The most fundamental aspect of the coupling between FEA and HyperSizer is the generation of equivalent ABD matrix used to model the overall stiffness of a stiffened panel. The stiffness is 'smeared' in that the contribution of the stiffeners is smeared into the skin.
The concept of a smeared stiffness for panels is directly equivalent using the generalized beam stiffness to model beams. For example the resistance to pure axial load is described using EA for beams (modulus times area). The plate equivalent is the A11 term from the membrane stiffness matrix.
| Beam Theory | Plate Theory |
|---|---|
| EA | A11 |
| EI | D11 |
| GJ | D33 |
Using the smeared stiffness, stiffeners do not need to be discretely modeled in the finite element model. This significantly decreases analysis execution time as well as the modeling effort. Also, optimization can be performed by simply rewriting new smeared stiffness properties for the shell elements. No remeshing is required.
The idea of smearing stiffeners into an equivalent plate has been used for many years. Simpler methods are sometimes referred to as 'orthotropic plate theory'. See NACA-TN-2289 for an example.
The smearing process is done by extending classical lamination theory (CLT) to stiffened panels. The same assumptions used in CLT apply to the HyperSizer formulation which are the same as those found in thin plate theory. These are sometimes referred to as the Kirchhoff-Love assumptions with the major assumption being that plane sections remain plane after bending. One of the advantages of applying CLT is that no restrictions on the type of laminate need to be imposed.
The major implications of the Kirchhoff-Love assumptions are:
See the HME document for more detailed information.