A B-splines based nonlinear GBT formulation for elastoplastic analysis of prismatic thin-walled members

Abstract

A beam finite element method based on Generalized Beam Theory (GBT) is developed for the modeling of nonlinear elastoplastic behavior of prismatic thin-walled members. The kinematic relationships, strains and nonlinear equilibrium equations are derived, and the corresponding numerical discretization and implementation schemes are presented. The buckling, warping and transverse extensions of cross-sections are defined by the linear combination of GBT cross-section deformation modes, and the longitudinal variation of amplitude of each GBT mode is approximated by the cubic B-splines. The cross-section rigid-body motion concerning global longitudinal extension, major/minor-axis bending and torsion is described by three translational displacements and three consecutive Euler angles (only four of them are independent variables). The J2-plasticity conjugated return mapping algorithm is introduced to integrate the rate equations of the constitutive model. In order to track the post-collapse equilibrium path, the arc-length control technique is utilized in solving the nonlinear equilibrium equations. Five illustrative examples are employed, and the validation of the proposed GBT formulation is verified by comparing GBT results with ANSYS FEM outputs. The modal decomposition analyses of five thin-wall members also provide a deep insight into their mechanical behavior, e.g., collapse mechanisms.