Substructuring-Based Parametric Model Order Reduction Strategies for Efficient Structural Dynamic Simulation of Mechanical System Assemblies

With the continuous advancement of mechanical system assemblies, including vehicles, aircraft and machines, the emphasis on lightweight design for ecological and economic considerations and the utilization of multi-material combinations have become increasingly prevalent. Joints play an important role in ensuring the performance of these structures, effectively connecting the lightweight and multi-material components. Moreover, the pursuit of weight reduction often comes at the cost of undesirable noise, vibration and harshness (NVH) characteristics, which joints are known to have a potentially strong impact on. Therefore, understanding the influence of these joints on the structural dynamic performance is crucial for the design and operation of mechanical assemblies.

Simultaneously, the industrial progression towards digital transformation underscores the need for enhanced digitization of mechanical systems. It holds the potential for advancements in various applications including design, identification, optimization, and operational monitoring. In this context, numerical models that can accurately represent real-world systems can be of great added value. The finite element method is a powerful and versatile numerical tool which is often used in industry, but can be computationally intensive for large-scale systems. To address this, model order reduction (MOR) techniques come into play to effectively reduce the model size, enabling fast computation yet accurate predictions. These methods are also extended to parametric MOR (pMOR) for more efficient parametric studies, which are common across various applications like design and optimization. Moreover, for large-scale systems, (p)MOR is often combined with substructuring, which breaks down the systems into smaller substructures. This approach simplifies the reduction process, allows isolation of local effects, and fosters modularity in system analysis. However, existing (p)MOR methods are not well-suited in such a substructuring context when joints are present in these assemblies, due to their complex physical properties and the phenomena involved within these joints. Among various joining techniques, adhesive bonding and bolted connections are widely used in lightweight designs and multi-material combinations. These locally introduce frequency dependent viscoelastic material properties for the adhesives, or contact nonlinearities for the bolt connections. Therefore, the primary goal of this dissertation is to develop pMOR strategies for structural dynamic simulation of mechanical system assemblies containing adhesive joints and bolted joints.

To enable substructuring-based model reduction of adhesive bonded assemblies, the first contribution is the proposal of a pMOR strategy for viscoelastic substructures. Improvements to the Craig-Bampton (CB) method and local interface reduction are proposed, alongside a novel interpolation variable. This strategy enables efficient parametric studies of systems with viscoelastic adhesive joints. A second contribution presents an adaptive reduction algorithm without approximation on viscoelastic material models. This more fundamental development, focusing on viscoelastic structures rather than the substructuring context, is achieved by using two layers of Krylov subspaces for frequency and viscoelasticity. This algorithm can generate more efficient (p)ROMs with the same accuracy level compared to approximation-based methods.

The third contribution is a sampling-free substructuring-based pMOR strategy for systems with bolted joints. This strategy uses two layers of the CB framework in combination with the Krylov subspace to address contact nonlinearity during reduction. The transformation of substructure models into multi-input systems eliminates the need for sampling. This strategy increases the computational efficiency, facilitating efficient evaluations across a wide range of parameters.

To enable the efficient transient dynamic analysis of multi-joint assemblies containing both adhesive and bolted joints, the fourth contribution is an efficient time domain simulation framework by combining the proposed substructuring-based pMOR methods and integrating different solution strategies.

To facilitate efficient model reduction for multi-substructure assemblies with many parameters, the fifth contribution introduces an adaptive multi-level pMOR algorithm. This algorithm is particularly effective for applications like locally resonant metamaterials, which are emerging as novel lightweight NVH solutions and consist of numerous unit cell substructures with possibly independent parameters. The multi-level pMOR shows improved efficiency over other reduction strategies. The adaptive algorithm, powered by a Kriging surrogate, robustly constructs pROMs more efficiently than conventional greedy search methods.