Large Elasto-plastic Deflection of Thin Beams with Roller Support Contact. (2017)

• Record Type: Journal Article
• Authors: Pandit, D.; Srinivasan, S.M.
• Is Part Of: Procedia engineering. Volume 173(2017)
• Page Start: 1079
• Page End: 1084
• Publication Date: 2017
• Subjects: Large deflection -- Bilinear hardening -- Elasto-plastic deformation -- Non-linear differential equation -- Three-point bending; Engineering -- Congresses; Engineering -- Periodicals; Engineering; Conference proceedings; Periodicals; 620.005
• DOI: 10.1016/j.proeng.2016.12.188
• Languages: English
• ISSNs: 1877-7058

Abstract

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.