Rainer Maria Johannes Groh

Indirect reduced-order models (ROMs) aim to dramatically reduce the cost of simulating nonlinear dynamic behaviour in large nonlinear finite element systems. Applied force based methods, most notably implicit condensation and expansion, are a classical approach. This work summarises and critiques the past 25 years of development whilst making the case for the continued relevance of the method in the context of the more recent and mathematically rigorous invariant manifold based reduction approach. To facilitate this, a novel applied force framework is developed: the Applied Force Reduction (AFR) method. This includes a more precise approach to evaluate the general accuracy of indirect ROMs through the distinction between verification (the correct implementation of the method) and validation (evaluating the accuracy of the ROM in replicating the full-order system). The former is the focus of this work, and a general verification algorithm is presented which is implemented in the new open source software package. The verification process involves studying the convergence of the underlying polynomial models to create a suitable dataset to inform the reduced-order model whilst minimising interactions with the FE model. This process is completely automated and allows for the efficient construction of ROMs capturing the dynamic behaviour of large systems. This efficiency is demonstrated through consideration of a curved double arch with over 1,000,000 degrees-of-freedom. A two degree-of-freedom ROM is constructed and verified in 60 min, on a desktop computer, and is able to accurately reproduce the internal resonance found in the full-order system.

Reduced-order modelling describes a powerful set of techniques for dramatically reducing the cost of dynamic simulations in complex engineering systems, with broad application for designing and understanding nonlinearity. For Reduced-Order Models (ROMs) to be useful in an industrial context, an analyst must have a high degree of confidence that the results reported by the ROM are reflective of the full-order system. Typically, some full-order results are required to demonstrate the accuracy of a particular ROM. For large and complex systems, this will significantly undercut the initial computational motivations for creating said ROM in the first place. This work presents a novel, full-order simulation-free validation method for applied force ROMs of conservative, geometrically nonlinear systems. This is achieved by testing prospective results to see if they could exist in a series of larger ROMs. If they can, then the smaller ROM has sufficiently approximated the relevant section of the full-order invariant manifold. This allows potential reduction bases to be rapidly tested and a valid, ideally small, basis chosen. This is especially valuable in an applied force context where any low-frequency mode could be required in the reduction basis. A two degree-of-freedom ROM, describing a 100,000 degree-of-freedom finite element model of a curved double arch exhibiting internal resonance, is constructed and fully validated in under 15 min on a desktop computer. Refining the mesh such that there are 1,000,000 degrees-of-freedom increases this time to 170 min. Equivalent full-order simulation validation would take days. Furthermore, no a priori assumption is made about the nature or even the presence of the internal resonance, which is not the case for other reduced-order approaches. This is an important step towards accessible and automatable reduced-order modelling software.

The multi-rotor wind turbine (MRWT, alternatively multi-rotor system, or MRS) is an emerging concept that promises benefits in aerodynamic, structural, economic and environmental performance over the existing single-rotor paradigm. However, research on MRWTs generally lacks detailed aero-servo-elastic design studies, and modelling efforts undertaken in recent years have mainly focussed on rotor interaction, wake mechanics and support structure optimisation, without detailed modelling of the rotor blades themselves. Partly due to the lack of small (<750 kW) reference rotor models, in the limited cases where rotors are modelled, blade designs are typically derived by geometrically scaling existing reference rotors. However, the choice of reference models and the underlying assumptions used for scaling can result in rough and non-optimised aerodynamic and structural blade designs, as well as significant variations in rotor performance. In this context, fair and transparent comparisons between multi-rotor configurations, and against single-rotor configurations, become very challenging. A roadblock in the comprehensive design of MRWTs therefore lies in the lack of bespoke blade and rotor models suitable for the MRWT use case. To address this limitation, we have developed an open-source library of reference blade and rotor designs, covering a rated power range of 100 kW–1 MW, which have been generated using an in-house aeroelastic optimisation software, ATOM. While the generation of these novel rotor designs has been motivated by their application to multi-rotor research, their use is not strictly limited to this context. The newly designed rotors are compared against existing reference models, showing good agreement in mass and aerodynamic properties. Moreover, we propose and demonstrate an interpolation procedure to generate intermediate rotors within the rotor library for custom multi-rotor models, enabling the generation of MRWT models of any overall power rating, using any number of rotors. This allows for comparative studies between MRWTs and greater exploration into multi-rotor scaling laws. In this paper, the design and optimisation process is discussed in detail, with the resulting designs shared as open-source models in the OpenFAST format, alongside a comparison of the aeroelastic responses predicted by ATOM and OpenFAST. The repository of rotor designs can be found at https://github.com/Abdi-SH/MRRL_OpenFAST_Files (last access: 19 February 2026).

Ermine moths produce bursts of ultrasonic clicks that protect them from their predators. The clicks are produced by a tymbal organ that features a series of corrugated striations in the membrane of the hindwings. In response to wing folding during the wingbeat cycle, individual stria snap-through sequentially to excite the natural frequencies of a scaleless patch adjacent to the striations. Based on morphological characterization of the aeroelastic tymbal of Yponomeuta moths, we propose an analogue origami-like creased shell model to reproduce the actuation and sequential click production of the biological structure. The origami-like model helps to explain the governing biomechanics of aeroelastic tymbals; namely, the burst of clicks occurs as a result of a series of snapping vertex folds, reminiscent of the origami waterbomb, that buckle and snap-through in sequence when actuated by a global stimulus (wing folding). Such sequential buckling behaviour often occurs in pattern formation events and in the structural failure of compressed cylindrical shells and sandwich panels. Interestingly, ermine moths instead use this instability phenomenon for functionality—namely, phased acoustic sound emission—creating opportunities for new engineering applications.

Indirect Reduced-Order Models (ROMs) aim to dramatically reduce the cost of simulating nonlinear dynamic behaviour in large nonlinear finite element systems. Applied force based methods, most notably implicit condensation and expansion, are a classical approach. This work summarises and critiques the past 25 years of development whilst making the case for the continued relevance of the method in the context of the more recent and mathematically rigorous invariant manifold based reduction approach. To facilitate this, a novel applied force framework is developed: the Applied Force Reduction (AFR) method. This includes a more precise approach to evaluate the general accuracy of indirect ROMs through the distinction between verification (the correct implementation of the method) and validation (evaluating the accuracy of the ROM in replicating the full-order system). The former is the focus of this work, and a general verification algorithm is presented which is implemented in the new open source AFR Tool software package. The verification process involves studying the convergence of the underlying polynomial models to select an optimal dataset that minimises interaction with the FE model. This process is completely automated and allows for the efficient construction of ROMs capturing the dynamic behaviour of large systems. This efficiency is demonstrated through consideration of a curved double arch with over 1,000,000 degrees-of-freedom. A two degree-of-freedom ROM is constructed and verified in 60 minutes, on a desktop computer, and is able to accurately reproduce the internal resonance found in the full-order system.

Reduced-order modelling describes a powerful set of techniques for dramatically reducing the cost of dynamic simulations in complex engineering systems, with broad application for designing and understanding nonlinearity. For Reduced-Order Models (ROMs) to be useful in an industrial context, an analyst must have a high degree of confidence that the results reported by the ROM are reflective of the full-order system. Typically, some full-order results are required to demonstrate the accuracy of a particular ROM. For large and complex systems, this will significantly undercut the initial computational motivations for creating said ROM in the first place. This work presents a novel, full-order simulation-free validation method for applied force ROMs. This is achieved by testing prospective results to see if they could exist in a series of larger ROMs. If they can, then the smaller ROM has sufficiently approximated the relevant section of the full-order invariant manifold. This allows potential reduction bases to be rapidly tested and a valid, optimal ROM chosen. This is especially valuable in an applied force context where any low-frequency mode could be required in the reduction basis. A two degree-of-freedom ROM, describing a 100,000 degree-of-freedom finite element model of a curved double arch exhibiting internal resonance, is constructed and fully validated in under 15 minutes on a desktop computer. Equivalent full-order simulation validation would take days. Furthermore, no a priori assumption is made about the nature or even the presence of the internal resonance, which is not the case for other reduced-order approaches. This is an important step towards accessible and automatable reduced-order modelling software.