## 1 Introduction
### Motivation and Literature Overview
[PERSON] (2017) analysed the stability of one- and two-way sinusoidally corrugated steel sections, illustrating their superior structural performance compared to conventional designs [8]. In addition to their use in welded plate girders, bidirectionally sinusoidal corrugated steel plates are employed in steel sandwich panels. These panels consist of two thin steel face sheets bonded to a lightweight core. This core, often made from corrugated steel, enhances the panel's load-bearing capacity and overall stiffness while maintaining a low weight. [PERSON] et al. (2018) performed a stability analysis of bidirectionally corrugated steel plates with an orthotropic plate model, highlighting the improved performance of these panels under various loading conditions [9]. [PERSON] et al. (2023) discussed the strength design of deeply buried circular corrugated steel arches, illustrating the broader applications of corrugated steel in various structural scenarios [10]. [PERSON] et al. (2022) analysed the buckling of corrugated-core sandwich plates using advanced computational methods, emphasising the importance of accurate modelling for their structural performance [11]. [PERSON] et al. (2024) explored the mechanical performance of bio-inspired bidirectional corrugated sandwich pressure shells under external hydrostatic pressure, highlighting their potential in challenging environments [12]. [PERSON] and [PERSON] (2019) examined the thermomechanical performance of bio-inspired corrugated-core sandwich structures for thermal protection systems, which is relevant to the optimisation of their structural performance under high thermal conditions [13]. [PERSON] et al. (2022) assessed the three-point bending performances of sandwich panels with various core types, demonstrating the structural benefits of different corrugation patterns [14]. [PERSON] et al. (2020) investigated the use of ultra-high-strength steel sandwich panels for lightweight applications, underscoring the role of advanced materials in reducing weight while maintaining performance [15]. [PERSON] et al. (2017) performed a crashworthiness investigation of bidirectionally corrugated-core sandwich panels under quasi-static crushing loads, revealing their enhanced energy absorption capabilities ([PERSON] et al. (2019)). [PERSON] et al. (2019) evaluated the out-of-plane compressive performance and energy absorption of multi-layer graded sinusoidal corrugated sandwich panels, providing insights into their structural benefits under compressive forces ([PERSON] et al. (2020)). [PERSON] et al. (2020) analysed the crashworthiness of multi-layered bidirectionally corrugated steel plate structures, demonstrating their resilience and impact resistance in various loading conditions ([PERSON] et al. (2020)). Furthermore, [PERSON] and [PERSON] (2021) discussed the design and fabrication of metallic thermal protection systems for spaceplane vehicles, highlighting the role of advanced materials in specialised engineering applications ([PERSON] et al. (2020)). These corrugated elements are also utilised in other industries, such as automotive and aerospace, where lightweight and high-strength materials are crucial. The ongoing research into bidirectionally sinusoidal corrugated steel plates aims to optimise these properties, ensuring that steel panels and other applications continue to meet the evolving demands of modern engineering practices.