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Example of Usage 7

Optimization of Reinforcing Member for Automotive Collision Safety Design.

YOKOHAMA National University / Honda R&D Co., Ltd.

Offset Impact Diagram

Improvements to computer-aided engineering (CAE) in recent years have allowed for highly precise designs for complex impact phenomena, contributing greatly to safety structural development. That said, there have been few practical optimized design methods for impact phenomena that represent non-linear dynamic issues. Yokohama National University and Honda R&D Group have used DesignDirector to propose an optimization method that enables efficient optimized design for non-linear dynamic issues such as impact phenomena. In this example, while designing automobiles, focus was turned to the critical importance of securing survival space for the driver and passengers in the event of a frontal impact. Optimization of the thickness of the reinforcement components used in the front end and cabin allowed for a lightening of the overall weight.

Analysis Model

Fig. 1: Analysis Model

The frontal impact sedan model published by the United States' National Highway Traffic Safety Administration (NHTSA) was used with some modifications (Fig. 1).

- Approximately 51,200 nodes
- Approximately 37,000 components
- Hybrid (Dummy) on board
- PAM-CRASH used as analysis software

Analysis Conditions / Valuation Characteristics

Fig. 2: Valuation Characteristic Values

Analysis calculations were performed up through 150 msec after an assumed offset impact with a deformable barrier while traveling at 56 Km/h. The following valuation characteristics were sought: the degree of Toe-Board intrusion, the displacement between A-C pillar (Fig. 2), and the weight.

Valuation Characteristics
- Toe-Board intrusion (Y Toe-Board)
- Displacement between Pillars A through C (YA-C pillar)
- Weight (Yweight)

Experimental Design Method

Eleven components were selected from the front-end and cabin as components that could particularly absorb energy during an impact. Those components were grouped, and their thickness was made a design factor (Fig. 3).

X1Rail inner
 Rail outer
X2Front floor upper
X3Hinge pillar inner
 Hinge pillar outer
X4Rail front floor pan
X5Rocker reinforcement
 Rocker inner
 Rocker outer
X6Engine cradle-left
 Engine cradle-right

Fig. 2: design factor

The group for all factors was configured to the standards indicated in Table 1. The values shown here represent those normalized against the upper limit values for the standard values' respective design factors. In addition, each factor was assigned to an orthogonal table, L18 (21x 37) (Fig. 4), with analysis performed in conjunction with the combinations of the orthogonal tables. The valuation characteristics, Toe-Board intrusion (YToe-Board), displacement between pillars A through C (Y A-Cpillar) and the overall weight (Y weight), were extracted.
Table 1: Levels of Factors
Level 1 Level 2 Level 3
All Factor 0.5 0.75 1.00

- Assigned to the L18 (21x 37)orthogonal table.
・ 18条件の解析を実施。

Fig. 4: Orthogonal Table Assignment

Distribution analysis was performed for these valuation characteristics. Degrees that were determined to be meaningful were used to set estimate equations (Eq (1), (2) and (3)). In addition, graphs of the comparisons between estimate values and characteristic values are shown in Fig. 5 through 7.

Fig. 6: Characteristic and Estimate Values for the Displacement Between A-C Pillar

Fig. 5: Characteristic and Estimate Values for Toe-Board Intrusion

Fig. 7: Characteristic and Estimate Values for Overall Weight

Optimized Calculation

The objective function used the estimate equations for the Toe-Board intrusion and displacement between pillars A through C for the constraint function as the estimate equation for the weight found with the degree of incidence analysis. The design factors were used as continuous variables and optimized design used sequential quadratic programming. Results are indicated in Tables 2 and 3. The Initial Weight of 1514.37 Kg was decreased to an Optimum Weight of 1494.61 Kg (Table 3).

Table 2: Optimization Results
Design Factor Set 6 Factors
Objective Function Weight (Yweight) -> minimum
+0.067X32+2.42X4+0.067X42+5.69X5+5.69X52+6.05X6+0.04X62 [kg]
Behavioral Constraint Conditions toe-Board≤0.1[m]
A-C pillar≤0.035[m]
Lateral Constraint Conditions 0.5≤Xi≤1 (i= 1, 2, ... , 6)
Optimization Results Target value: 1494.61 [Kg]
Variable value: X1 = 0.55, X2 = 0.711, X3 = 0.565, X4 = 0.83, X5 = 0.662, X6 = 0.5
Table 3: Comparison between Initial State and Post-optimization
  Target value Constraint value Design Variables
Weight [kg] Toe-Board
Intrusion [m]
Displacement between
Pillars A through C [m]
X1 X2 X3 X4 X5 X6
Initial State 1514.37 0.0226 0.0720 1.0 1.0 1.0 1.0 1.0 1.0
Post-optimization 1494.61 0.1 0.035 0.5 0.711 0.565 0.83 0.662 0.5


Optimization for automobile collision safety design was performed using DesignDirector. Quantitative analysis on non-linear dynamic issue impact phenomena was made possible despite such phenomena normally being difficult to handle for optimization. As a result, a lighter weight was realized while restricting the amount of cabin deformation stemming from offset impacts.


Proceedings of the Annual Meeting of the Japan Society of Mechanical Engineers, Materials & Mechanics Division, (Vol. B), Yu, Yoshimoto, Yajima, Shiratori, Motoyama, pp. 335-336, 1998.

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