The increasing demand for renewable energy sources presents challenges to the offshore wind industry. As wind turbine generators grow in size, their foundations must scale accordingly. The growing monopile weights are posing risks to existing jack-up vessels that install these components. The increasing weight of monopiles results in larger deck loads, which requires engineers to assess the structural integrity of these vessels using the finite element method. However, due to the substantial size of these vessels, finite element models require significant computational resources. Therefore, efficient methods are needed to reduce model size and complexity.

While the literature does not specifically address finite element techniques for jack-up vessels, similar challenges have been extensively studied in the field of aerospace engineering. Such finite element techniques include, surrogate models, adaptive mesh refinement, submodelling, substructuring and model order reduction. The application of these techniques is mainly due to the significant size of the structures they are used to deal with, resulting in a reduction of computational time. A combination of substructuring and model order reduction results in a superelement. Its potential in this engineering discipline is the main reason for its selection in this research.

To understand the behaviour of superelements and their impact on computational time and accuracy, an exploratory study was conducted, comparing the results to a reference model without superelements. Parameters that potentially influence the performance and outcome of the results are studied. These parameters include model complexity (1D versus 2D finite elements), the number of superelements applied to the model, the mesh size of the superelement, the number of modes incorporated in the superelements solution, and the connection type. Based on the outcome of the exploratory study, the parameters are reevaluated and used to validate the applicability to an existing model of a jack-up vessel via a case study.

The case study utilises the outcomes of the exploratory study to a real-world model of a jack-up vessel. Several locations at the structural elements of a jack-up vessel are compared while reducing the size of the model's stiffness matrix with five variations. The first serves as the reference model with no superelements. The second introduces superelements for the legs, the third adds the stern, the fourth incorporates the bow, and the fifth further includes detailed deck geometry to the superelement of the stern already made in the third iteration. As a result, the stiffness matrix decreases up to 42%, reducing the computational time by 47% in the fifth variation. However, the fifth variation shows inaccuracies in total deformation and underestimates the von Mises stress by up to 15%. In contrast, the fourth variation demonstrated a more reliable balance between efficiency and accuracy, with a 21% reduction in the size of the stiffness matrix, a 23% improvement in computational time per single run, and deformation and stress deviations of 3% and 10%, respectively.

A more representative measure for evaluating computational efficiency is the scenario in which an engineer is required to solve a model 50 times due to changes in its geometry. In this case, the superelements computational time is included, but it should be noted that this is only required for the initial run. The cumulative computational time for variation four demonstrates that the application of superelements becomes more efficient than the conventional approach from the sixth run onwards. This results in a 26% increase in efficiency over 50 runs.

This study shows that superelements can effectively reduce model size and computational effort when assessing jack-up vessels' structural integrity. While accuracy deviations must be evaluated carefully, this research presents that superelements can substantially increase the efficiency with minimal loss in accuracy. This suggests that superelements are a promising method to apply for structural integrity analysis on large structures such as jack-up vessels.