Elastic Relationships
The constitutive equations for a symmetric angle ply laminate, where each layer has the same thickness, are

(13) 
where

(14) 
and where l = cos and m = sin and the Q_{ij} are defined as

(15) 
The terms C_{11}, C_{22}, and C_{33} are the laminate stiffness coefficients in the meridian, , hoop, , and shear directions, respectively. The C_{12} term is the stiffness coupling between the meridian and hoop direction. Strictly speaking, filament wound structures are not symmetric, but alternating plus/minus plys, but because there are generally multiple plus/minus layers, the nonsymmetric aspects of the laminate quickly fade. It is assumed here that the C_{13} and C_{23} terms are zero. Since all plies have the same rotation angle, the stiffness terms are the same as in a single rotated lamina.
© 1997 Kurt Gramoll, The University of Oklahoma, All Rights Reserved.