The following is a summary from a recent discussion within the AIAA Structures Technical Committee.
The problem was brought up by an engineering from a major aerospace company. During initial sizing of composite aerospace structures, the input is not a stacking sequence but a representation of the partial thicknesses in each ply direction. The use of smeared properties is needed for preliminary sizing where no exact stacking sequence is known yet. Most commercial software have a consistent smearing for in-plane stiffness matrix A and bending stiffness matrix D=1/12 T^2 A with T as the total thickness.
However, existing commercial software do not have a consistent way of computing the smeared transverse stiffness matrix G. Based on the requirement, the right approach with a rigorous theoretical justification is:
- Find the smeared 3D properties C (a 6 by 6 matrix) in terms of layer thickness and layup angles.
- Construct a Reissner-Mindlin model out the plate made of a homogeneous continuum with properties obtained in Step 1. A will be the same as the in-plane stiffness of the classical lamination theory (CLT), D=1/12 T^2 A.
- G will more complicated. It can be either computed by a 3D elasticity solution of the homogeneous plate subject to plate transverse shear resultants, or using FOSDT applies to the plate made of smeared properties with a shear correction factor, or using MSG.
However, theoretically speaking, smearing property approach only works if the laminate is symmetric and subject to in-plane loads, or the stack is a sub-laminate and the entire laminate contains many repetitions of this sub-laminate. If the situation is the former (symmetric laminates subject to in-plane loads), D and G do not matter. On the contrary, for the former, if you still need bending behavior, the smeared D and G will not work because it could introduce significant errors (e.g., considering how D will be different for 0/90/90/0 and 90/0/0/90). In this case, I would like to suggest to compute in-plane properties (corresponding to A), flexural properties (corresponding to D), and shear properties (corresponding to G) for different stack sequences (I assume there are only a finite number of stack sequences allowed by manufacturing). During initial sizing, we can treat different stacking sequences as different materials for selection.