## 1 Introduction  
The past two decades have witnessed a surge in technological progress, fueled by the rise of numerical methods as a key driver of innovation across diverse engineering disciplines, particularly mechanical engineering. This progress has been further supplied by the impressive growth in computational power witnessed since the late 20 th century. The development of increasingly rapid, efficient, adaptable, and user-friendly computational tools has led to the widespread adoption of complex numerical methods in engineering simulations [1]. Notably, their application in various computational mechanics techniques has revolutionised the entire mechanical construction industry, allowing for the design of optimised components based on the constraints imposed by the manufacturer, enabling accurate predictions of how these components will behave under real-world operating conditions. In the automotive industry, for instance, structural optimisation of various parts plays a crucial role in the performance and behaviour of a vehicle during driving. This approach has led to successful results by considerably reducing the component's weight and, at the same time, maintaining the necessary strength to ensure that components meet all their mechanical requirements [2]. In the automotive manufacturing sector, reducing weight across various components offers a pathway for manufacturers to improve profitability. Lighter vehicles often require less material, leading to a direct decrease in production costs [3]. By integrating weight reduction strategies, in addition to frequent optimisation processes during the parts design phase, manufacturers can achieve substantial financial benefits through these combined effects. Beyond the significant financial incentive, even modest weight reductions throughout the vehicle can significantly improve overall vehicle performance. Growing public demand and stricter regulations within the automotive industry are driving the need to develop lighter, safer, and more production-efficient components across all vehicle functionality areas [4]. For some components, weight reduction also contributes to enhanced comfort. To meet these evolving requirements, the application of structural optimisation methods in the automotive field has surged in recent years, keeping pace with advancements and refinements in computational techniques. The rise of electrification and increased programming intelligence in automotive electronics has led to a trend of increasing overall mass in passenger cars [5]. This trend further emphasises the need for weight reduction and, consequently, a decrease in inertia. Reducing weight offers a multitude of benefits for the vehicle itself [4], including the following:  
* Reduced fuel/energy consumption (particularly crucial for electric vehicles with inherent weight and range limitations);
* Lower emissions of greenhouse gases and air pollutants;
* Decreased wear and tear on public roads and various vehicle components, such as tyres, brakes, suspension, engines, and transmissions;
* Improved acceleration, deceleration, and overall drivability;
* Enhanced safety for pedestrians, drivers, and passengers. Computer-aided structural assessment techniques equip engineers with powerful tools to analyse the behaviour of components and systems under various loading and stress conditions. These techniques complement the overall optimisation process for the studied structure. Through computer simulations, engineers can predict stresses, strains, and displacements, allowing for the identification of critical failure points and efficient design optimisation. The Finite Element Method (FEM) has historically been the dominant discretisation technique in research, development, and education within computational mechanics [6]. However, new techniques have emerged to address limitations of FEM, such as its lack of precision for high deformation analysis. These techniques aim to improve the accuracy and efficiency of numerical simulations.