Prediction of Sectional Collapse of Thin-Walled Structure Under Pure Bending by Nonlinear Composite Beam Theory

Abstract

Brazier [1] found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper extends the Variational Asymptotic Beam Sectional Analysis (VABS) theory to consider finite cross-sectional deformations. The three-dimensional (3D) continuum is reduced to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws regarding nonlinear elasticity and progressive damage. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.