Theory for Section Stiffness
The Section Stiffness node in the Shell interface allows modeling of a shell by directly entering the effective stiffness or compliance matrices without specifying the geometrical and material properties of the cross section. A typical use case is for modeling shells with homogenized properties, for example, perforated or corrugated sheets.
The background and theory of the Section Stiffness model is based on the Theory for FSDT Laminated Shell. However, instead of performing a numerical integration in the extra dimension to account for the through thickness variation of geometrical and material properties, this is assumed to have been done beforehand. Hence, you directly enter the coefficients of the A, B, and D matrices in Equation 5-4 to Equation 5-6 to define the effective properties of the cross section. Additionally, shear correction factors are needed so that the transverse strains and stresses give the correct contributions to the strain energy.
A consequence of this formulation is that stresses are not straightforwardly available for result evaluation, since they are not part of the formulation. Stresses can, however, be evaluated using the following equations
where matrices SN, SM, and SQ are user inputs. They are by default populated with coefficient that gives the stress on the top surface of the shell.