Numerical analysis of highly deformable elastoplastic beams

Abstract

The objective of the present study is to develop a numerical formulation to predict the behavior of highly deformable elastoplastic thin beams. Following the Euler-Bernoulli bending, the axial and shear effects are neglected, and the nonlinear second-order differential equation regarding the angle of rotation is defined based on the specific moment-curvature relationship. Although the formulation can be used for general materials, three constitutive models are employed: linear-elastic, bilinear elastoplastic, and linear-elastic with Swift isotropic hardening. The resultant boundary value problem is solved by means of the fourth-order Runge-Kutta integration procedure and the one-parameter nonlinear shooting method. The performance of the present formulation is investigated via three numerical problems involving finite bending of slender beams composed of elastoplastic materials. For these problems, numerical solutions regarding rotations, displacements and strains for the loading, unloading and reloading phases are provided. Finally, it is shown that the present methodology can also be used to determine the post-buckling behavior of elastoplastic thin beams.

Keywords:
Finite bending deformations; thin beams; elastoplastic material; post-buckling behavior; fourth-order Runge-Kutta integration; nonlinear shooting method