Introduction of Two Analytical Theories as Applied to Developable Surfaces

In this paper, two analytical shell theories of linear elasticity which were suggested by Goldenweiser (Theory of elastic thin shells (1953) [2]) and Krivoshapko (Appl Mech Rev 51(12):731–746 (1998) [5]) are analyzed and applied to developable surfaces. The problem is discussed in an arbitrary system of curvilinear coordinates. It is shown in the paper that both theories are applicable for developable surfaces but can give different results for other types of surfaces. The particular differences in terms and determinations of two analytical theories are shown and discussed, and the limits of the technical theory are presented. Developable helicoid has been chosen as a test surface in order to investigate the differences in two theories. There are also some recommendations for the application of each of the theory to different types of surfaces. © Springer Nature Switzerland AG 2020.