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Force Deflection Relationship in a Laminate
After transforming the constitutive relationship of each lamina, you can build
up a resultant force-deflection relationship for the entire laminate, where the
in plane stress vector N and Moment vector M are related to the mid-plane
strain and curvature as follows:
Where, zk being the distance of each layer from the geometric mid-plane,
The matrices A, B and D are essentially functions of the ply angle,
arrangement and the ply thickness. For example, a completely symmetric
arrangement of ply lay-up like [0,30,30,0] would result in B=0, indicating the
decoupling of the behaviour of the laminate. Again a symmetric ply lay-up of
the type ( ± q ) would farther result in shear coupling terms in the A-matrix to
become zero. Thus a designer has lot options starting from the choice of
fibre, volume fraction to ply arrangement in composite material
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