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Structural Optimization of a Pickup Frame Combining Thickness, Shape and Feature Parameters for Lightweighting.


To boost the fuel economy and meet the emission standards, OEMs are puting much effort on reducing vehicle weight by using more efficient structural designs, adopting light-weight materials and thinner gauges, applying structural adhesives, etc. Lightweighting proves to be the ultimate solution for fuel economy [1, 2, 3]. Advanced high strength steels (AHSS) offer a lightweighting solution through thinner gauges while still meeting the crash safety requirements [4, 5, 6, 7, 8]. The AHSS grades have been applied extensively on the Body-In-White (BIW) parts and closures [9, 10, 11, 12]. Now steel companies are launching the next and 3rd generation AHSS grades which have even higher yield and tensile strength than traditional AHSS, and offer more lightweighting opportunities.

One problem with thinner gauge of any material sheet, however, is the reduced stiffness of the parts and thus compromised stiffness and NVH performance for vehicles. Balancing the lightweighting with vehicle stiffness and NVH performance is crucial in vehicle design [13, 14]. A design change is necessary usuallly to make up for the compromised stiffness performance due to reduced part gauges. Methods and techniques on enhancing the vehicle stiffness have been studied and applied in vehicle design, such as designing the part thickness using tailored blanks, enlarging the cross section of enclosed structures, identifying and reinforcing the local joints, adding additional adhesive bonding besides spotweld connections, optimizing the spotweld spacing and locations, etc. [15, 16, 17, 18, 19, 20, 21].

Structural optimization techniques have been developed to find the optimal thickness (sizing and topometry optimization) and shape (shape, topometry and topology optimization) of structures for stiffness and strength performance [22, 23, 24, 25, 26, 27]. With the optimal gauge and shape design, the material properties can be utilized more efficiently to meet vehicle stiffness and NVH performance and still achieve the lighweighting design. Simultaneous optimization has also been discussed to combine multiple techniques and reach the best design configuration [28, 29, 30, 31].

The pickup chassis frame is the main supporting structure of the truck and bears the loads from engine, chassis, body and other assemblies [32, 33]. The frame is made of steel typically, especially the AHSS grades, and is most crucial for the stiffness, NVH and crash safety performance of the vehicle. When doing a lightweighting design, the static and dynamic characteristics of the pickup frame have to be maintained or improved. This research continues former study of evaluating the methods and techniques for improving the pickup frame stiffness [34] and explores the optimal light-weighting design combining multiple methods through simultaneous optimization. These methods discussed include adding bulkhead feature to the rails as reinforcement, enlarging the closed cross sections on the rails, and increasing the part thickness on frame. Structural optimization analysis was conducted for each technique to insure an optimal solution with maximal stiffness improvement and minimal mass increase. In this study, simultaneous structural optimization combining multiple techniques was discussed to get the best lightweighting design. A material efficiency ratio [micro] proposed in former study is used as a criterion to evaluate the effectiveness of the final design change obtained through simultaneous optimization.

Methods to Improve the Torsion Stiffness of a Pickup Frame

For the lightweighting designs of truck and sedan using thinner gauge of materials, the vehicle stiffness would be reduced and thus the NVH performance be compromised. Especially the torsion stiffness, which is most critical for the vehicle static and dynamic performance, would be compromised [8]. For optimization, the static and dynamic characteristics of vehicle body or frame, such as torsion and bending stiffness, vibration modes, or a criterion combining above two or more characteristics, are choosen as design targets usually to be improved. In this study, the torsion stiffness improvement was set as design target. VR&D Genesis software is used for linear analysis and optimization [25, 29]. The loading and boundary conditions are shown in Figure 1. The frame torsion stiffness is calculated as [34]:

[mathematical expression not reproducible] Eq. (1)


[mathematical expression not reproducible] Eq. (2)

[mathematical expression not reproducible] Eq. (3)

In above equation, T is the torsion load represented by a pair of vertical forces F applied at shock towers in opposite directions with distance B. [phi] is the angular deflection under torsion load based on vertical deflections of both shock towers ([v.sub.l] and [v.sub.r]) as well as the distance between shock towers B.

Multiple stiffness improvement methods including adding bulkheads to the frame rails, increasing the thickness of frame parts, and enlarging the cross sections on the frame rails were evaluated utilizing a material efficiency ratio defined as [34]:

[micro] [[K.sub.T ]- [K.sub.To]/M - [M.sub.o]] Eq. (4)

Where [K.sub.To] is the baseline torsion stiffness and [K.sub.T] the torsion stiffness after a design change. [M.sub.0] is the baseline mass of the structure and M the mass after the design change. This material efficiency ratio evaluates the efficiency of the design change in respect of stiffness and NVH characteristics to the change in mass. Under a certain torsion improvement target, the optimal design with maximal material efficiency ratio can be obtained by minimizing the mass increase in optimization. The coupling effects among those methods will be discussed in the following chapters.

Increasing Part Thickness on Frame

The first method studied is to increase the part thickness on chassis frame to improve the torsion stiffness. Sizing optimization was conducted and the thickness of 62 parts on frame was set as deisgn variable (with 1.0 mm increase limit), as shown in Figure 2. The thickness design is symmetrical between the left and right sides of the frame, therefore a total of 31 design variables were defined.

For torsion improvement of 2.5%, 5.0% and 10.0%, the optimization results are shown in Tables 1 and 2. The symbol X means no thickness increase for that particular part. Part T173, T206 and T418 were found important in reinforcing the frame and improving the torsion stiffness, followed by T169, T237, T196 and T183. The values of the material efficiency ratio are very low, indicating that increasing part thickness alone does not offer an effective solution.

Adding Bulkhead Feature inside the Frame Rails

Bulkhead feature was added in pairs to the left and right sides inside the frame rails and other closed sections to reinforce the structure and improve the global performance of vehicles. The bulkhead locations were determined based on a topometry optimization study of rails to reinforce the frame. As in Figure 3, the bulkhead was connected to the four inside surfaces of the rail by spotwelds on flange. Sizing optimization with all bulkheads taken into account was conducted.

The thickness of each pair of bulkheads was set as design variable within discrete design range (0.0 mm, 0.65 mm, 0.8 mm, 0.9 mm,..., 1.9 mm, 2.0 mm). The mass increase was set as design constraint, and the maximal torsion stiffness that can be achieved was calculated. The final optimized results are shown in Tables 3 and 4 (Bkd short for bulkhead). The symbol X means that pair of bulkhead feature was not added by optimization. The material tends to be added to the bulkheads with high material efficiency ratio (e.g. bkd1, bkd9, bkd6, etc.) in order to maximize the torsion stiffness while minimizing the mass increase. The material efficiency ratio obtained through adding bulkhead feature is very high as in Table 4 compared to the method of increasing the frame part thickness. Adding local bulkheads is an effective way to improve the vehicle torsion.

Enlarging the Cross Section of Frame Rails

Another method to improve the vehicle torsion stiffness is to enlarge the cross section of the rails. A larger closed cross section of structures will increase the section area, moment of inertia, and other parameters controling bending and torsion. The height of the middle and rear frame rails was increased (to a maximum of 50 mm) using the shape morph tool within VR&D DesignStudio, as in Figure 4. All section morphs are symmetrical between the left and right sides.

Shape optimization was conducted combining these three cross section morph options. The minimal mass increase required was calculated through optimization for stiffness increase targets of 3.0%, 6.0% and 9.0% respectively. The optimized morph values are shown in Table 5. Section morph-3 is always assigned higher values by optimization and has reached the limit for 9.0% target. Morph-1 also has high value at 9.0% target (42.44 mm) because of its great potential in improving the torsion. Section morph-2 does not have as much potential in improving the torsion and thus its value is always below 24 mm. Table 6 shows the material efficiency ratio obtained. The material efficiency ratio is reduced with higher torsion improvement targets. At 6% improvement and above, the efficiency ratio is low and the mass increase is not efficient anymore.

Design with Adding Bulkhead Feature and Enlarging Rail Cross Section

The torsion improvement techniques of adding bulkhead feature and enlarging frame cross section can be combined to achieve a better lightweighting design. A simultaneous optimization combining both methods was conducted with torsion improvement targets of 2.5%, 5.0%, 10.0% and 12.0%, respectively. For 2.5% improvement target, the enlarging rail section option was found not effective, and thus not selected by optimization. Only the addition of bulkheads was adopted and the same results were obtained as the 3.208% torsion improvement in Tables 3 and 4. For 5.0%, 10.0% and 12.0% targets, the optimization iterations are shown in Figures 5-7. Tables 7 and 8 show the optimized bulkhead gauges and cross section morph values. The morph value for each shape increases with higher stiffness improvement target. All added bulkheads are assigned 0.65 mm thickness, which is the minimal allowed and the most efficient for lightweighting.

The interaction between adding bulkhead feature and enlarging the rail cross section is significant. With the added bulkheads, section morph-2 becomes more significant and was assigned higher morphing values than the other two morph shapes. This combined optimization is necessary to achieve a more efficent design (higher material efficiency ratio and torsion improvement potential) than each individual technique. Table 9 shows the torsion improvement achieved, the mass increase required and the corresponding material efficiency ratio. The material efficiency ratio [micro] is reduced with higher stiffness improvement target. When the target is above 10%, the value becomes very low, and the addition of bulkheads and enlarging the rail cross section become less efficient.

Design with Adding Bulkhead Feature, Enlarging Rail Cross Section and Increasing Part Thickness

A comprehensive structural optimization combining all three techniques previously discussed was conducted including the addition of bulkheads, enlarging the cross section on frame rails and increasing the part thickness on frame. The gauge range of those bulkheads is 0.65-2.0 mm if added by the optimization program. The morph limit is set as 50 mm for all three morph shapes. All the parts chosen on frame were given 0-1.0 mm thickness increase range for optimization.

For a 5.0% stiffness improvement target, the same design and improvement results were obtained as observed in Figure 5. Increasing the part thickness was found not as efficient as the other two methods, and thus not adopted by the optimization. A 10% and 15% stiffness improvement target was set and minimal mass required was calculated by the optimization. Figures 8 and 9 show the optimization iterations for 10% and 15% stiffness improvement target. Tables 10, 11 and 12 show the added bulkhead gauges, frame morph values and part thickness increase respectively through optimization. Part T173, T206 and T418 are efficient in reinforcing the frame on torsion with an improvement target over 10%. Table 13 shows the final stiffness improvement reached, the mass increase and the efficiency ratio [micro]. The value of [micro] is reduced with the higher stiffness improvement target.

Comparison of the Torsion Improvement Methods and Their Combinations

The optimization results for all the improvement methods are compared based on the material efficiency ratio, and plotted in Figure 10. More detailed stiffness improvement achieved and the corresponding material efficiency results are shown in Table 14. Among those torsion improvement methods, adding bulkhead feature gives the highest material efficiency ratio, but the stiffness improvement range is very limited. Enlarging the rail cross sections and increasing the panel thickness can improve the torsion to over 9% while the material efficiency ratio is relatively low. The design combining the addition of bulkheads and enlarging rail cross section gives a higher efficiency ratio and stiffness improvement range than could be achieved individally The design with all three improvement methods together achieves the highest material efficiency ratio and highest stiffness improvement range.

The configurations with both increasing part thickness and adding bulkhead feature, and with both increasing part thickness and enlarging the rail cross section, are not evaluated in this study. But the design combining all three improvement methods has covered those two combination configurations not evaluated and should give the optimal solution. The cost increase related with the design changes for each stiffness improvement method and for the combination configurations is not discussed. Basically the design changes will effect the cost in multiple ways and the aim of this study is to obtain the most lightweighting design. Automotive OEMs will be willing to pay extra dollars for the mass saving achieved. And the cost increase in design changes can be offset by improved fuel economy of vehicles.


For this pickup truck frame, methods to improve the torsion stiffness including adding bulkhead feature, enlarging the enclosed cross sections on the rails and increasing the part thickness were evaluated using the material efficiency ratio. Structural optimization for each improvement method and the combinations of above two and all three improvement methods were conducted to get the optimal lightweighting design. The optimal design is dependent on the torsion improvement target, as shown in Table 15. For torsion improvement target within 3.2%, adding bulkhead feature is the most efficient design with material efficiency ratio [micro] high (>7.936 kN-m/rad/kg). For an improvement target of 3.2%-5.4%, the design combining the addition of bulkheads and enlarging the closed sections on rails is most efficient with [micro] in range of 3.861-7.936 kN-m/rad/kg. For a further improvement target of 5.4%-10.3%, the design combining all three improvement techniques gives the maximal stiffness improvement with reasonable mass increase, and with relatively low material efficiency ratio (2.333-3.861 kN-m/rad/kg). For target over 10.3%, the above stiffness improvement methods do not have significant improvement due to low material efficiency ratio. Larger geometrical change or a total frame redesign becomes necessary to achieve the torsion requirement.

The material efficiency ratio is valuable in evaluating the effectiveness of a design change for stiffness and NVH improvement. It is beneficial to vehicle design to balance the stiffness improvement with lightweighting. Simultaneous structural optimization allows the designers to combine different improvement techniques and achieve the optimal design with the highest material efficiency. The vehicle stiffness and NVH performance can be effectively maintained using those methods and optimization techniques while the crash safety and fuel economy be further improved with the usage of the next and 3rd generation AHSS steel grades.

The material efficiency results for those stiffness improvement methods apply to this pickup frame only. For other pickup frame models, the structural optimization needs to be re-conducted following the procedures proposed here to obtain the most accureate material efficiency evaluation.

Contact Information

Jianyong Liang, Ph.D.

CAE Engineer at AK Steel Corporation

Company address: 14661 Rotunda Dr, Dearborn, MI, U.S. 48120

Work phone: (313) 317-6712


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[34.] Liang, J.Y, Powers, J., and Stevens, S., "A Material Efficiency Ratio to Evaluate the Methods for Improving the Torsional Rigidity of a Pickup Chassis frame," SAE Technical Paper 2018-01-1024, doi:10.4271/2018-01-1024.

Jianyong Liang, Jonathan Powers, and Scott Stevens, AK Steel Corporation


Received: 08 Mar 2018

Revised: 05 Jun 2018

Accepted: 11 Jun 2018

e-Available: 08 Aug 2018


AHSS, Lightweighting, Sizing optimization, Shape optimization, Torsion stiffness, Material efficiency ratio, Bulkhead


Liang, J., Powers, J., and Stevens, S., "Structural Optimization of a Pickup Frame Combining Thickness, Shape and Feature Parameters for Lightweighting," SAE Int. J. Mater. Manuf. 11(3):183-191, 2018, doi:10.4271/05-11-03-0018.

TABLE 1 Optimized part thickness increase on frame.

                              Torsion improvement
Part thickness increase (mm)  2.5%  5.0%  10.0%

T169                          X     0.09  0.25
T173                          0.44  0.56  0.99
T183                          X     X     0.09
T196                          X     X     0.14
T206                          0.23  0.37  0.73
T237                          X     0.17  0.36
T418                          0.04  0.22  0.30

TABLE 2 Optimization results of increasing part thickness on frame.

Torsion                              Material efficiency
improvement (%)  Mass increase (kg)  ratio (kN-m/rad/kg)

 2.5              2.30               1.710
 5.0              5.03               1.565
10.0             10.70               1.471

TABLE 3 Optimized bulkhead thickness on frame.

                         Added mass (kg)
Bulkhead thickness (mm)  0.255  0.636  1.129  2.492

Bkd1                     0.65   0.65   1.20   1.90
Bkd2                     X      0.65   0.65   0.80
Bkd3                     X      X      X      1.00
Bkd4                     X      X      X      0.65
Bkd5                     X      X      X      0.65
Bkd6                     X      0.65   0.65   1.30
Bkd7                     X      X      0.65   1.10
Bkd8                     X      X      X      0.65
Bkd9                     0.65   0.90   1.40   1.90
Bkd10                    X      X      0.65   1.10

TABLE 4 Optimization results of adding bulkhead feature on frame.

                 Torsion          Material efficiency
Added mass (kg)  improvement (%)  ratio (kN-m/rad/kg)

0.255            2.020            12.472
0.636            3.208             7.936
1.129            3.748             5.227
2.492            4.358             2.751

TABLE 5 Optimized morph values of rail cross section.

                       Torsion improvement
Rail morph value (mm)   3.0%   6.0%   9.0%

Morph-1                 9.50  19.42  42.44
Morph-2                10.46  23.05  23.42
Morph-3                12.32  43.33  50.00

TABLE 6 Optimization results of enlarging the rail cross section.

Stiffness improve  Target       Added      Material efficiency
target (%)         reached (%)  mass (kg)  ratio (kN-m/rad/kg)

3.0                3.02         2.18       2.174
6.0                6.00         4.95       1.903
9.0                9.01         9.44       1.499

TABLE 7 Optimized bulkhead thickness for design with adding bulkhead
feature and enlarging the rail cross section.
                      Torsion improvement
                      2.5%  5.0%  10.0%  12.0%

Bulkhead gauges (mm)  0.65  0.65   0.65   X
Bkd1                  0.65  0.65   0.65   0.65
Bkd2                  X     0.65   0.65   0.65
Bkd3                  X     X      0.65   0.65
Bkd4                  X     X      0.65   0.65
Bkd5                  0.65  0.65   0.65   0.65
Bkd6                  X     0.65   X      0.65
Bkd7                  X     X      0.65   0.65
Bkd8                  0.90  0.65   0.65   0.65
Bkd9                  X     0.65   0.65   0.65

TABLE 8 Optimized morph values of rail cross sections with adding
bulkhead feature and enlarging the rail cross section.

                  Torsion improvement
Morph value (mm)  2.5%  5.0%  10.0%  12.0%

Morph-1           X     5.16  25.07  34.19
Morph-2           X     6.07  34.23  49.92
Morph-3           X     4.69  13.97  38.07

TABLE 9 Optimization combining adding bulkhead feature and enlarging
the rail cross section.

Torsion          Target       Added      Material efficiency
improvement (%)  reached (%)  mass (kg)  ratio (kN-m/rad/kg)

 2.5              3.208       0.636          7.936
 5.0              5.40        2.2            3.861
10.0             10.05        6.85           2.310
12.0             12.01        9.68           1.953

TABLE 10 Optimized bulkhead gauges on frame for design with adding
bulkhead feature, enlarging the rail cross section and increasing part

             Torsion improvement
gauges (mm)  5.0%  10.0%  15.0%

Bkd1         0.65   0.65   0.65
Bkd2         0.65   0.65   X
Bkd3         0.65   0.65   0.65
Bkd4         X      X      X
Bkd5         X      X      0.65
Bkd6         0.65   0.65   0.65
Bkd7         0.65   0.65   0.65
Bkd8         X      X      X
Bkd9         0.65   0.65   0.65
Bkd10        0.65   0.65   0.65

TABLE 11 Optimized morph values of rail cross sections for design with
adding bulkhead feature, enlarging the rail cross sections and
increasing part thickness.

                  Torsion improvement
Morph value (mm)  5.0%  10.0%  15.0%

Morph-1           5.16   7.40  29.86
Morph-2           6.07   5.49  41.60
Morph-3           4.69   4.66  29.69

TABLE 12 Optimized panel thickness for design with adding bulkhead
feature, enlarging the rail cross section and increasing part thickness.

                              Torsion improvement
Part thickness increase (mm)  5.0%  10.0%  15.0%

T173                          X      0.59   0.74
T199                          X      0.04   X
T206                          X      0.36   0.24
T237                          X      0.03   X
T239                          X      X      0.01
T418                          X      0.21   0.67

TABLE 13 Optimization results for design with adding bulkhead feature,
enlarging rail cross section and increasing part thickness.

Torsion          Target       Added      Mass efficiency ratio
improvement (%)  reached (%)  mass (kg)  (kN-m/rad/kg)

 5.0              5.40         2.2       3.861
10.0             10.30         6.95      2.333
15.0             15.01        11.58      2.040

TABLE 14 Comparison of all the torsion improvement methods and their

Improvement           Torsion          Material efficiency
methods/techniques    improvement (%)  ratio (kN-m/rad/kg)

Increasing part       2.5-10.0          1.710-1.471
Adding bulkhead       2.02-4.36        12.472-2.751
Enlarging rail cross  3.02-9.01         2.174-1.499
Adding bulkhead       2.02-12.01       12.472-1.953
feature & enlarging
rail cross section
Combination of all    2.02-15.01       12.472-2.040

TABLE 15 The optimal design for torsion improvement.

Torsion                                 Material efficiency
improvement (%)  Optimal combination    ratio (kN-m/rad/kg)

0-3.2            Adding bulkhead        >7.936
  3.2-5.4        Adding bulkhead         3.861-7.936
                 feature & enlarging
                 cross section
  5.4-10.3       Adding bulkheads,       2.333-3.861
                 enlarging rail cross
                 sections & increasing
                 part thickness
>10.3            Larger geometry        <2.333
                 change or frame
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Author:Liang, Jianyong; Powers, Jonathan; Stevens, Scott
Publication:SAE International Journal of Materials and Manufacturing
Article Type:Technical report
Date:Sep 1, 2018
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