Analytical and numerical modelling of a buckling in a plastic regime of a homogeneous console with symmetrical cross section

The method of numerical-analytical modeling using Maple 18 of the strong buckling of a uniform console with a symmetrical cross-section is presented. The range of plastic deformations in a materials with conditional yield strength (CYS) is studied. Standard profiles and sections made of low-carbon steel, titanium, polyethylene etc. were investigated. Were found and compared with the proper Eulerian values the critical loads of $F_{cr}$, $N$, the shape of buckled console $y(z)$. The quasi-identity of the latter is established for the same slope $p_f = dy/dz$ near the free console end. The method can be applied in robotics, structural mechanics, medical prosthetics, etc. where the materials been used with relatively high Young's modulus and low the CYS.