

   

sin 2 ( θ )

cos 2 ( θ )

2 cos( θ ) sin( θ )

T ( θ ) =

sin 2 ( θ ) − 2 cos( θ ) sin( θ ) − cos( θ ) sin( θ ) cos( θ ) sin( θ ) cos 2 ( θ ) − sin 2 ( θ ) cos 2 ( θ )

(3)

Fig. 1: Rectilinear orthotropic composite circular plate.