Transformation of the shape formation scheme by covering on the principles of symmetry

We assume that the concept of symmetry plays an important role in improving the theory and practice of the forming process by covering load-bearing thin-sheet shells of double curvature, which guarantees the production of contour-forming parts of the skin of modern aircraft with an exact geometric shape and minimal variation in thickness. To understand our assumption, it is necessary to remember that the complexity of the theory of plastic shells lies in the geometric and physical nonlinearity and the need to take into account shear stresses and deformations along the surface of the shell and its variability in curvature, therefore there is still no unified approach to the analysis of the formative processes of covering from sheet material. This assumption applies only to thin-sheet shells of double curvature, providing a different isometric position (curved surfaces one on top of the other) of the open surface as a whole, and not closed like a sphere. Therefore, the process of shaping a sheet blank into a shell part of an aircraft has some form of symmetry with respect to a given set of surface transformations, unless certain properties or relationships, the so-called invariants of the set of transformations, change when they are performed.