A body-fitted coordinate substructure method for highly flexible structures: Theory and application to offshore wind turbines

Abstract

Highly flexible structures are prone to global geometric nonlinearity under strong environmental loads because of their low lateral stiffness and slender configurations. Such nonlinear behavior is typically dominated by large overall rotations, while the deformation may remain relatively small. In conventional finite element analysis formulated in the global coordinate system, these large rotations cause extensive changes in the structural stiffness matrix as the configuration evolves. Consequently, repeated stiffness updating and large-scale matrix factorization become a major source of computational cost. To address this issue, this paper proposes an efficient parallel substructure method for geometric nonlinear analysis based on body-fitted coordinate systems. The structure is divided into a series of substructures, each associated with a body-fitted frame that follows its overall motion. In this manner, the global nonlinear deformation is represented by the large rotations of the substructures together with relatively small deformations within their local body-fitted frames, so that the remaining stiffness variation is primarily associated with localized material nonlinearity. The inelasticity-separated finite element method (IS-FEM) is then employed to efficiently solve the nonlinear response within each substructure through a low-rank representation of the stiffness variation. A least-squares-based scheme is introduced to update body-fitted frames, and the dual-primal finite element tearing and interconnecting (FETI-DP) method is used to enforce compatibility and equilibrium across substructure interfaces. The Woodbury formula is employed to efficiently handle low-rank stiffness updates without repeated factorization of the complete substructural matrices, while parallel computing is further incorporated to accelerate the overall solution process. Finally, nonlinear seismic time-history analyses of an offshore wind turbine (OWT) tower demonstrate that the proposed method achieves close agreement with the reference solution while substantially reducing computational time, confirming its efficiency for geometric nonlinear analysis of highly flexible structures dominated by large global rotations.