Thin-walled orthotropic shells of arbitrary form reinforced from the concave side by a cross-sectional stiffening system oriented in parallel to coordinate lines are examined. Geometrical nonlinearity and transverse shears are taken into account, but it is presumed that a shell is shallow.
Mixed-form equations are more simplified equations of a shell theory as compared to displacement equations, but they are more convenient for some types of fixing of the shell edges (for example, for movable pin fixing).
Forces are expressed using a stress function in a middle surface of a shell in such a way that the first two equilibrium equations are satisfied identically. Shell deformation is also expressed using this function.
The third equation of strain compatibility is used to form one of the mixed-form equations. Curvature and torsion change functions for this equation are written in the same way as for the Kirchhoff–Love model, though also taking into account transverse shears.