THE SOLUTION OF GEOMETRICALLY NONLINEAR PROBLEMS ON DEFORMATION OF ELASTIC CANTILEVER BEAM UNDER ECCENTRIC COMPRESSION

The problem of the stability of building structures in recent years is particularly acute, and the main reason for this is economic. The desire to reduce the material consumption of structures leads to an increase in their compliance. However, the methods used to date to assess stability, based on the formulas created in the 18th and 19th centuries, give only approximate values of critical loads. In this paper, we posed an exact nonlinear problem of the deformation of an elastic cantilever rod with all the rigidities taken into account. Its solution is based on the asymptotic method of expanding the solutions in powers of the small parameter. The results obtained in this article will allow us to find in the future the exact solution of the stability problem for an eccentrically compressed rod.