Coupling of beam and shell finite elements for the rapid analysis of tubular structures

Abstract

The research presented in this thesis focuses on the development of a technique to couple beam and shell elements, with the purpose of creating one finite element (FE) model to capture the global and local structural behaviour of an offshore wind turbine foundation design: the Inward Battered Guide Structure (IBGS). The technique is proven to be computationally efficient in that less storage capacity is required as there are fewer degrees of freedom (DOF) than compared with an equivalent analysis that uses only hexahedral elements, for example. Furthermore, the method is effective in providing reliable results in a shorter amount of time as it mitigates the necessity of the Design Engineer to perform separate local and global analyses. Although the beam-shell coupling is applied to the numerical analysis of the IBGS here, the technique is applicable to any tubular structure.

Initially, the simple theories of bending and torsion are reviewed and the formulation of the three-dimensional (3D) Euler-Bernoulli (EB) beam element is given. In addition, the concepts of plate and shell theory are discussed with an emphasis on finding a reliable general shell element. The formulation of the isoparametric degenerate continuum (IDC) shell and the mixed interpolation of tensorial components shell element with nine nodes (MITC9) for linear static analysis are given. It was found that the IDC shell was inadequate to solve simple benchmark problems due to shear locking. It is shown that the MITC9 formulation does not suffer from this problem. The thesis then proceeds to discuss various methods to impose multi-point constraint (MPC) equations, including the transformation equations, penalty functions and Lagrange multipliers, for the purpose of coupling different types of finite elements. The MPC equations to couple EB beam and MITC9 shell elements are developed through a purely geometric approach. The capability to couple these elements is successfully demonstrated in the numerical analysis of the IBGS.

Through the application of the beam-shell coupling, it is concluded that the twisted jacket arrangement of the IBGS shows reduced stiffness and higher stresses under static loading. It is found that an untwisted jacket arrangement of the IBGS is two-to-three times stiffer than the twisted jacket arrangement for the case of linear static analysis. The analyses are undertaken with firstly a FE model containing only EB beam elements and secondly a FE model that employs the beam-shell coupling technique. The beam-shell coupling enables both the stress distribution through the structural joints, modelled with shell elements, and the axial/bending behaviour of the main structural members, modelled with beam elements, to be assessed in a single analysis.