General Deformation Behaviour of Laminates

The previous section has illustrated a simple convenient means of analysing in-plane loading of symmetric laminates. Many laminates are of this type and so this approach is justified. However, there are also many situations where other types of loading (including bending) are applied to laminates which may be symmetric or non-symmetric. In order to deal with these situations it is necessary to adopt a more general type of analysis. 

In this more general analysis it is essential to be able to define the position and thickness of each ply within a laminate. The convention is that the geometrical mid-plane is taken as the datum. The top and bottom of each ply are then defined relative to this. Those above the mid-plane will have negative co-ordinates and those below will be positive. The bottom surface of the /th ply has address hf and the top surface of this ply has address hj-. Hence the thickness of the /th ply is given by 

The general deformation analysis of a laminate is very similar to the general deformation analysis for a single ply. 

This is called the Extensional Stiffness Matrix and the similarity with that derived earlier for the single ply should be noted. 

The Coupling Matrix will be zero for a symmetrical laminate. 

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