Hierarchical beam finite elements for geometrically nonlinear analysis coupled with Asymptotic Numerical Method

Abstract

This paper couples the Carrera's Unified Formulation (CUF) with the Asymptotic Numerical Method (ANM) for investigating geometrically nonlinear behaviors of beam structures. On the basis of CUF, a family of advanced one-dimensional beam models is firstly established by deriving a fundamental nucleus. The ANM that is an efficient and robust nonlinear solver is then used to solve the resulted nonlinear systems. Several typical nonlinear problems in thin/thick beam structures are carried out, and numerical results demonstrate the validity and efficiency of the proposed framework. Besides, the importance of using high-order kinematics for beam structures undergoing large deformations is emphasized.