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.

Keywords:

• Beam structures
• geometrical non-linearity
• Carrera’s Unified Formulation
• Asymptotic Numerical Method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the National Natural Science Foundation of China (Grant Nos. 11902227, 11920101002 and 11772238), the China Postdoctoral Science Foundation (Grant No. 2018M642904); the European Union within the Horizon 2020 research and innovation program under grant agreement (GA No: 642121) and COMPOSELECTOR project (GA No: 721105).