Chapter 1 Introduction and Research Context
1.1 Background and Research Significance
As a researcher deeply engaged in the field of vehicle passive safety, I have witnessed significant transformations in automotive technology and safety assessment over the past decade. In China the rapid growth of the automotive industry has been accompanied by substantial increase in vehicle ownership. By the end of 2024, the total number of motor vehicles in China has reached 453 million. Among them, new energy vehicles have demonstrated a remarkable growth in adoption reaching 31.4 million units, which accounts for 8.90% of total vehicle population. Within the new energy vehicle sector, pure battery electric vehicles dominate with 22.09 million units representing 70.34% of all new energy vehicles. In 2024 alone the new registration volume of new energy vehicles reached 11.25 million, registering a year-on-year increase of 51.49%. This growth in vehicle population inevitably raises critical concerns about road traffic safety.
Recent national statistics from traffic accident data over 2018–2023 show that China has consistently recorded between 245,000 and 255,000 road traffic accidents annually. These incidents result in approximately 60,000 fatalities and 260,000 injuries per year with direct property losses reaching 1.3 billion CNY. Vehicle frontal collisions constitute the most common accident pattern accounting for more than 50% of all collision scenarios. Within frontal collision accidents, moderate overlap collisions represent the largest proportion. This distribution has led to the development of safety standards and test protocols that specifically target these crash scenarios.
The advancement of active safety technologies has contributed to far fewer accidents, but limitations remain. Historical analysis has demonstrated that even with advanced active safety systems, only around 5% of potential accidents can be prevented. This technological constraint highlights the critical importance of passive safety systems in occupant protection. Therefore my research interest has been consistently directed toward improving vehicle structural performance in crash scenarios.
In comparison with conventional internal combustion engine vehicles, the electric car poses several additional safety-related challenges. The battery pack that is situated in the floor area introduces high-voltage electrical system hazards, potential thermal runaway risks, and additional structural masses. These factors must be attentively considered in all structural design and crash safety assessments. The introduction of the 50% overlap moving progressive deformable barrier test protocol by the China New Car Assessment Programme has elevated the standards for both self-protection and partner-protection performance in vehicle crash testing. This study seeks a deeper understanding of the crashworthiness and crash compatibility of electric cars under the MPDB condition using finite element simulation and multi-objective optimization tools.
1.2 Research Trends in Vehicle Crash Simulation
Crash simulation research in the international community has progressed from actual vehicle testing toward high-fidelity computational approaches. Automakers in Europe and the United States began vehicle crash experimental studies in the late 1960s. With the advancement of the finite element analysis theory during the 1980s, computer simulation progressively became an efficient complement to the physical crash testing. Numerous engineering studies have confirmed that finite element analysis methodology can accurately represent realistic crash responses when calibrated properly.
In the international domain, researchers have made substantial contributions in this field. Ford engineers applied LS-DYNA for frontal crash simulation and systematically compared numerical results with real vehicle tests, establishing the credibility of computational methods for vehicle crashworthiness evaluation. European researchers have explored various aspects of Moving Progressive Deformable Barrier testing protocols, evaluating consistency across different accredited laboratories regarding measurements of barrier deformation standard deviation, occupant load criterion, and intrusion depth indicators. Their findings underscored the possibility that future regulatory actions would demand improved structural performance objectives for chest and lower limb protection. Other parametric studies investigated structural interaction behavior of large vehicles, examining whether mass and stiffness variations affect the safety of smaller vehicle occupants. The results indicated that mass and stiffness variations hold considerable influence over frequency measures.
Reliability-based optimization studies have also been introduced in electric car side-structure design. Through integrating finite element simulation with optimal Latin hypercube experimental design, researchers have established systematic reliability optimization frameworks using response surface approximation modeling. These methods are demonstrated to be capable of producing designs satisfying crash safety requirements when uncertainty factors are considered. Research dedicated to the crash behavior and structural performance of vehicle sub-structures showed that square cross-sectional shapes possess better specific energy absorption capacity than rectangular shapes. Specific energy absorption and peak load improvements in the order of 16% and 15% respectively have been achieved through optimal cross-sectional geometric selection.
Domestic Chinese research on crash safety has shown marked progress since the late 1980s. Following the foundation of the safety technical committee in 1985, the initial high-speed vehicle crash laboratory at Tsinghua University was established. Research achievements in the domestic sphere have covered full-vehicle simulation and structural optimization for different crash modes. Chinese scholars investigated electric vehicle models having special attention to battery protection in bottom impact scenarios. Novel step-featured underbody scrape barrier conditions were proposed based on real accident data, combining simulation and experiments for validation of these test protocols.
Several compatibility-focused investigations applying the MPDB procedure have been reported. Studies on mini electric shuttle vehicles examined the influence of bumper stiffness, front longitudinal beam stiffness and ride height on compatibility behavior. The results concluded that increased bumper stiffness, lower front rail stiffness and greater ride height can simultaneously improve compatibility and crashworthiness. Additional work addressed evaluation conditions for electric vehicles, involving analysis and optimization of energy-absorption capability correlated with optimal acceleration waveforms in the whole-body frontal crash. Lower occupant chest acceleration and total safety improvement were reported by matching actual body collision waves to target optimal configurations. In compatibility research for MPDB conditions, various strategies such as reduced curb weight, increased collision contact area, improved stiffness distribution, and added energy transfer paths have been explored for controlling the energy interaction between vehicles. Evaluations showed that adding energy transfer paths had the highest beneficial influence on compatibility.
1.3 Regulatory Framework for Electric Car Collision Safety
China’s vehicle safety regulatory framework operates through various national, industrial, and enterprise-level standards. After the approval of the National Technical Committee for Automobile Standardization in 1988 and following involvement in WP29 in 1996, mandatory standards in China gradually converged with international practices. Among these national standards, those enforced as compulsory norms specifically address the aspects of automobile safety including occupant protection in frontal collisions, side crashes, and high-voltage electrical system integrity for electric cars.
C-NCAP, established as the authoritative consumer information rating system, evolved through various editions. The 2021 edition introduced a major regulatory reform that replaced the conventional Offset Deformable Barrier test with the MPDB test protocol, effective from January 2022. The 2024 version continues this trend with further refinements. The MPDB procedure simulates a vehicle-to-vehicle collision scenario close to reality. In this procedure, test vehicle and barrier vehicle approach each other at velocities of 50 km/h each resulting in approximately 100 km/h relative impact speed, where the overlap area between them is 50% of the vehicle width. A trolley of 1,400 kg with an aluminum honeycomb barrier attached on the front surface acts as the opponent vehicle.
The MPDB test condition presents greater technical demands compared to the ODB condition. The stiffness of the MPDB barrier element exceeds that of the older ODB specification, thus the required occupant restraint time duration is shorter. Additionally, since the evaluation system uses the deformation of the deformable barrier face, the test incorporates partner protection into the evaluation protocol. Different vehicle types produce different frontal force distributions affecting the opposing vehicle during collisions, especially when large mass differences are present.
Important differences must be emphasized between self-protection and partner-protection. Traditional vehicle safety design would tend toward higher structural stiffness for improvement in self-protection capabilities. However, in MPDB evaluation, excessive vehicle stiffness and mass generate high structural load to the partner vehicle, making the test vehicle more aggressive in terms of compatibility. For future safe vehicle design, appropriate body strength balancing between self and partner protection should be sought.
1.4 Vehicle Crash Research Methodologies
Vehicle crash research depends strongly on actual crash testing methods to provide realistic overall vehicle behavior. Experimental crash tests allow observation of structural deformation, safety system effectiveness, and occupant injury parameters in a very direct way. However, actual vehicle crash tests are extremely costly, time consuming and require tedious sample preparation. They cannot easily provide vehicle responses over wide parametric ranges because of resource requirements.
Numerical simulation strategies have become central in crashworthiness research. Among many numerical approaches, the finite element analysis method holds a fundamental position. Finite element modeling of vehicle crashes subdivides full vehicle structures into many finite element types and solves the nonlinear transient dynamic equations. This method offers practical advantages for investigating crash events because detailed data can be obtained at any location and time from the digital model, highly repeatable test conditions can be produced, and parametric changes can be efficiently evaluated. Modern CAE methodology allows automotive engineers to reduce actual physical crash test runs by about 60%–70% in typical development cycles.
1.5 Main Contents and Scope of This Thesis
The primary objective of this thesis is to investigate the crash characteristics and compatibility of a production pure-electric car under the MPDB test protocol as mandated by C-NCAP 2024. In this thesis I have conducted simulation analysis and structural optimization work encompassing several research components:
First, theoretical background associated with dynamic nonlinear finite element formulations is presented. This includes fundamental kinematic relations, Lagrange formulations and contact-impact solution algorithms related to transient dynamic structural analysis.
Second, the complete finite element model is constructed. This process ensures geometry clean-up, high quality mesh generation, material definition, component connection modeling, contact definitions and load specifications consistent with MPDB protocol conditions.
Third, simulation results are analyzed with respect to general deformation history, energy transformations, acceleration response, crush behavior of front-end energy-absorbing parts, occupant compartment deformations, door/Rocker/A-pillar intrusion amounts and high-voltage electrical system safety concerns.
Fourth, vehicle-to-vehicle compatibility is assessed following C-NCAP procedures through barrier test zone deformation standard deviation, occupant load criterion, intrusion depth and intrusion height criteria.
Fifth, structural modification for the front longitudinal rail by introducing aluminum foam material is developed. The compression behavior of aluminum foam and the crash behavior of foam-filled longitudinal beams are validated based on finite element simulation predictions.
Sixth, multi-objective optimization involving six thickness design variables and three performance objective functions is performed using the Kriging-based approximate modeling methodology combined with Non-dominated Sorting Genetic Algorithm II.
Finally, the optimized vehicle design is verified through full-vehicle finite element simulation, showing improved performance in terms of B-pillar acceleration, OLC value, SD value, occupant compartment intrusion parameters and compatibility evaluation results.
Chapter 2 Theoretical Foundations of Vehicle Crash Simulation
The vehicle collision event is characterized by the transient large displacement and strain response of elastic-plastic thin-walled structural members. Under severe collision loading conditions, nonlinear effects arise from geometric changes, material inelastic behavior, boundary contact variations, and strain-rate sensitivity. The mathematical description of the vehicle crash process thus relies on nonlinear continuum mechanics and nonlinear finite element methodology.
2.1 Finite Element Formulations for Crash Analysis
2.1.1 Kinematics of Deformable Bodies
From the continuum mechanics point of view, the deformable body can be described in terms of a reference configuration and a current configuration. In Figure 1, I consider a material point, initially at position X in the reference configuration at time t=0, evolves at a later time t to a new position x. This motion is represented mathematically by the deformation mapping:
$$x_i = x_i(X_{\alpha}, t) \quad (i=1,2,3)$$
where Xα denotes the reference coordinates of a material particle and xi denotes the coordinate of the same material particle at time t. Initial conditions of position and velocity satisfy:
$$x_i(X_{\alpha},0) = X_{\alpha}$$
$$x_i(X_{\alpha},0) = v_i(X_{\alpha})$$
in which vi is the initial velocity of the particle.
For large deformation simulations typical of crash scenarios, the updated Lagrangian description technique has been widely implemented in computational tools. In this formulation, all static and kinematic variables are referred to the configuration at time t while the equilibrium of the body is expressed at time t + Δt.
2.1.2 Fundamental Conservation Equations
The conservation principles of mass, momentum and energy govern the deformation in a continuous medium. The mass conservation in the Lagrangian description is expressed as follows:
$$\rho \gamma = \rho_0$$
Here, ρ is current density, 0ρ is initial density and γ is the relative volume. For the energy equation, I employ the following expression:
$$\dot{E} = V S_{ij} \dot{\varepsilon}_{ij} – (p+q)\dot{V}$$
In this equation E is the internal energy, V is volume, p is hydrostatic pressure, q is bulk viscosity, ε̇ij is strain rate tensor and Sij is deviatoric stress tensor defined as:
$$S_{ij} = \sigma_{ij} + (p+q)\delta_{ij}$$
$$p = -\frac{1}{3}\sigma_{ij}\delta_{ij}$$
Here σij is the Cauchy stress tensor. Momentum equilibrium in the current configuration is written as:
$$\frac{\partial \sigma_{ij}}{\partial x_j} + \rho f_i = \rho \ddot{x}_i$$
where fi denotes the body force per unit mass. These equations form the foundation for the discretization scheme in nonlinear finite element analysis.
2.1.3 Boundary Conditions
Three types of boundary conditions describe the constraints and loading of the deformable body. The traction boundary condition on surface S1 is given by:
$$\sigma_{ij} n_j = t_i(t)$$
where nj is the outward normal component and ti(t) denotes the surface traction vector. The displacement boundary condition on surface S2 imposes constraints on the motion:
$$x_i(X_j,t) = G_i(t)$$
where Gi(t) is a prescribed displacement function. On the internal contact-discontinuity boundary S0 between two bodies in contact, the jump condition is written as:
$$\left(\sigma_{ij}^+ – \sigma_{ij}^-\right)n_j = 0$$
These conditions couple the local contact behavior of separate structural members.
2.2 Key Numerical Issues in Crash Simulation
2.2.1 Explicit Time Integration Scheme
The dynamic equilibrium equations obtained from the finite element spatial discretization form a system of ordinary differential equations in the temporal domain. The commercial explicit finite element solver LS-DYNA utilizes the central-difference time integration technique, solving the acceleration at each step using the mass matrix and internal/external force vector as follows:
$$\boldsymbol{a}_t = \boldsymbol{M}^{-1} \left[ \boldsymbol{F}_t^{ext} – \boldsymbol{F}_t^{int} \right]$$
in which at is the nodal acceleration vector at time t, M is the mass matrix, and Ftext and Ftint are external and internal force vectors. The internal force vector has the form:
$$\boldsymbol{F}_t^{int} = \sum_n \int_{\Omega} \boldsymbol{B}^T \boldsymbol{\sigma} \, d\Omega + \boldsymbol{F}_{contact} + \boldsymbol{F}_{hourglass}$$
where B is the strain-displacement matrix, σ is the stress vector, Fcontact are contact forces and Fhourglass includes hourglass control forces. With acceleration known, nodal velocity and displacement updates follow.
$$\boldsymbol{v}_{t+\Delta t/2} = \boldsymbol{v}_{t-\Delta t/2} + \boldsymbol{a}_t \Delta t_t$$
$$\boldsymbol{u}_{t+\Delta t} = \boldsymbol{u}_{t} + \boldsymbol{v}_{t+\Delta t/2} \Delta t$$
The explicit integration scheme is conditionally stable, requiring that the integration time step cannot exceed the critical time step determined by the highest natural frequency of the discretized model.
2.2.2 Time Step Control
Time step size control is essential for the stability of explicit integration. The critical time step for the shell and beam element types is determined by the element characteristic length and material acoustic wave speed as:
$$\Delta t_c = \frac{L}{c}$$
where c is the sound speed of the material, expressed as:
$$c = \sqrt{\frac{E}{\rho(1-\mu^2)}}$$
For quadrilateral shell elements the characteristic length is determined by the ratio of element area to the maximum diagonal:
$$L = \frac{A}{\max(L_1, L_2, L_3, L_4)}$$
The global time step is then scaled by a time step factor, typically taken as 0.9 in explicit crash analyses, to avoid numerical instability.
2.2.3 Contact Algorithm
Numerous metallic structural parts interact and undergo relative sliding as well as separation during a vehicle crash event. Therefore, robust contact algorithms are needed to enforce no-penetration conditions between independent surfaces and between different regions of the same deformable body. The contact algorithms implemented in LS-DYNA include the penalty method, dynamic constraint method, and distributed parameter method. Among these methods, the penalty method is the default contact handling technique in LS-DYNA. It checks for penetration of a slave node into a master surface segment at each integration step. Once the penetration is detected, an interface spring force that is proportional to the penetration depth and stiffness is introduced to push the slave node back toward the master surface. The proportionality is ensured through a penalty parameter that is related to the material stiffness of the contacting entities. This formulation is computationally efficient and preserves momentum well in the contact interaction.
2.2.4 Hourglass Control
One-point quadrature elements are widely used in large-scale crash simulation for reduced computational cost. However, this scheme introduces potential spurious zero-energy deformation modes, commonly known as hourglass modes. The hourglass modes cause non-physical oscillatory deformation patterns which can lower structural stiffness of the model and distort energy balance. They originate because the reduced integration element stiffness matrix has insufficient rank, lacking stiffness related to certain deformation shapes. Energy-based controls are required to resist these deformation modes. For this analysis, hourlyglass controlling coefficients have been chosen so that hourglass energy remains under 5% of total internal energy. The common hourglass control scheme applied here is the stiffness-type control method, where artificial stiffness contributions are included into the element formulation to suppress zero-energy modes. Careful control has been maintained across all components.
Chapter 3 Development of the Vehicle and Barrier Finite Element Models
The fidelity of the simulation results depends mainly on the correctness of the finite element approximations of geometry, component property, boundary condition and loading application. I now describe the detailed model-building procedure conducted on the HyperMesh preprocessing platform and solved by the LS-DYNA explicit solver.
3.1 General Modeling Procedure
The geometry source for this model originates from a CAD model of an electric car. After geometry clean-up operations, the mid-surface mesh is generated for thin shell structures that form most body sheet metal parts. Whereas for massive components such as suspension sub-frames, solid meshes are used. The established modeling workflow includes the following steps:
(1) Importing the original geometry into HyperMesh;
(2) Geometry repair and mid-surface extraction;
(3) Mesh generation with quality control;
(4) Material property assignment;
(5) Connection definition for various joining types;
(6) Contact interfaces specification;
(7) Boundary condition and load specification;
(8) Export of the model deck from HyperMesh in Keyword format;
(9) Execution of LS-DYNA simulation and result processing.
3.2 Geometry Preparation and Meshing of the Vehicle FE Model
In the pre-processing stage, several simplifications have been applied to accelerate computation within the scope of frontal crash simulations. The components attached within the engine compartment that do not have major influence on structural energy absorption are simplified or eliminated. Parts that are critical for frontal crash behavior, such as front rails, bumper beams, crash boxes and body structure, are retained in detail.
Selection of element size and type has direct implications for computation time and accuracy. In this analysis I used 10-mm shell elements, adaptive to the local size for curved areas where the mesh must follow geometric details. A fine mesh pattern in critical crush zones plays the key role in accurate simulation. Figure 3.2 shows the full-vehicle finite element mesh, consisting of about 2.7 million nodes and elements. Mesh quality parameters considered for this task included aspect ratio, warpage, skewness, jacobian and minimum length, all constrained within acceptable limits.
According to the C-NCAP evaluation protocol, 50% overlap arrangement plus bounding constraints demands exact positioning of the test car and barrier trolley with respect to each other. The barrier car model has a total mass of 1400 kg and velocity of 50 km/h; the electric car also velocity equals 50 km/h.
3.3 Barrier Model Establishment
The MPDB barrier consists of a trolley frame model with wheel assemblies and the front-mounted progressive deformable element. The barrier trolley model used here incorporates front-end crash structure with aluminum honeycomb blocks. As illustrated in the relevant figures, the honeycomb block is constructed as three horizontal layers, each having a height of 570 mm. These layers are separated by aluminum sheets and mounted on the rear plate attached to the trolley.
The first 250 mm of the honeycomb barrier in the longitudinal direction has uniform crushing strength. The next 450 mm long portion has linearly increasing crushing strength. A shorter supporting portion occupying 90 mm is bolted to a stiff aluminum plate on the trolley. This structural grading is intended to reproduce a representative opposing vehicle front-end compliance behavior.
The frame and ground floor components of the trolley are modeled as rigid bodies using material type 20 to minimize the total computational expense.
After the vehicle moves into full contact with the barrier face, the vehicle front end is positioned in such a way that the horizontal overlap is configured to satisfy the condition of 50% ± 25 mm relative to vehicle width.
3.4 Model Parameter Definition
3.4.1 Material Model and Property Cards
Reliability of crash simulation needs accurate material laws for metals. In the frontal crash model, shell components that undergo substantial elastic-plastic deformation are represented by the Material Type 24 (*MAT_PIECEWISE_LINEAR_PLASTICITY) formulation. This material law offers the combination of cost effective computational operation and correct deformation behavior for most vehicle steels under crash loading. Inputs define the elastic modulus, yield stress, tangent modulus, plastic strain to failure and optional strain-rate dependent flow table. Moreover, due to a desired scaling of yield stress, a Cowper-Symonds strain-rate relation is included. A rigid material model was specified for those parts that typically do not suffer significant deformation (e.g., engine block models, flywheels). Spot-weld models use the *MAT_100 parameterization formulated for simplified failure representation based on force-based failure criteria. The aluminum foam filler and compressive cellular material behavior are represented by a material model that suits crushable foam behavior with the stress plateau in compression. Material model and unit abbreviation using millimeter, kilogram, millisecond relationships guarantee coherent system of units.
3.4.2 Connections
Accurate joint characteristics determine overall load transmission in the vehicle frame under impact. For weld representation, my model uses *CONSTRAINED_SPOTWELD type elements connecting respective node groups at the weld locations with failure criteria. Seam weld connections are modeled by a set of rigid beam elements that tie adjacent node sets with relative degree-of-freedom coupling. Bolt locations are simulated by using *CONSTRAINED_RIGID_BODY set definitions; this modeling method is acceptable since the bolt itself is considered not to fail or deform during the simulation. Adhesive joints at windscreen glazing and roof panels are simulated using solid elements representing the glue layer that connect two parts. Finally, hinge definitions are used to connect movable members that operate in rotation.
3.4.3 Contact Parameters
The interaction between components of the car during deformation modeling is built with self-contact definitions. A general single-surface contact algorithm that uses penalty formulation is defined for the vehicle. Setting one self-contact type across the car parts works robustly in most large-deformation crash analysis, although some detailed component contacts are modelled separately. An automatic surface-to-surface contact is defined for all structural surfaces that undergo compressive loading.
Contact between spot-weld elements and the parts they connect is also defined to permit failure, using node-to-surface contact at these connections. In contact definitions, the static coefficient of friction is set around 0.2. The model includes contact formulations avoiding the initial penetration of various parts located in the crush zone. Barrier-to-vehicle contact uses symmetric penalty surface-to-surface contact with static/dynamic coefficients of friction as stated in the C-NCAP protocol.
3.4.4 Ballasting and Vehicle Mass
The target mass of the simulated electric car is 1.99 t. The complete FE mesh normally does not include the accurate total mass since some vehicle systems such as seats and auxiliary systems are not modeled in full detail. Mass distribution errors are corrected by the introduction of concentrated mass elements. The concentrated masses are added to the vehicle model at the appropriate positions to adjust the total mass and center-of-gravity position. This ballasting procedure incorporates both rigid and deformable body connections. Weight distribution was arranged such that the CG position and total mass correspond to the test vehicle weight specifications. The boundary conditions are listed in the model file as follows: initial velocity for the electric car equals 13,890 mm/s along X axis (+X direction); similarly, the trolley has initial velocity of -13,890 mm/s. Gravity of 9,800 mm/s² is specified.
3.5 Control Cards and Output Variables
Appropriate simulation control parameters must be set. The total simulation time is set to 120 ms according to rebound phenomenon observation in previously recorded tests. The time-step control method with a scale factor of 0.9 is used. In addition the hourglass coefficient is specified at 0.1 in stiffness form for crash analysis. To generate time-history data for vehicle accelerations, an *OUTPUT request is specified for the B-pillar accelerometer location.
The finite element model of the full vehicle and barrier contains 2,702,773 nodes and several different element types. The crash simulation runs on LS-DYNA with 20 CPU cores in processing configuration. Approximately 12–18 hours of wall-clock time are needed to analyze a single simulation.
Chapter 4 Simulation Results and Safety Assessment
4.1 Model Reliability Check
Before extracting collision results, I inspected the model output for physical plausibility. First the energy balance of the system is considered. The total energy should essentially be constant in accordance with conservation of energy for the mechanical system if no errors take place. The internal energy evolution and the kinetic energy decrease mirror each other, while total energy remains at almost fixed value in the energy-time plot. The hourglass energy must be examined as a numerical check: if hourglass energy exceeds too large fraction of total energy, the model behavior is not reliable. The hourglass energy reached about 1.38% of the total at the end of the simulation, which satisfies the 5% rule [52].
The mass increase due to the numerical mass-scaling algorithm must be low so as not to influence dynamic behavior. At time 0.12 s mass increase was 2.98%, below the 5% limit, indicating good mass control in the model. These checks evidence that the result quality can describe actual physical phenomena.
4.2 Full Vehicle Acceleration Response
The acceleration time-history is obtained at the base of the B-pillar on the struck side, which is a point of high stiffness and low local deformation. Both acceleration peaks and integrated velocity history indicate the severity of the body shell deceleration. In this simulation, the maximum acceleration of B-pillar (X direction) is around 34.11 g. This magnitude is below the engineering threshold of 40 g for general occupant loading in a frontal impact. The acceleration pulse duration lasts around 0.1 seconds, which is typical for a 50% overlap crash at the tested speed.
4.3 Overall Crash Deformation Analysis
The response of the vehicle during the MPDB impact shows deformation progression throughout the vehicle’s front structure. In the initial phase of 0 to 20 ms, the bumper beam and crash cans contact the face of the barrier; they are loaded in compression. Due to the stiffness of the crash boxes, energy absorption is maintained on the struck side while the non-struck side begins to bend slightly. During the interval from 20 to 60 ms, the main front-rail crush mechanism develops. The 50% offset configuration generates an asymmetric load distribution that promotes bending of the front rails on the struck side and causes lateral yaw motion of the vehicle and mobile barrier. The barrier indentation becomes pronounced in this period, especially in the area facing the front rail. From 60 to 120 ms, the elastic spring-back of the aluminum honeycomb and partial unloading of the crushed vehicle front members causes the barrier trolley to separate from the contacting side of the vehicle.
These processes are visible from the deformation snapshots at different times of the collision event. They clearly show the occupant compartment stays visually intact in most of the initial crash, except for some deformation at the frontal zone.
4.4 Deformation Analysis of Key Structural Components
4.4.1 Front-End Energy Absorbing Components
The front bumper beam, crash boxes and front side rails are the primary energy-absorbing members during a frontal crash event. The investigation of their collapse modes gives direct insight into the structural energy absorbing performance. In this simulation, I analyzed the front-end deformation modes of the structure, where the bumper is slightly bent backwards in the overlap region. The crash box on the struck side has collapsed completely and has reached the end of its crush stroke. On the opposite non-struck side, the crash box mainly deforms elastically while tilting inward to follow the bending movement of the bumper beam.
Meanwhile, the front side rail on the struck side experienced severe plastic folding and lateral bending in the forward region. It did not display the progressive compression crumple, which in an ideal case would help maximize energy absorption. The end of the non-struck rail deformed moderately as the rail bent toward the struck side, as a consequence of the offset load. Deformation modes show that the longitudinal beam on the crash side is not leveraging full crush load efficiently; instead, the fold pattern is accompanied by the significant bending that yields to the lateral kick. Thus, structural improvement to control the rail bending and increase axial crush, or alternative energy-absorbing filling, is needed.
4.4.2 Door Frame Intrusion Quantities
For occupant survival space evaluation in the frontal offset crash, control of door frame collapse is the primary goal. C-NCAP rules require at least one side door able to be opened after the crash for occupant extraction. The door frame deformation is checked at the front and rear door hinge pillar zones. The measurement was performed on points at the upper and lower hinge region relative to the B-pillar in X direction. My analysis indicated that the upper point displacement relative to B-pillar reached 15.74 mm while the lower point displacement had a maximum of 18.90 mm at the end of the crash. At the lower hinge region, this deformation exceeded the typical limit of 15 mm to keep the door functional. In actual door opening scenarios the prescribed acceptable limit is 25 mm for upper hinge and 15 mm for lower hinge. Therefore, the door opening potential at the lower area may be compromised.
4.4.3 Analysis of A-Pillar Bending and Intrusion
The A-pillar is part of the occupant survival cell. During the crash, its possible collapse modes can cause forward roof structure displacement and result in some amount of displacement of the instrument panel toward the occupant. In the simulation, three selected measurement points along the A-pillar on the struck side are used to compute the change in angle (which reflects bending). The angle in the baseline measurement equals approximately 27.99°; the maximum change during the collision equals 0.6°; and the final residual change equals only 0.18°. This mainly elastic response proves that the A-pillar has good stiffness, and there is only negligible permanent bending deflection after the entire impact.
Additionally, displacement of the A-pillar relative to the B-pillar in X direction at the upper door frame point was found to be only 13 mm. According to C-NCAP, when the measured displacement is less than 100 mm, the tested vehicle gives good structural behavior. Thus the A-pillar design satisfies the regulation.
4.4.4 Front Bulkhead Intrusion Analysis
The dash panel (front bulkhead) is the last structural member between front compartment and occupant compartment. Its rearward deformation reduces legroom and can load the occupant lower limbs. In the model, the maximum intrusion into the passenger compartment in the longitudinal direction reached 107 mm in the X direction on the driver footwell area corresponding to the root of the longitudinal rail. In practical regulation, dash panel intrusion in the lower zone below instrument panel in a moderate-overlap crash should generally be below 150 mm. Hence, this value still lies inside the allowed envelope.
4.4.5 High-Voltage Electrical System Safety
For an electric car the main battery pack is positioned underneath the floor of the passenger cell, between the longitudinal sills. In this area, the battery pack can be exposed to large shear/ crush loading caused by the floor deformation and side sill deformations in a frontal collision. My investigation has assessed both the deformation state of the battery frame and the potential for intrusion into the electrical components.
From the strain distribution map of the battery pack, the maximum equivalent plastic strain in the battery housing and support frame is approximately 0.094. This value is far below the failure strain threshold of 0.2 for the aluminum alloy housing material, meaning that no crack or rupture of the pack casing happens. Visual inspection of the battery pack after deformation at the end of the analysis shows no measurable deformation, indicating no high-voltage cable compression or battery cell impact in this MPDB event.
The absence of direct contact of the pack with the surrounding vehicle systems and no meaningful packaging intrusion contributes to the high-voltage electrical safety evaluation for this electric car in the given crash mode.
4.5 Barrier Deformation Analysis
In an MPDB test protocol, the impact energy is dissipated by the vehicle front structure as well as the front aluminum honeycomb block mounted on the mobile trolley. The deformation of the barrier face, together with its acceleration response, provides the necessary data for the compatibility assessment. In my simulation, the barrier is loaded locally by the longitudinal rail and bumper. Given the offset loading condition, the barrier face was deformed more on one side, while the other side remains almost undeformed. The maximum barrier crushing depth at the central zone of rail contact reaches a large value, up to nearly 700 mm, which is beyond the available crush stroke of the barrier. This obviously gives an indication of high attacker aggressiveness, which is measured by the intrusion depth and the deformation uniformity.
4.6 Crash Compatibility Evaluation
The MPDB protocol not only measures occupant protection in the tested car but also investigates the vehicle’s collision compatibility. The C-NCAP established a series of metrics obtained from the barrier face and trolley acceleration. The evaluation indices are described as follows.
4.6.1 Standard Deviation of Barrier Deformation (SD)
The C-NCAP evaluation area is a rectangular region of the deformable barrier face with width consisting of the total evaluation area of integer coordinates. This zone is selected within the measured barrier contact area and characterized by vertical distances from ground of 250 mm to 650 mm. The evaluation on the region is made among 640 evaluation grid cells, and the standard deviation of the depth of deformation over these grid points is defined by equation:
$$SD = \sqrt{\frac{ \sum_{i=1}^{n} (X_i – \bar{x})^2}{n-1}}$$
Here n is number of evaluation points, Xi is the measured depth of intrusion at each grid point, and x̄ is the arithmetic average intrusion depth over the evaluation zone. When SD below 50 mm, no penalty is assigned; above 150 mm, full two-point penalty; between these limits, the penalty is computed via linear interpolation.
The computed SD time-history curve indicates that peak SD is around 89.8 mm at roughly 25 ms. At the end, SD reaches 82.8 mm. The location of the deformation is deep in the central region and shows obvious uneven deformation distribution. The homogeneous evaluation grid is highly intruded near the areas corresponding to the vehicle main energy-absorbing path. That is typical when vehicle frontal stiffness is concentrated through the longitudinal rail and the magnitude of local load is high yet broad structural engagement is limited.
4.6.2 Occupant Load Criterion (OLC)
The Occupant Load Criterion is computed to represent loads imparted to an occupant of the opponent vehicle in a two-vehicle crash scenario. The calculation starts with the acceleration of the mobile deformable barrier in longitudinal direction. Integrating this acceleration produces a velocity history for the barrier trolley. The occupant model of the virtual dummy assumes 65 mm of free travel before the restraint force engages and an additional 235 mm of available occupant displacement with the restraint stroke. The formulation proceeds through:
$$V(t) = \int_0^t A_x(t)\,dt + V_0$$
The algorithm searches for time t1 when the occupant relative displacement equals the free displacement:
$$\int_0^{t_1} V(t)\,dt – V_0 \cdot t_1 = 0.065$$
Then at time t2 the total available relative displacement within the restraint stroke reaches 0.235 m:
$$\int_0^{t_2} \left[ V_0 – V(t) \right] dt – \int_0^{t_1} \left[ V_0 – V(t) \right] dt = 0.235$$
The OLC equivalent constant deceleration is found by the linear fit of the occupant velocity curve between t1 and t2.
$$OLC = \frac{V(t_1)-V(t_2)}{t_2 – t_1}$$
According to this calculation, the trolley X-acceleration curve peaks at 35.2 g at around 0.065 s. The barrier’s velocity response is integrated. By applying these equations to the barrier acceleration data, OLC = 30.4 g is obtained. C-NCAP requires OLC ≤25 g for no penalty and OLC ≥40 g for maximum penalty; in between the penalty is determined by linear interpolation. The value of 30.4 g falls in the penalty zone, suggesting that the studied electric car is not sufficiently compatible with lighter and/or softer opponent vehicles.
4.6.3 Barrier Bottoming-out and Intrusion Depth
The last item in this evaluation is the determination of “barrier bottoming”. In order to check this, cells in the evaluation area where amount of deformation depth exceeds 630 mm are found. These cells indicate deep intrusion through the energy absorbing barrier material and potential rigid contact between vehicle structure and the barrier trolley support plate. In the evaluation zone, the local area having intrusion depth > 630 mm is bigger than the allowed tolerance zone of 40 mm × 60 mm. Such barrier bottoming is present, thus a further penalty must be allocated.
4.6.4 Barrier Intrusion Height
Another special evaluation criterion is the height measure of the deformation zone when applicable to high-front-end vehicles. Since this sedan has a front longitudinal rail ground clearance below 508 mm, the height intrusion criterion is judged as not applicable. No additional penalty occurs from this evaluation.
Compatibility evaluation before optimization is summarized in Table 4.1.
Table 4.1 Compatibility parameters before optimization
| Metric | Value | Penalty (points) |
|---|---|---|
| SD (mm) | 82.8 | 0.656 |
| OLC (g) | 30.4 | 0.720 |
| Barrier bottoming | Yes | 2.000 |
| Total compatibility penalty | — | 3.376 |
The original design of this electric car shows poor compatibility in frontal offset collisions due to the locally stiff frontal structure, high mass, and non-uniform barrier loading. It is therefore essential to improve.
Chapter 5 Structural Improvement and Multi-objective Optimization Design
5.1 Improvement Plan Using Aluminum Foam
The longitudinal front side members are the principal structural elements subject to crash and absorb impact energy through the plastic folding. In the analysis results, the rail is shown to have severe folding and bending that prevents efficient usage of material for crash energy absorption. To overcome the poor efficiency and increase energy absorption robustness, I proposed the filling of aluminum foam into the hollow cross-section of the longitudinal rail with consideration of packaging constraints in the vehicle front area.
Aluminum foam has drawn attention for crashworthiness applications because of the long flat plateau of compressive stress response at relatively low stress level. During foam compressive collapse, large amounts of energy are dissipated at roughly constant crushing force. Filling metallic thin-walled structures with aluminum foam can stabilize folding, enhance energy absorption capacity, and increase the specific energy absorption without excessive mass increase. Such a method also helps in many events to change deformation mode from Euler buckling and local bending into progressive crushing.
5.2 Verification of Foam-Filled Longitudinal Member Behavior
5.2.1 Computational verification of aluminum foam compressive characteristics
Using the unit-cell modeling technique, the mechanical behavior of an open-cell foam is simulated using the body-centered cubic arrangement of circular struts. Figure 5.2 depicts a body-centered cubic unit cell with a side dimension a and porosity created by the overlapping spheres of radius r. The total void volume fraction P is computed from the geometric model of similar open-cell foam.
The porosity is defined as:
$$P = \frac{8\pi}{3} \left( \frac{r}{a} \right)^3$$
For cellular solids, the relative density of foam is related to the solid volume ratio as:
$$\frac{\rho_{foam}}{\rho_{solid}} = 1-P$$
Therefore the foam density in terms of porosity and base material:
$$\rho_{foam} = \rho_{solid} \left[ 1 – \frac{8\pi}{3} \left( \frac{r}{a} \right)^3 \right]$$
This indicates the density can be tailored by varying geometric parameter ratio r/a.
For uniaxial compression, finite element analysis of the periodic unit cell model replicated the three-stage response of aluminum foam. The model of open-cell foam has been assigned different material parameters, including density 2.7 g/cm³, Poisson coefficient 0.3, and elastic modulus 70,000 MPa. The simulation comprised a rigid platen moving at constant vertical velocity while the lower base is fixed. Surface-to-surface contact between platen and foam as well as internal contact on the foam itself were included.
Compression deformation of the unit cell illustrates progressive cell wall collapse. The plateau stage corresponds to stress localization bands where the walls of pore collapse plastically; once cells are fully crushed, the stress increases sharply with the densification stage. A complete stress-strain curve is obtained from finite element model and is compared with the experimental results from the literature. The predicted stress-strain curve reproduces typical stages of foam deformation, with initial elastic loading being followed by the plateau and subsequent densification. The stress magnitudes and the plateau slope show good agreement with established experimental response of aluminum foam at corresponding relative density. In the plotted experimental stress-strain curves [67], three independent tests consistently demonstrate the same trends. Thus, the unit-cell finite element analysis proves the material’s energy absorption capacity.
5.2.2 Feasibility check of foam-filled longitudinal rail FE model
In my modeling approach I have inserted the foam into the crash zone of the longitudinal rail. This interaction of the foam and the thin wall plate has the potential to be complex, especially concerning the failure modes. However, due to simplification of the foam as a solid part tied to the rail inner surface, the continuous mesh tying constraints are adopted. The foam filler element group is constrained to coincide in the displacement field with the inner surface of the rail via tied contact.
After modifying the rail model and carrying out offset-frontal crash simulation, the system energy balance at completion time remained conservative. Total energy from beginning to end varies within less than 0.5% deviation, whereas hourglass energy percentage remains at 1.1%, under the acceptable limit. This solution is thus a valid basis for the subsequent full vehicle optimization.
5.3 Multi-objective Optimization Design
Considering the multiple demands of the crashworthiness and compatibility, a set of structural performance indicators are simultaneously optimized. I choose as objectives: the peak B-pillar acceleration, the OLC value based on barrier acceleration, and the standard deviation of barrier face deformation (SD). The multi-objective problem takes the following mathematical form:
$$\text{Minimize: } F(\boldsymbol{x}) = \left[ f_{A}(\boldsymbol{x}), f_{OLC}(\boldsymbol{x}), f_{SD}(\boldsymbol{x}) \right]^T$$
$$\text{Subject to: } m(\boldsymbol{x}) \leq m_0$$
$$x_i^{(L)} \leq x_i \leq x_i^{(U)}, \quad i=1,2,\ldots,6$$
where x denotes the vector containing the design variable values, m(x) is the total mass of the selected parts, and m0 is the mass of original parts. The lower and upper bounds of each variable are chosen to meet the overall vehicle constraints.
5.3.1 Optimization Variables
Six design variables are selected from the principal load path components in the vehicle front end:
X1: thickness of the front bumper beam;
X2: thickness of the crash box;
X3: thickness of the longitudinal rail inner plate;
X4: thickness of the longitudinal rail rear extension;
X5: thickness of the longitudinal rail outer plate;
X6: density parameter of the aluminum foam filler material.
The thickness ranges are constrained within ±50% of the baseline values for manufacturing feasibility and packaging. Ranges of the variables are as follows:
Table 5.1 Design variable range specification
| Variable ID | Original thickness (mm) | Lower bound (mm) | Upper bound (mm) |
|---|---|---|---|
| X1 | 2.50 | 1.25 | 3.75 |
| X2 | 2.10 | 1.05 | 3.15 |
| X3 | 1.80 | 0.90 | 2.70 |
| X4 | 2.00 | 1.00 | 3.00 |
| X5 | 1.80 | 0.90 | 2.70 |
| X6 | 0.60 | 0.30 | 0.90 |
5.3.2 Design of Experiments
For proper construction of the metamodel, a design of experiments is needed to get response samples over the design space. In this study, optimal Latin hypercube sampling is used. The Optimal Latin Hypercube design technique distributes sample points uniformly across all factor dimensions with relatively small set of samples. In this thesis, 40 sampling points are generated using the ISIGHT platform. The sample design matrix is partially listed in Table 5.2.
Table 5.2 Sampling points from DOE
| Run | X1(mm) | X2(mm) | X3(mm) | X4(mm) | X5(mm) | X6(mm) |
|---|---|---|---|---|---|---|
| 1 | 1.76 | 2.94 | 2.29 | 1.51 | 2.38 | 0.56 |
| 2 | 1.83 | 1.37 | 1.41 | 1.62 | 1.27 | 0.84 |
| 3 | 2.79 | 1.59 | 1.18 | 1.21 | 1.32 | 0.42 |
| 4 | 1.64 | 1.97 | 0.90 | 2.39 | 1.22 | 0.49 |
| 5 | 3.17 | 2.13 | 2.70 | 1.72 | 2.29 | 0.75 |
| … | … | … | … | … | … | … |
| 36 | 1.89 | 1.10 | 2.10 | 2.10 | 1.09 | 0.44 |
| 37 | 2.47 | 2.18 | 2.56 | 2.56 | 1.55 | 0.32 |
| 38 | 2.28 | 2.61 | 2.05 | 2.05 | 1.69 | 0.90 |
| 39 | 2.66 | 1.48 | 1.55 | 1.55 | 1.92 | 0.30 |
| 40 | 1.31 | 2.88 | 1.50 | 1.50 | 1.64 | 0.81 |
For every sample, the LS-DYNA solver calculates the desired output responses from the finished FE model. These computed output values (A, OLC, SD and mass) from selected DOE are listed in Table 5.3.
Table 5.3 Response values from full vehicle simulation
| Run | Acceleration A(g) | OLC(g) | SD(mm) | Mass m(kg) |
|---|---|---|---|---|
| 1 | 32.48 | 28.47 | 71.99 | 20.25 |
| 2 | 28.57 | 25.60 | 66.65 | 18.52 |
| 3 | 29.46 | 27.78 | 80.70 | 16.61 |
| 4 | 28.31 | 26.25 | 65.41 | 17.02 |
| 5 | 35.62 | 32.81 | 91.43 | 22.48 |
| … | … | … | … | … |
| 36 | 29.74 | 26.66 | 67.43 | 16.94 |
| 37 | 32.51 | 28.83 | 79.40 | 18.06 |
| 38 | 31.91 | 28.18 | 77.67 | 21.08 |
| 39 | 31.90 | 30.81 | 80.90 | 18.20 |
| 40 | 30.19 | 28.23 | 64.53 | 20.41 |
5.3.3 Kriging Surrogate Model Construction
Full vehicle crash finite element analysis is computationally expensive; therefore a surrogate-assisted optimization technique is required. Kriging method is a surrogate model using statistical interpolation over the sampled design space. Its estimator y(x) is composed of a parametric regression part and a non-parametric stochastic process part.
$$y(\boldsymbol{x}) = \sum_{i=1}^{k} \beta_i f_i(\boldsymbol{x}) + Z(\boldsymbol{x})$$
where fi(x) is a regression basis function, βi are regression coefficients, and Z(x) is assumed to be a Gaussian stationary process with zero mean, constant variance and spatial correlation. The covariance between two sample points is characterized by the correlation function.
$$Cov\left[ Z(\boldsymbol{x}_i), Z(\boldsymbol{x}_j) \right] = \sigma_Z^2 R\left( \boldsymbol{x}_i, \boldsymbol{x}_j \right)$$
The Gaussian correlation function employed in this investigation has the expression:
$$R\left( \boldsymbol{x}_i, \boldsymbol{x}_j \right) = \exp \left[ -\sum_{k=1}^{n} \theta_k \left( x_i^k – x_j^k \right)^2 \right]$$
where θk is the unknown correlation parameter that controls the smoothness of the model.
Kriging is useful for very nonlinear response with interacting design variables. The model parameters are evaluated by maximizing the concentrated log-likelihood function:
$$\Phi(\theta) = -\frac{n}{2} \ln(\hat{\sigma}^2) – \frac{1}{2} \ln\left| \boldsymbol{R} \right|$$
where R is the correlation matrix. After the optimal correlation parameters are fixed, the value of the response at an untried location x0 is computed as:
$$\hat{y}(\boldsymbol{x}_0) = \boldsymbol{f}(\boldsymbol{x}_0)^T \hat{\boldsymbol{\beta}} + \boldsymbol{r}(\boldsymbol{x}_0)^T \boldsymbol{R}^{-1} \left( \boldsymbol{Y} – \boldsymbol{F}\hat{\boldsymbol{\beta}} \right)$$
where r(x0) is the vector of correlations between the prediction point and the sample data points.
5.3.4 Accuracy Check of Approximate Model
To assess surrogate model accuracy, the coefficient of determination (R²) is used, which is defined as:
$$R^2 = 1 – \frac{\sum_{i=1}^{n_{test}} \left( y_i – \hat{y}_i \right)^2}{\sum_{i=1}^{n_{test}} \left( y_i – \bar{y} \right)^2}$$
The Kriging models were trained on 40 sample runs. The computed R² values for each response are given in Table 5.4.
Table 5.4 R² accuracy metrics for Kriging models
| Response | Acceleration | OLC | SD | Mass |
|---|---|---|---|---|
| R² | 0.967 | 0.973 | 0.975 | 0.973 |
All R² values are above 0.95, indicating that the Kriging models have a very strong fit to the simulation data. Scatter plots of predicted versus actual responses further confirmed the consistency and accuracy of the surrogate model. Since these approximate models met the quality targets, they are applicable for the subsequent multi-objective optimization.
5.3.5 Multi-Objective Optimization via NSGA-II
In this thesis the multi-objective evolutionary algorithm NSGA-II (Non-dominated Sorting Genetic Algorithm II) is adopted to solve the Pareto optimization problem. NSGA-II has advantages in preserving population diversity and ensuring convergence toward the real Pareto front. This algorithm first generates a random parent population, then performs genetic operations (selection, crossover, and mutation) to produce offspring. Non-dominated sorting is applied on the combined parent and offspring population. Crowding distance calculation is used as a tie-breaker that maintains solution diversity.
The complete optimization workflow couples ISIGHT with the Kriging model, where each NSGA-II evaluation is fast and does not require additional finite element simulation. At algorithm termination, a total of 241 Pareto-optimal solutions is obtained. The 3D plot of the trade-off among the three objective values shows that improving the acceleration response often causes the deterioration of SD and OLC. Therefore designers must balance the different objectives. Considering also the mass saving target, I selected a solution from the middle zone of the Pareto front. The selected optimization results, together with the rounded engineering values adopted for numerical verification, are summarized in Table 5.5.
Table 5.5 Comparison of design variables between initial and optimized configuration
| Design variable | Initial(mm) | Theoretical Optimum(mm) | Adopted value(mm) |
|---|---|---|---|
| X1 | 2.50 | 2.1623 | 2.20 |
| X2 | 2.10 | 1.8631 | 1.90 |
| X3 | 1.80 | 1.9830 | 2.00 |
| X4 | 2.00 | 2.1437 | 2.10 |
| X5 | 1.80 | 1.8760 | 1.90 |
| X6 | 0.60 | 0.5803 | 0.60 |
5.4 Results and Discussion of Optimized Design
The optimized values were implemented into the complete finite element model. Then a simulation was run for the optimized configuration. Evaluation values obtained from the model are compared to the expected Kriging prediction in Table 5.6.
Table 5.6 Accuracy of Kriging predictions with full simulation results
| Output Response | Kriging Prediction | Simulation result | Error (%) |
|---|---|---|---|
| B-pillar Accel A(g) | 29.80 | 30.04 | 1.14 |
| OLC (g) | 25.65 | 26.20 | 2.14 |
| SD (mm) | 60.65 | 63.06 | 3.97 |
The error margin of all targets is less than 4%. This confirms robustness of the developed optimization methodology.
5.4.1 Crashworthiness Evaluation after Optimization
The B-pillar acceleration time history of the original and optimized vehicles is compared. The maximum acceleration is reduced from 34.11 g to 30.04 g, giving a reduction of 12%. Such reduction can improve occupant protection performance. The optimized front rail deformation gives a better progressive folding pattern of the rail. In the earlier model, a sharp localized fold occurred at mid rail; in this optimized version, the front portion of the side member is crushed more as an axial fold and the remaining segment remains relatively straight. The collapse pattern demonstrates an increased energy absorbing path and lower risk of buckling into the footwell region.
The door-frame metrics after optimization indicate the upper point displacement at the hinge reaches 20.40 mm, which increases but remains below the allowable 25 mm. Lower-hinge displacement reduces to 12.3 mm. For the lower door region this value has considerably improved and remains less than the 15 mm regulation limit. The optimized structure is safe for door opening requirement after crash. The deformation of the A-pillar after optimization remains almost unchanged as indicated by angle time histories. Front bulkhead intrusion improved from 107.49 mm to 93.74 mm, a decrease of about 13.75 mm. This result reduces loading on the lower legs and feet.
Battery pack analysis was repeated in the optimized vehicle. Maximum equivalent strain observed in the pack structural member equals 7.9%, still much less than 20% failure threshold. Thus the optimized vehicle meets the required high-voltage electrical protection.
5.4.2 Effects of the Improvement on Compatibility Parameters
The SD time-history of the barrier after the optimized vehicle configuration shows a marked decrease. The maximum SD value decreased from 89.8 mm to 71.79 mm, while the final SD is reduced to 63.06 mm from 82.8 mm. This indicates more uniform loading of the barrier, meaning lower risk of locally overloaded frame structures in real collisions. This improvement corresponds to a reduction in the penalty due to SD.
Barrier deformation contour after the optimization shows visibly smaller high intrusion zone above 630 mm. The deep intrusion region (red colored) in the evaluation area decreased significantly. Consequently the bottoming area is reduced but still slight bottoming remains. In the optimized version, the local concentration on the main structural engagement zone is diminished, indicating that more components on the front end now share the crash load.
OLC indicator is computed after the optimized design. The time from barrier acceleration and the virtual occupant velocity curve are processed at post-simulation stage. The occupant load criterion is reduced from 30.4 g to 26.2 g. This reduction of 4.2 g has positive influence on the protection of the driver of the opponent car, especially in terms of restraint load demand. The optimized vehicle is less aggressive.
A summary of the compatibility criteria for the baseline model and the optimized vehicle is shown in Table 5.7.
Table 5.7 Comparison of compatibility metrics
| Configuration | SD(mm) | OLC(g) | Barrier Bottoming | Total penalty |
|---|---|---|---|---|
| Original | 82.80 | 30.40 | Yes | 3.376 |
| Optimized | 63.06 | 26.20 | Yes | 2.421 |
| Change | -19.74 | -4.20 | — | -0.955 |
The compatibility penalty was reduced by 0.955 points. With the designed foam filling and the optimized thickness distribution, the body structure of the electric car offers improved partner-protection, while preserving (and partially enhancing) the self-protection performance.
From a mass standpoint, the optimized front structure has a total mass increment of about 0.49 kg from baseline (calculated from the member thickness changes). It slightly increases compared with the original configuration since the chosen Pareto solution prioritized performance improvement while limiting mass. The increase in mass is small enough to be acceptable.
Chapter 6 Conclusions and Future Outlook
6.1 Conclusions
In this thesis, the frontal crash behavior and compatibility of a pure electric car were studied under the MPDB test procedure introduced in C-NCAP. A full-vehicle finite element model was built and solved with LS-DYNA, and improvements have been proposed. From the obtained simulation results I draw the following conclusions:
(1) Vehicle crash simulation results confirmed that the model energy balance and hourly-glas energy values meet the criteria of 5% limit. The model mass increase remains small and the total energy is conserved throughout the event. So the simulation model provides a reliable basis for analysis and further design.
(2) Main structural deformation at front side rails reveals inefficient collapse behavior, resulting in relatively large occupant compartment intrusion for the lower door hinge area and footwell area. In particular, the maximum front bulkhead intrusion is 107 mm, door frame lower point intrusion is 18.9 mm and the B-pillar deceleration peak equals 34.11 g. The existing structure still satisfies basic occupant space requirements, but improvements could further improve safety.
(3) Compatibility evaluation shows that the studied electric car generates high barrier intrusion depth, non-uniform deformation distribution, and notable local bottoming of the MPDB barrier. From the barrier-related evaluation indicators, total compatibility penalty reaches 3.376 points. This result indicates need for structural tuning.
(4) The proposed structural foam filling approach for the front rail region was technically validated using finite element analysis of the foam compressive behavior. The computed stress-strain characteristics of an aluminum foam unit cell correlate closely with the known experimental behavior of aluminum foam and reproduce the characteristics of elastic, plateau and densification stages. The aluminum foam-filled model is energy conservative in dynamic crash simulations and greatly lowers the risk of global buckling of the rail.
(5) A surrogate-based multi-objective optimization was implemented. The Kriging models of the objectives were built using samples from Optimal Latin Hypercube design, and NSGA-II optimization was applied. Comparison between the Kriging prediction and direct crash simulation confirms that the approximate model is accurate. A Pareto solution was chosen as the new design of vehicle front with thickness variations around +8% ~ +12% for some structural elements and no addition of mass.
(6) The performance of the optimized electric car has been comprehensively verified. The B-pillar peak acceleration decreased to 30.04 g, reducing 4.07 g from the original. The upper and lower door frame intrusion limits are now in the acceptable zone, with lower hinge intrusion equal to 12.3 mm, and the A-pillar angle change remained minor. The dash panel intrusion decreases. The compatibility outcomes indicate that final SD value equals 63.06 mm and OLC equals 26.2 g, improving 19.74 mm and 4.2 g respectively compared with the baseline. The C-NCAP compatibility penalty decreases from 3.376 to 2.421. The optimized structural design improves both crashworthiness and collision compatibility of this electric car.
6.2 Innovation Points
The main innovation of this work is twofold:
(1) By way of filling the longitudinal rails of electric car with aluminum foam and simultaneously optimizing the influencing dimensions, an effective improvement of collapse stability of the longitudinal rail crash is achieved without losing mass efficiency.
(2) The work establishes a systematic front-end crashworthiness and crash compatibility optimization flow under MPDB conditions for electric car, combining the nonlinear finite element model, Kriging approximation and evolutionary multi-objective algorithm. The results produce a trade-off solution that reduces both self-injury and aggressivity to the opponent vehicle and offers scientific insight into the compatibility evaluation in the C-NCAP protocol.
6.3 Limitations and Future Work
This study has only considered the thickness of parts, whereas the collaboration or grading between material properties and structural thickness could produce better results. The investigation considered only the MPDB case; vehicle safety in other scenarios like ODB and side crash may require a multi-condition optimization approach. Integrating high-fidelity dummy models for injury criteria, such as HIC and chest deflection, into the same optimization process could refine the occupant protection objective. Finally, actual prototype testing will be required for final engineering validation of this optimized structure.
The research can be extended in the following directions: (1) simultaneous optimization of material properties, foam density and structural geometry considering manufacturing feasibility; (2) incorporation of full vehicle-sled occupant restraint simulations in the optimization procedure; (3) multi-load case design optimization considering frontal, side, rear and pole scenarios for safer electric car design.
It must be stressed that the compatibility metrics introduced by MPDB evaluate only the tested car in one fixed condition. Since a fleet is mixed with many car shapes and masses, a robust structural design should probably aim at load-path agnostic behavior in variable frontal contacts. Advanced topology optimization methods might be applied to the front sub-frame to achieve optimum force distributions. It is also important to maintain some degree of deformability in the engine cradle and other load path elements so that loads are transmitted as widely as possible and concentrated forces are avoided.
In summary, the results of this thesis indicate significant potential for designing electric car with balanced self- and partner-protection under the MPDB protocol. The simulated improvements are promising and can support actual vehicle development. The research work should continue to take into account all additional complexity of real electric car crash events for enhanced occupant safety across families of car sizes and weights.