Linear Approximation Parameters of Nonlinear Bending and Buckling of Elastic Rods.

The problem of finite deflections of a buckled pole and cantilever is considered by the approximation method of nonlinear differential equilibrium equations using Chebyshev's polynomials. The linear differential equation of the heavy cantilever loaded at its free end by the concentrated force has a form suitable for direct integration. The algorithm for calculations of parameters of the postcritical states of the buckled pole and nonlinear bending of the cantilever is worked out accounting for the boundary conditions. The detailed results of calculations are presented in figures and graphs.