Novel adaptive time integration and consistent coupling of structural components in an aeroelastic simulation framework

authored by

David Märtins

supervised by

Raimund Rolfes

Abstract

Aeronautical structures play a pivotal role in the context of climate protection. While the expansion of wind energy is making an increasingly significant contribution to the transition towards renewable energy sources, aviation remains in the spotlight due to its substantial share in global greenhouse gas emissions. In order to enhance the efficiency of aeronautical systems, there is an increasing tendency to develop slender, thus highly flexible structures made from composite materials. However, this leads to increased susceptibility to vibrations and amplifies the complexity of fluid–structure interaction, thereby posing considerable challenges for the accurate prediction of the behaviour. The reliable design of such structures requires the use of novel computational methods capable of accurately capturing both geometric nonlinearities and the intrinsically nonlinear coupling between airflow and structural response. This gives rise to a fundamental trade-off: while high-fidelity numerical methods offer superior accuracy, their computational costs often render them impractical, particularly during the early stages of the design process. As a result, attention is increasingly directed towards mid-fidelity approaches, which seek to achieve a well-balanced compromise between modelling accuracy and computational expense. This thesis aims to advance the development of an aeroelastic simulation environment that combines the Unsteady Vortex Lattice Method with geometrically exact beam theory, employing a strongly coupled interaction between aerodynamic and structural models. The central objective is to improve the trade-off between accuracy and efficiency through targeted methodological enhancements. To this end, a consistent geometrically exact node-to-node coupling element is introduced, enabling the connection of structural components. Its formulation ensures objectivity and path independence, conserves mechanical invariants such as linear and angular momentum as well as total energy, and also permits the inclusion of mass distributions and damping effects. The performance of this coupling element is demonstrated through modal, static and dynamic analyses. In order to reduce computational costs, a heuristic adaptive time-stepping approach is developed, based on the temporal evolution of physical system variables. This allows for the detection of near-quasi-steady-state conditions without additional computational costs, enabling an increase in time-step size and thus a reduction in total simulation time. In addition, a second adaptive strategy is introduced to improve numerical robustness, based on local error estimation. This method employs Richardson's extrapolation along with a more accurate approximation of unsteady aerodynamic forces, allowing the time-step size to be dynamically adjusted according to the estimated local error. Numerical experiments demonstrate that this approach not only enhances robustness in the presence of instability or strong nonlinearities, but can also lead to reductions in computational costs. A comparison of both adaptive time-stepping strategies confirms the intended development goals. The heuristic method, while requiring case-specific parameter tuning, is particularly well suited for accelerating large numbers of similar simulations. The error-based approach, in contrast, selects time steps more efficiently with respect to the deviation from a reference solution but entails higher computational demands. The comparison further shows that the developed coupling element can be effectively integrated with both time integration schemes. In summary, the thesis demonstrates that the targeted enhancement of existing mid-fidelity approaches can improve the trade-off between modelling fidelity and computational efficiency. In doing so, it contributes to the less computational expensive and more robust development of future lightweight and flexible aeronautical structures.

Organisation(s)

Institute of Structural Analysis
CRC 1463: Integrated Design and Operation Methodology for Offshore Megastructures

Type

Doctoral thesis

No. of pages

165

Publication date

17.07.2025

Publication status

Published

Sustainable Development Goals

SDG 7 - Affordable and Clean Energy, SDG 13 - Climate Action

Electronic version(s)

https://doi.org/10.15488/19284 (Access: Open)