ResearchING NONLINEAR PLANE bending of a beam

V.B. Mintyuk

Numerical solutions of several geometrically nonlinear problems of plane bending of a beam under assumption of deformed axis are developed using Raleigh-Ritz method. Rapid convergence and high accuracy of solutions obtained are shown. Governing equations are obtained basing on theories with different level of nonlinearity: complete nonlinearity, assumption of small deformations, Euler’s elastic, flexible wire, assumption of small of small deformation and square of deviation, and linear theory. Following problems are analyzed: pure bending of a beam, bending of simply supported beam with approaching and non-approaching supports, transverse bending with consideration of post-buckling behaviour. Comparative analysis or results is carried out.

Keywords: beam, simple bending, geometrically nonlinear problem, deformation of axis, numerical solution