When the approach is adopted, matrices allow the calculation of out-of-plane shear stress from the global out-of-plane shear force:
Actually, one is interested in stresses in ply axes, rather than in laminate axes. If is the orientation of the ply in laminate axes, then:
Then, one has simply:
One stores a matrix for each station through laminate thickness where out-of-plane shear stress might be requested. Actually it is done at top, mid and bottom surfaces in each ply. This means that matrices are stored in the ClaLam object.
One first estimates the components of bending moments gradient in laminate axes with equation (II.1.49):
Then, the laminate out-of-plane shear stresses can be estimated by an expression like (II.1.43):
In this expression, is given by (II.1.44):
The three matrices , and are calculated recursively using the expressions (II.1.46), (II.1.45) and (II.1.45):
To resolve the recursion for one need an estimate for the first ply. One uses (II.1.47):
Again, one is more interested in the out-of-plane shear stresses in ply axes than in laminate axes.
One stores a matrix for each station through laminate thickness where out-of-plane shear stress might be requested. Actually it is done at top, mid and bottom surfaces in each ply. This means that matrices are stored in the ClaLam object.