The problem of formalizing the elastic line of a thin steel strip of great flexibility arose in the process of creating elastic elements with a nonlinear characteristic for use in various kinds of damping devices. Such elastic rods experience large displacements when the material operates within the elastic range, in particular when axial loading in the supercritical region, when the axial load exceeds the Euler force, but in the subcritical region the movements are not significant enough to obtain a regressive-progressive characteristic.The paper investigates the possibilities of softening the elastic characteristics under axial loading in the initial period by applying a rigid cantilever arm mounted on the end of the elastic rod with a vertical load applied to it. Simultaneously, the influence of the vertical force on the elastic characteristic of the circular trajectory is investigated. To formalize the stress-strain state of a thin steel plate of great flexibility, the method of elliptic parameters is applied. The resulting elastic characteristic actually has a regressive-progressive character. The results obtained using the ANSYS computation complex for a system with given geometric parameters correlate quite well with the theoretical dependences derived. It follows from the diagram that the eccentric compression of the elastic element forms a regressive part of the elastic characteristic, and the circular trajectory of the point of application of the vertical force forms a progressive section.

Keywords: elastic line, thin strip, greater flexibility, formalization, off-axis loading, elliptical parameters, regressive-progressive characteristic