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Classical Laminate Theory

Consider an orthotropic material:

Lamina stiffness given by:
where:

and: Modulus in material's 1-direction

Modulus in material's 2-direction

Shear modulus

Poisson's effect of 2-direction on 1

Poisson's effect of 1-direction on 2

in vector form: Consider the transformation matrix:

where:

Note also the inverse of T:

Hence,

Premultiplying by :

From above,

Where is the Global Stiffness matrix.

In long hand:

Strain in this layer given by:

where k is the curvature.