Crashworthiness optimisation of a coach under frontal impact conditions

Accidents involving coaches may endanger the physical integrity of their occupants. The driver, who stands very close to the collision region, is at higher risk. In the event of a frontal impact, there is a violation of the driver's residual operational space, which may endanger the driver's safety depending on the crash's energy. The most decisive factor in achieving a successful design of structural vehicles is to design innovative solutions that safely control the high energy released due to the high accelerations involved during impacts. Long-course coaches lack design techniques and up-to-date technologies to absorb the kinetic energy released in the collision in a controlled way (Lopes et al., 2023a). Thus, to fill this gap in the passive safety of these vehicles, it is necessary to conduct structural optimisation research to improve passive safety in the event of a frontal collision. The main goal of this research is to develop new solutions for passive safety used in coaches. This research represents the culmination of a project aiming to study a coach's structure subjected to a frontal collision. From this project, the references (Lopes et al., 2022a, b, c, 2023a, b, 2024, 2025a, b; Silva et al., 2024) complement this manuscript from the first studies of the current coach to the optimisation of different parameters to have a structure compliant with the regulation.

In this study, the primary focus is on optimising the design of coach structures to enhance their performance in frontal impact conditions. During a frontal collision, the vehicle's front structure absorbs most of the impact energy, causing plastic deformation that intrudes into the driver's area. This phenomenon was verified experimentally and numerically in the Lopes et al. (2022a, 2023a) study. To achieve this, it is intended that the proposed structure, when subjected to impact according to the adaptation of the ECE R29 regulation (ECE-R29, 2010), ensures no contact between the driver and non-resilient parts of the vehicle structure, thereby preserving the survival space. This will be the central premise for having a vehicle that complies with the regulations.

Collision simulations are computationally intensive due to their size and non-linear nature. Consequently, applying gradient-based methods becomes challenging, given the unrealistic computational demands for obtaining gradient information in models with numerous elements. After having a numerically validated model, improving the objective function $f(ρ)$ within a limited number of iterations is facilitated, which is considered satisfactory in this domain. However, these methods do not guarantee perfect solutions (Silva et al., 2024).

A commonly found strategy in the literature involves identifying and optimising weaker regions of a structure through profile reinforcement, increased thickness and incorporating energy-absorbing elements. Firstly, this study intends to optimise the structure by incorporating energy-absorbing components for crashworthiness applications, commonly known as a crash box (still not used in the original model). In the case of frontal impact, deformable yet rigid front structures are crucial for absorbing kinetic energy and minimising the transmission of collision energy to occupants. Thin-walled tubes, particularly, have received attention due to their controlled progressive folding pattern under axial compression (Bhutada and Goel, 2022). To this end, this research follows the work developed by Javier et al. (Silva et al., 2024). By referring to the study by Javier et al., the authors developed an optimised crash box for the vehicle under study through topological optimisation. The crash box study implemented the model without exterior panels, incorporating only the rigid chassis. Thus, the aim is to use this crash box and implement it in the final model to ensure compliance with the regulations.

Automotive accidents are a common occurrence, with the majority of fatalities and severe injuries resulting from frontal collisions, presenting an opportunity to enhance protection in this crash mode (Jermakian et al., 2019). Since the early days of the automotive industry, the paramount objective of crashworthiness has been to minimise deformation in the event of an accident. Advances in science and innovation have allowed the incorporation of progressive crush zones in vehicles to absorb kinetic energy in a controlled and efficient manner through plastic deformation, thus preserving passenger integrity (Du Bois et al., 2004; Ibrahim, 2009). Currently, experimental models and finite element simulations are the two main approaches for impact analysis (Hou et al., 2013).

Vehicle safety can be quantified through contact forces, intrusion, and accelerations during impact (Fang et al., 2005; National Highway Traffic Safety Administration, 1999). These parameters are directly associated with the vehicle's absorbed energy before reaching the passengers. Incorporating finite element software in this domain makes it feasible to conduct collision simulations and assess these parameters. This involves incorporating non-linear models and tools to enhance the crashworthiness parameters iteratively. Noteworthy software in this regard includes Ls-Dyna and PamCrash® (Fang et al., 2005).

As a foundation for analysing vehicle optimisation, there are available criteria for vehicle manufacturers to ensure passenger safety in case of a collision. These are employed to assess the performance of components during impact. Ha and Lu, (2020) compiled criteria for collision resistance, emphasising indicators related to “deformation efficiency”, “structural effectiveness” and “energy-absorbing effectiveness”. These indicators encompass Initial Peak Crushing Force (IPCF), Energy Absorption (EA), Deformation Efficiency (DE), Crushing Efficiency (S_e), Crushing Force Efficiency (CFE), Specific Energy Absorption (SEA) per unit mass, Undulation of Load-Carrying Capacity (ULC) and/or Energy Efficiency (E_e) (Ha and Lu, 2020). Some of these indicators were discussed in the ref (Lopes et al., 2024). In addition, Fang et al. (2017) incorporate injury-based metrics into the criteria for crashworthiness classification. The authors consider factors such as Head Injury Criteria (HIC), chest acceleration, chest deflection and femur load during impacts. This suggests that their approach is specifically oriented towards ensuring the physical well-being of passengers.

Over the years, several researchers have determined that thin-walled structures offer notable advantages over solid components, demonstrating a more remarkable ability to endure substantial loads while achieving the desired deformation. This represents improved energy absorption capabilities within impact engineering (Sun et al., 2014, 2018). Consequently, such structures result in lighter and more cost-effective designs. From a statistical standpoint, a $10%$ reduction in vehicle weight leads to fuel consumption savings ranging from $6−8%$ (Zhang et al., 2006). In the last 20 years, design optimisation has focused on increasing crashworthiness while minimising the structure's weight (Fang et al., 2017). In the 1960s, Alexander (1960) conducted a study to evaluate the behaviour of circular-geometry components in crashworthiness. The author intended to propose a theoretical formulation to predict the mean crushing load. Subsequent researchers later expanded their investigations to include the behaviour of other geometries (Abramowicz and Jones, 1986; Wierzbicki and Abramowicz, 1983). Besides this, a crucial consideration for redistributing impact forces must be redirected away from the vehicle occupants (Bhutada and Goel, 2022). To achieve this, the vehicle body incorporates designed structures, known as energy absorbers or crash boxes, to control the deformation (Bhutada and Goel, 2022). A crash box is a passive safety system placed in the front of the vehicle, estimated to absorb kinetic energy during a frontal collision and maintain the vehicle's deceleration within a safe limit (Dimas et al., 2014; Abdullah et al., 2020).

A crash box is a component that researchers have been working on to enhance its dynamic response when subjected to loading. The study varies depending on factors such as the type of material and structure design (square, conical, polygonal and others). Important parameters include thickness, size, and internal geometry, which may be hybrid and/or multicellular (Abdullah et al., 2020). In this domain, Abdullah et al. (2020) provided a summary for comparing different crash boxes with diverse cross-sectional geometries. The author highlighted the work performed by Samer et al., (2013), who employed magnesium alloy and numerically estimated, using a non-linear algorithm (⁠$mass=275 kg$⁠; $impact speed=15.6m/s$⁠), the absorbed energy and initial peak load considering three different geometries (circular, rectangular and elliptical), with elliptical being identified as the optimal choice. Nasir Hussain et al. (2017) compared square, cylindrical, hexagonal and decagonal geometries when subjected to axial crushing loads for GFRP (glass fibre-reinforced plastics). The simulation was conducted using Ls-Dyna, and the impactor crashed into the crash box at $16 km/h$⁠. The author suggests that the use of triggers improves the energy absorption capability. Tarlochan et al. (2013) employed a model similar to (Samer et al., 2013), adding the behaviour of the crash box subjected to oblique loading equal to $θ=30°$⁠, under the same loading conditions. They considered circular, rectangular, quadrangular, hexagonal, octagonal and elliptical geometries for A36 steel (mild steel). The hexagonal geometry responded best to the request, absorbing 26, kJ and 16 kJ for oblique impact. Alavi Nia and Haddad Hamedani (Alavi Nia and Haddad Hamedani, 2010) conducted a similar study, successfully incorporating experimental models in addition to the numerical model. They used aluminium alloy Al 3003 H12 and considered cylindrical, hexagonal, square, rectangular, triangular, frusta and pyramidal geometries. The maximum absorbed energy per unit mass was for cylindrical tubes. In this field, studies are extensive, with several authors researching to enhance the energy absorption of crash boxes. Noteworthy studies may be found in the most recent studies (Hou et al., 2023; Memane et al., 2023; Jafarzadeh-Aghdam et al., 2023; Kulkarni et al., 2023; Hwang and Han, 2024; Kale et al., 2023; Doodi and Balamurali, 2023; Xiao et al., 2024; Jonsson and Kajberg, 2023). Recently, the focus has shifted towards optimising bumpers, where the author aims to improve performance in collisions. Li et al. (2017) study attempts to optimise this behaviour by filling with foam, thereby increasing the energy absorption capacity of a bumper (Acar et al., 2020).

In earlier times, engineers designed vehicles based on experience, with the process and product optimisation being somewhat limited. In 1996, Mayer et al. (1996) introduced the topological optimisation method in structural crashworthiness problems (Wang and Xie, 2020). The method employs a homogenisation technique, with the formulated problem aiming to minimise internal energy while adhering to mass constraints. The crashworthiness design concept seeks to achieve this goal while simultaneously minimising intrusion into the driver's compartment, which is a conflicting objective noted by Patel et al. (2009). In this regard, topological optimisation techniques emerge as a promising approach to developing optimised geometries that meet intended purposes with reduced weight, as mentioned by Soto (2004). In engineering, this field is highly complex and challenging, currently drawing the attention of many researchers to achieve more efficient methods and algorithms. Therefore, in this context, the ongoing activity related to developing other, more effective topological optimisation algorithms remains a growing innovation (Afrousheh et al., 2019). This technique generally involves the redistribution of material within a specified domain. Currently, topological optimisation is applied to various static and linear-elastic problems, but is somewhat limited in dynamic events where parameters such as accelerations and intrusions are crucial (Forsberg and Nilsson, 2007). This technique will be applied in developing an optimised crash box, and a more thorough study can be observed in ref (Silva et al., 2024).

Optimisation studies on long-distance coaches are limited, especially when subjected to frontal collisions. Although efforts are being directed towards this goal, it remains an area of significant development and potential investment. Tang et al. (2016) investigated a coach-to-car frontal collision. The author found that the vehicles' impact performance could be enhanced through numerical simulations by adding secondary energy-absorbing beams. The works most closely related to this effect were conducted by Güler et al. (2020) and Cerit et al. (2010). Other authors have focused on studying frontal collisions in buses/coaches, considering the baseline structure. They assess whether the structure complies with standards and suggest some improvement proposals based on numerical finite element models.

According to Sun et al. (2011), crashworthiness designs traditionally emphasise deterministic optimisation, treating variables and parameters as specific with no variability in simulation outcomes. However, the present analysis aims to evaluate whether the vehicle complies with the standard when subjected to a frontal collision. In case of non-compliance, the structure is optimised to meet the criteria. Thus, it is possible to outline the procedure to be adopted to assess and optimise the current structure.

The UNECE R-29 regulation was developed for truck cabs and does not account for structural layouts or driver positions in buses, nor does it mandate frontal crash testing for such vehicles under study (Lopes et al., 2023a). Consequently, coach structures lack crumple zones and technologies to absorb collision energy in a controlled manner (Lopes et al., 2023a). Other studies (Güler et al., 2020; Jongpradist et al., 2015; Abramowicz, 2003) emphasise the need for innovative design strategies to improve energy absorption and reduce cabin intrusion, although these studies are quite limited. Research has focused on optimising geometry, identifying weak zones and incorporating attenuators to enhance crashworthiness. These efforts highlight the urgent need for continued development of coach/bus design solutions to increase safety, focusing on the requirement for geometry optimisation and energy absorption strategies in addressing crashworthiness in coach design, in order to mitigate the severity of accidents (Ali et al., 2024). It is therefore imperative to further extend research in this area. Although studies on this topic have increased, study (Lopes et al., 2023a) shows that the current structure does not comply with the regulation, largely confirming the assumptions raised by other authors, despite the limited number of experimental investigations. Consequently, it is essential to build on the tested structures and propose new design solutions to meet regulatory requirements, potentially paving the way for the development of a regulation specifically tailored for these vehicles.

The optimisation process will centre around key parameters, notably introducing a crash box (currently absent in the structure) and considerations for material and geometry. The P-diagram is visually represented in Figure 1, and the process of obtaining a crashworthy structure is referred to in the diagram depicted in Figure 2.

The present work will allow coach manufacturers to reformulate their models and validate passive safety solutions. It is also worth noting that using coaches is expected to be the most complex case, owing to the higher speeds attained. The strategy may later be extended to cover other coach/bus families.

This chapter aims to develop an optimised structure that complies with the ECE R29 regulation and ensures the passive safety of the driver in the event of a frontal collision. It has been previously noted that the vehicle does not comply with the regulation (Lopes et al., 2023a), providing an opportunity for improvement and, ultimately, the design of safer cars in the future. To achieve this, the safety of occupants should be ensured, along with the incorporation of eco-friendly materials, aiming to achieve a balance between a structure capable of excellent crashworthiness metrics and the use of environmentally friendly materials.

Therefore, this chapter addresses the proposed optimised structure to meet the ECE R29 criteria. The proposed modifications result from an iterative process aimed at ensuring compliance with the regulatory requirement of preserving the driver's residual space, with the final configuration comprising the three combined changes, successfully guaranteeing this compliance. The main imposed changes are at the vehicle chassis and the incorporation of DCPD panels, which were estimated to improve the total use of panels in GFRP (glass-fibre-reinforced polymer) (Lopes et al., 2024). Figure 3 details the two additional reinforcements added to the chassis in red. In this location, it was found that plastic joints were weakened by a 90° curvature, which introduced a higher degree of intrusion into the model. Therefore, 2 bars measuring $30×30×3 mm$ and $50×30×3 mm$ were rigidly connected to the primary front cross member of the vehicle (which is also rigidly connected to the vehicle's longitudinal beams).

Another significant introduced change in the model is the replacement of the current S355 steel alloy used in most chassis components with the DP780 steel alloy, whose mechanical characteristics are detailed in Table 1. According to the literature, for instance, the work of Khan et al., (2023), it is stated that DP steels have excellent mechanical properties that allow them to be used in structural parts that ensure vehicle safety, such as bumpers, B-pillars, or side impact beams. DP780 steel has a minimum ultimate tensile strength (UTS) of 780 MPa, which is standard intermediate steel. This change can be observed in Figure 4. Finally, the last modification concerns the study reported in ref (Silva et al., 2024), which enabled the development of an optimised crash box through topological optimisation. Detailed information about this crash box, including its energy absorption capacity, the percentage of total energy absorbed and the evaluation justifying the introduction of a new component into the structure, can be found in ref (Silva et al., 2024). This component is then incorporated into the vehicle, as demonstrated in Figure 5.

Additionally, the mechanical properties of DP780 steel, characterised for different strain rates, were introduced into the FEM model. This may be seen in Figure 6, adapted from Sun et al.'s (2019) study.

In previous studies (Lopes et al., 2023a, 2024), it is possible to observe the mechanical properties of the materials. However, these properties are obtained from quasi-static tests. These properties may not truly reflect the actual characteristics of the materials when subjected to dynamic events, where their response may differ with varying loads. In automobile accidents, specifically in the case of a coach, deformations can occur over a wide range of strain rates, where 100 1/s is usually used to characterise a wide range of automotive crashes (Salisbury et al., 2006). A numerical model that considers the materials' response to different strain rates allows for a more realistic prediction of the vehicle's behaviour in a collision (Shkolnikov, 2004; Mahadevan et al., 2000). Therefore, compared to the previously presented model, this updated model incorporates mechanical properties to account for the influence of strain rate in the computational analysis.

Thus, focusing on the metallic structure, where the body is mainly made up of the S355 steel alloy, being predominant. So, it is crucial to have a reliable mechanical characterisation. The literature notes that this material is commonly used in several fields, such as automotive, aerospace, building construction and offshore structures (Cadoni et al., 2018). This enables accurate material characterisation for a wide range of strain rates. On the other hand, according to Zhou and Liu's study (Zhou et al., 2022), the material properties for both tension and compression for ductile materials are similar. Guo et al. (2020) report that S355 steel has a high degree of ductility, which, in our case, makes tension properties a good approximation.

Thus, Forni et al. (2016) characterised S355 steel for different tensile strain rates, as presented in Figure 7. Therefore, this information was incorporated into the presented numerical model.

On the other hand, the door panel is manufactured by AW 5754 H111. This material is central to numerous studies that evaluate the potential incorporation of aluminium alloys in automotive body structures. Furthermore, it is imperative to ascertain its efficacy when subjected to crash events. Salisbury et al. (2006) conducted quasi-static (QS) tensile tests and high-strain-rate tests using tensile split Hopkinson bars ranging from 500 1/s to 1,500 1/s. The findings suggest that the tested material exhibits minimal sensitivity when exposed to different deformation rates (Salisbury et al., 2006).

Another update involves the materials used for the outer panels regarding previous studies (Lopes et al., 2023a, 2024), which were previously classified based on QS tests. It is important to note that both the mechanical behaviour of GFRP (glass-fibre-reinforced polymer) and DCPD polymer are supplied by tensile tests performed at INEGI's facilities according to ASTM D3039 (ASTM International, 2000) and ASTM D638 (ASTM International, 2010) for QS tests and non-standard tests to access the dynamic mechanical properties, respectively, found on ref (Lopes et al., 2025a). Regarding the numerical simulation, a detailed description of the structure, FE model, software, material behaviour implementation and boundary conditions is provided in more detail and follows the same assumptions as in ref (Lopes et al., 2023a). and ref (Lopes, 2024). which focused on a more technical approach to the simulation procedure.

It is aimed to present the results obtained from the FEM simulation of the optimised model and contrast it with the original model experimentally tested. The visual progression of intrusion during impact is illustrated in Figure 8 within the time interval of $0−0.4s$⁠. It is noticeable that the introduced modification in the model allows for less intrusion of the driver's compartment components. This evolution can be observed through the steering wheel, which experiences less displacement at $x−$ axis.

1. Strain results

This results focus on numerical simulations, while further information on the experimental data, related to the original (non-optimised) model, can be found in detail in ref (Lopes et al., 2023a). Regarding the measured strain of the strain gauges at the experimentally monitored points, their temporal deformation evolution will also be analysed, as represented in Figure 9. The measured points are the same as those presented in Figure 7 of Ref (Lopes et al., 2023a) and detailed in Table 2. The presented strain plots show three distinct curves: the experimental and numerical evolution for the original model and the numerical values for the proposed optimised structure. It is observed that the BTD strain gauge (on the side where the crash box is positioned), LET, LDT, LDF, FEC, FDM and FDI show significant improvement, meaning that for the same impact conditions, there is less deformation at these points.

On the other hand, the BTE, TE and TD show no significant changes; these are points of low deformation where the impact has less influence. Conversely, the FDD, FEI and FDC experience increased deformation. These strain gauges are located near the impact area and have a greater capacity for material deformation, which is positive due to the material's superior ability to resist compared to allow steel S355. Since the weakened intrusion of the components is avoided, the material tends to elongate more in the tensile direction.

1. Comparison of FEM contours: original vs optimised structure

In the experimental test, the DIC technology provided valuable information about the deformation and displacement of the driver's side of the vehicle in the $x−axis$ and $y−axis$⁠. Thus, it is chosen to follow the same guideline and compare the original and optimised models Figures 10 and 11 provide a detailed comparison of the displacements in the $x−axis$ and $y−axis$ of the driver's side, respectively. The $x−axis$ will be the most influential in the intrusion of the driver's volume, so the aim is to minimise it. When the pendulum reaches zero velocity, it is observed that there is a reduction in intrusion from $48.74 mm$ to $25.27mm$ (a decrease of $48.75%$ compared to the original model). On the other hand, the difference is not as significant for the vertical axis, there was a reduction from $11.99 mm$ to $6.76 mm$ in the negative direction of the y-axis, and from $28.32 mm$ to $12.62 mm$ in the positive direction. Furthermore, the deformation in the side panel for both the $x−axis$ and $y−axis$ is schematised in Figures 12 and 13, for the same impact moment. Notably, the optimised structure has less deformation on the side in the x-direction. This fact is confirmed by the colour distribution shifting from the surrounding area of 0.005 deformation to the range from $−0.0005 to 0.0005$⁠. On the other hand, the deformation in the y-axis shows a less significant change, despite the colour distribution possibly indicating otherwise. However, it is essential to note that the optimised structure exhibits less material crushing at the impact point with the pendulum. In contrast, in the original structure, there was significant material crushing, leading to higher deformations and obscuring the contour in the remaining monitored area.

1. Regulation ECE R29 compliance

This section aims to quantify the differences observed between the original and optimised models. By examining Figure 14-a), it is possible to estimate the absorption energy capacity of both structures. The original model absorbs around 47.4 kJ, while the optimised version absorbs 48.8 kJ, indicating an increase of approximately 2.95% in absorbed energy compared to the original. Moreover, the impactor velocity curve in Figure 14-b) reveals a more significant decrease in impactor velocity, highlighting the optimised structure's superior ability to halt the impact in a shorter period.

Additionally, Figure 15 depicts the displacement in the $x−$direction of two monitored points on the primary cross member of the front section, as mentioned in ref (Lopes et al., 2024). Node 97 in the original structure displaces approximately $453 mm$⁠, whereas in the optimised structure, it displaces $356 mm$⁠, representing a reduction of about $21.41%$ compared to the original. Similarly, node 1937 shows a decrease in horizontal displacement from 421 mm to 322 mm, estimating a reduction of approximately 23.52% relative to the original model.

Regarding the displacement on the primary cross member of the front section, Figure 16 provides a graph allowing assessment of the displacement evolution of the entire node line of this component, projected onto the $xOy$ plane, where x denotes the direction of the impactor's movement. This figure shows the intrusion evolution in this member (highlighted by the yellow line, representing the set of nodes) at several steps until reaching the maximum intrusion, which corresponds to the moment when the impact velocity reaches zero. The comparison at the same time step is made between the original structure (black line) and the optimised one (red line). Overall, it can be observed that the red line undergoes less intrusion, demonstrating the improved performance of the optimised structure.

In the first two moments following $t=0s$⁠, a notable similarity is observed, although there is already a small difference, suggesting that the original structure tends to experience greater intrusion. However, as the impactor reaches zero velocity, a pronounced difference becomes evident. Once again, it is apparent that the optimised structure excels in preserving the driver's operational space, greatly enhancing the likelihood of compliance with the ECE R29 regulation.

Through the previous approaches, it is possible to ascertain that the introduced modifications in the structure efficiently reduced the longitudinal displacement of the components, thereby increasing the possibility of safeguarding the driver. However, it will be necessary to proceed with a study of compliance with the adaptation of the ECE R29 standard. It is important to recall that the standard stipulates that, after the test, a dummy should be placed in the driver's intermediate position and should not contact the non-resilient components with a Shore hardness of 50 or higher. To better assess the compliance of the structure with the regulation, an additional study is conducted that will allow us to visualise not only if there is a violation of the volume occupied by the driver after the test (as described in the regulation), but also to visualise if there is a violation during the test, mainly at the moment of maximum intrusion (when the impact reaches null velocity). This study is interesting since when the impactor begins its recoil movement, the structure has an elastic restitution coefficient that allows for the recovery of residual space for the driver.

To achieve this, the CAD model of the dummy used for the test is employed, as shown in Figure 17, and positioned in the active driving posture (intermediate position). The monitored point on the steering wheel is located approximately $113.88 mm$ from the dummy's trunk (⁠$x−$axis) and approximately $54.57 mm$ from the driver's thigh (⁠$y−$axis). This approach aims to estimate the physical integrity of the driver during the test, thus enriching the investigation.

In Figure 18, the measured intrusion of a selected point on the steering wheel, for both the original and optimised structures, is observed. The steering wheel is modelled with solid elements, and the displacement is monitored at the node closest to the dummy's torso, which provides the most representative assessment of wheel movement. It becomes apparent that the modifications implemented in the structure significantly improved the longitudinal movement of the steering wheel. In the original structure, the maximum displacement on the $x−axis$ reaches approximately $143.4 mm$⁠, whereas in the optimised structure, this displacement was reduced to $59.01 mm$⁠, representing a reduction of $58.85%$ compared to the original structure.

In Figure 19, the trajectory of the point on the steering wheel on the $xOy$ plane for both the original and optimised structures is presented. Each curve represents the stage $a,b,c,d,e,$ which links to Figure 20. This linkage allows the identification of the steering wheel position represented by the reference point (which is the graph origin) and the visualisation of its relation to the implemented dummy. In Figure 20, the temporal evolution of the dummy and the steering wheel during the impact can be visualised at the moments indicated in Figure 19.

At first non-detailed analysis, it is possible to observe from the plot that the reference point displacement in the original structure collides with the dummy during the impact. This observation arises since the maximum displacement in the $x−$axis is $143.4 mm$⁠, and the spacing between the steering wheel and the trunk (Figure 17) should be at most $113.88 mm$⁠. Concerning the vertical axis, the point moves $55.84 mm$ in the downward direction, which should not exceed $54.57 mm$⁠. The steering wheel collides with the driver in both directions, being more influential in the $x−axis$⁠, while on the y-axis, it also occurs, but with a minimal margin.

Following the same analogy, for the optimised structure, the maximum horizontal displacement is observed for stage $d$⁠, with $59.01 mm$⁠, quite below the maximum allowable. For the vertical axis, the maximum occurs at moment $c$⁠, approximately $38.64 mm$⁠, which is also below the maximum permissible value. Therefore, it can be asserted that the proposed structure ensures compliance with the ECE R29 regulation and guarantees non-collision of components with the driver during the impact.

Additionally, in order to verify the ECE R29 compliance, the dummy must be positioned in the driver's seat after the test. This procedure is demonstrated in Figure 21, which shows no contact with other components, indicating that the structure complies with the regulation.

This research aimed to assess the structural behaviour of a coach when exposed to a frontal collision. The research is particularly conceived to quantitatively ascertain the inherent consequences of the impact on the vehicle's passive safety and the occupants' physical integrity. This is accomplished by applying the ECE R29 regulation, which UNECE provides.

Through experimental monitoring, such strain gauges, accelerometers and Digital Image Correlation (DIC), the numerical model created with VPS/PamCrash® FEM software was validated. This research builds on previous analyses where the current structures proved inefficient in absorbing kinetic energy during frontal impacts, particularly in meeting the ECE R29 regulation requirements. Following this, an iterative process was conducted to design a structure compliant with the ECE R29 regulation.

Two reinforcements (30 × 30 × 3 mm and 50 × 30 × 3 mm) were added to the vehicle's main front cross member to strengthen weakened plastic joints characterised by a 90-degree curvature. The use of a DP780 steel alloy in the chassis was analysed, and an obtained optimised crash box was incorporated into the structure. These modifications aim to protect the driver by monitoring intrusion and deformation at several points, significantly improving these parameters. To better understand driver safety, the steering wheel was monitored to ensure it did not collide with the driver during the crash test, even though the regulation does not require this. Indeed, the proposed structure can ensure compliance with the ECE R29 and prevent collision with the driver during the test. Therefore, this study opens avenues for research in developing new structures to be used in the automotive industry, capable of providing greater safety to occupants in the event of a frontal impact.

Adapting the ECE R29 regulation proved successful in terms of intrusion evaluation. However, this test indicates that the simplification of the vehicle makes the system stiffer, thus amplifying the felt accelerations by the driver. In a future approach, it will be important not to suppress the pneumatic and suspension systems to guarantee the test's realism. Additionally, the regulation indicates that the dummy should be placed in the driver's seat after the test. This factor can lead to decisions that mask the vehicle's efficiency in protecting the driver, as during the test, there is a violation of the driver's residual space. In a future revision of the regulation, it would be essential to monitor the space during the test, especially when the impactor reaches null velocity (when intrusion is maximum) and to incorporate limit accelerations that must be ensured. Regardless of the intrusion obtained, the accelerations felt can significantly affect the integrity of the occupants. Thus, ensuring the maximum permissible value is adhered to is extremely important.

Rogério F. F. Lopes wrote the manuscript, performed the numerical analysis and treated the data. M. P.L. Parente and Pedro M. G. P. Moreira supervised. All authors reviewed the manuscript.

The findings within this manuscript are detailed in the methodology section, and the investigation into coach crashworthiness is outlined in the numerical analysis section. These results are reproducible through the implementation of the optimised structure model and simulated process as described in this article. More information may be found in detail in the Ref (Lopes et al., 2023a). The data generated from the results are available upon request.

Since no human subjects are involved in this article, ethical approval is not required.