PSI - Issue 24

Alessandro Pirondi et al. / Procedia Structural Integrity 24 (2019) 455–469 Author ame / Structural Integ ity Procedia 00 (2019) 000 – 000

462 8

( ) = 2 2 1 1 ⁄ .

(7) The bending stiffness is characterized as a function of by the change of a shape coefficient with respect to a moment applied in that direction . The definition of the shape coefficient is given in Betts (2012). The bending stiffness is evaluated by , and submatrices of SMAC and by substituting Eqn. (8) into Eqn. (7) and then transforming to align with the direction either 1 or 2 the mathematical expressione of the objective function is obtained. The forces and moments in the transformed direction except are set to zero and the remaining system is solved to give an expression in the terms of A, B, D and . This is used to determine the objective function of Equation (7) which is to be minimized. The incorporation of SMA wires as an additional epoxy/SMA layer at the mid plane of the composite host laminate clearly violates the above design rules but, since the contribution of this layer to the overall bending stiffness of the SMAC laminate is negligible (see Section 3.2), the approximation related to the violation of the design rules is negligible, too.

11 12 16 12 11 − 16 16 − 16 66 11 0 16 0 11 − 16 16 − 16 0

11 0 16 0 11 − 16 16 − 16 0 11 12 16 12 11 − 16 16 − 16 66 ] [

0 0 0 − − − ] ,

] = [

(8)

[

Fig. 5 (a) Schematic of n-ply laminate (white) geometry with SMA/Epoxy layer (grey); (b) Directional stiffness positive in anticlockwise direction; (c) Deflection between two stable states for a cross -ply laminate (Gandhi et al. (2019)).