Large Elasto-plastic Deflection of Thin Beams with Roller Support Contact

Abstract

Here, an explicit numerical approach is presented to solve the problem of a three-point bending of a thin elasto-plastic beam undergoing large deflection supported on cylindrical rollers with radius comparable to the deflection. There are three sources of non-linearity in this problem: roller to beam contact, plastic deformations and large deflections. An incremental form of moment- curvature based constitutive law is derived from a uniaxial linearly hardening stress-strain material model. The governing boundary value problem in terms of its slope is transformed into an initial value problem, with the domain up-to the point of contact. The non-linear initial value problem is linearized about the current step and solution for the subsequent step is obtained by employing the classical Runge-Kutta fourth-order method. This solution procedure is repeated for a range of lengths and end angles of beam. Subsequently, a feasible data set is created from the solution space which satisfied the contact configuration condition. It is found that the increase in the radius of roller introduces a stiffening effect in the force response of the structure. A springback analysis is also performed for the beam data from a feasible set which satisfies plastic deformation condition. It is found that springback decreases with the increase in the radius of roller supports.