Extensional stiffness matrix

A] is the Extensional Stiffness Matrix although it should be noted that it also contains shear terms. 

Having obtained all the terms for the extensional stiffness matrix [A], this may then be inverted to give the compliance matrix [a]. 

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

It is seen that [A] is the extensional stiffness matrix, [D] is the flexural stiffness matrix and [B] is the bending-stretching coupling matrix. 

Thus the addition of the stiff carbon fibers has a very great effect in stiffening the epoxy matrix. Eor the commonly used fiber volume fraction of 0.6 the unidirectional carbon—epoxy lamina has a predicted extensional stiffness E = 145 GPa (2.1 x 10 psi)-... 

Similarly, under suitable constraints, deformation is possible in which only one extensional strain arises or is applied. Again, work is produced by the corresponding stress alone. Thus, because the work done is determined by the diagonal elements of the stiffness matrix, those elements must be positive, that is,... 

Symmetric angle-ply laminates were described in Section 4.3.2 and found to be characterized by a full matrix of extensional stiffnesses as well as bending stiffnesses (but of course no bending-extension coupling stiffnesses because of middle-surface symmetry). The new facet of this type of laminate as opposed to specially orthotropic laminates is the appearance of the bend-twist coupling stiffnesses D. g and D2g (the shear-extension coupling stiffnesses A. g and A2g do not affect the transverse deflection w when the laminate is symmetric). The governing differential equation of equilibrium is... 

Extensional or membrane terms of laminate stiffness matrix... 

For symmetric laminates it is possible to define effective in-plane moduli in terms of the in-plane stiffness or extensional compliance matrix, since there is no coupling between in-plane and bending response. The effective... 

There is an important group of laminates that exhibit in-plane isotropic elastic response. These laminates are called quasi-isotropic. This group includes all symmetric laminates with IN (N > 2) laminae with the same thickness and N equal angles between fibre orientations (A0 = nIN), i.e. = 60° for N = 3, A6 = 45° for N = 4, Ad = 30° for = 6 and so on. It is possible to prove that the in-plane stiffness or extensional matrix of quasi-isotropic laminates is given in reduced form as [14]... 

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