Large Deflections of Cantilever Beam Obeying Generalized Ludwick’s Material Model Subjected to Follower Distributed Load

Abstract

This thesis presents the large deflection behavior of a cantilever beam subjected to follower distributed load where material of the cantilever beam obeys the generalized Ludwick’s constitutive law. The cross-section of the beam is prismatic and rectangular. The follower distributed load is applied in transverse direction and it always keeps the right angle to the beam axis. The stress-strain relationship of such materials is presented by generalized Ludwick’s constitutive law. To derive the set of governing differential equations, equilibrium equations, moment-curvature relation obeying the generalized Ludwick’s material model and nonlinear geometric relations have been considered. A set of highly nonlinear simultaneous first-order differential equations with boundary conditions is established. The shooting method is employed to solve the problem. Furthermore, two cases of parametric studies are considered...