Stress and Strain Variation in a Laminate

We will proceed in the next section to define the strain and stress variations through the thickness of a laminate. The resultant forces and moments on a laminate will then be obtained in Section 4.2.3 by integrating the stress-strain relations for each layer. Equation (4.6), through the laminate thickness subject to the stress and strain variations determined in Section 4.2.2. 

Knowledge of the variation of stress and strain through the laminate thickness is essential to the definition of the extensional and bending stiffnesses of a laminate. The laminate is presumed to consist of per- 

But because, under deformation, line ABCD further remains perpendicular to the middle surface, p Is the slope of the laminate middle surface in the x-direction, that is. 

the displacement, u, at any point z through the laminate thickness is 

The laminate strains have been reduced to e, Sy, and by virtue of the Kirchhoff hypothesis. That is, ez = Yw -r 0- small strains (linear elasticity), the remaining strains are ned in terms of displacements as 

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