Large Displacement Analysis Of Elastoplastic Bending Of Non-Uniform Beam

Abstract

The aim of this work is to simulate the elastoplastic behavior in large displacements of a beam of non-uniform section subjected to flexion. First, a mathematical formulation of the elastoplastic behavior based on the moment-curvature relation in the framework of the classical beam theory is developed where the non-uniformity of the section is taken into consideration. The curvature is then evaluated numerically by means of the Newton-Raphson method. Then a formulation in large displacements is put in place. The geometric nonlinearity governed by differential equations is analyzed. The integration method of Euler is favored to solve the problem and thus determine the deflection of the beam. The results of the elasticity simulation are compared with other results of the literature and a good coherence was found in the light of which the approach was applied in elastoplasticity.