Global/local buckling analysis of thin-walled I-section beams via hierarchical one-dimensional finite elements

Abstract

Buckling instability is one of the factors that limit the ultimate load-carrying capacity of I-section beams, and the coupling of global buckling and local buckling makes it difficult to predict the mechanical behavior of I-section beams. Hierarchical one-dimensional finite elements for the global/local buckling analysis of I-section beams are presented in this paper. Within the framework of Carrera’s Unified Formulation (CUF), a model is built by using Lagrange polynomials to describe the three-dimensional displacement field as an arbitrary order approximation by displacement variables over the beam cross-section. One-dimensional finite elements are obtained by discretizing the governing equation along the beam length. Due to its high efficiency and step length adaptability, the Asymptotic Numerical Method (ANM) is adopted to solve the nonlinear governing equations. Several typical buckling problems in I-section beams, including global buckling, local buckling and global–local coupled buckling, are investigated. The numerical results demonstrate the validity and efficiency of the proposed model. The critical buckling load and displacement field can be precisely predicted, and a good agreement is found in comparison with results obtained via three-dimensional finite element solutions.