Study on Optimal Design of Automotive Body Structure Crashworthiness

In this paper the optimal model of thin-walled sections of automotive body for structural crashworthiness is built. With computer design of experiment (DOE), the response surface model (RSM) of design can be obtained by carefully choosing a small quantity of samples in the design space. Pareto genetic algorithm (GA) is used in subsequently optimal design. With optimal design of thin-walled sections, the effects of the section parameters such as dimension and thickness on crashworthiness property are researched. Simulation Technology (2) 7 International LS-DYNA Users Conference 9-42 INTRODUCTION Improving the safety of automotive is one of main content researched by world automotive industry now. Body structure has played a significant role in automotive passive safety. Improving body structure design by impact test and computer numerical simulation technology has an active action on advancing the body crashworthiness. In recent years there has been a close attention on optimal design of body crashworthiness. Optimal design of impact structure is a difficult problem due to the nature of numerical crashworthiness analysis. The instability and uncertainty of impact analysis make the simulation process having to go through several iterations before obtaining one satisfactory result. At same time, because of the cost of explicit FEA, the fully integrated optimization process becomes impossible. During the nonlinear dynamic analysis such as impact analysis, the derivatives of response functions are mostly extraordinary discontinuous. With the assistance of global approximation method such as response surface methodology, the design response can be smoothed and obtaining a global optimal result becomes relatively easy. In this paper the optimal model of typical part with thin-walled sections in automotive body is built. With HyperMesh as preand post process tools, LS-DYNA as calculating core, the structural crashworthiness is analyzed. With computer DOE, the response property of design can be obtained by carefully choosing a small quantity of samples in the design space. The response surface models of the optimal objects are built with the basis of these samples and used in subsequently optimal design. Then the functions of response surface models are analyzed by Pareto GA to obtain the multi-objective optimal results. The crashworthiness index which indicate the deformed energy absorbed by unit mass structure, the maximal impact force, the mean impact force etc. are the basic indexes to evaluate the crashworthiness optimal design. With optimal design of the part with thin-walled sections, the effects of the section parameters such as dimension and thickness and connection type on crashworthiness property are researched. OPTIMAL DESIGN MODEL OF THIN-WALLED SECTIONS FOR AUTOMOTIVE BODY STRUCTURAL CRASHWORTHINESS Design Objective There are several indexes to measure the crashworthiness, which indicate the property of structure to endure the impact: Crashworthiness Index c η . The definition of crashworthiness index is: under some limit conditions, the number of energy by unit structure mass to absorb, that are s d c M E = η (1) where, d E is the absorbing energy of structure; s M is the mass of structure. For the thin-walled sections having same section shape, the crashworthiness index can be calculated used by the following equation (OHKUBO, 1974 ): ( ) l A P s m = c η (2) where, m P is the mean crash force; s A is the area of section; l is the length of the thin-walled sections. 7 International LS-DYNA Users Conference Simulation Technology (2) 9-43 Maximum Crash Force max P (or Maximum Acceleration). The maximum crash force acquired from the experiment may be occurred at two positions: one is at the beginning of bulking which is critical state determined by the structure elastic-plastic bulking. The other is at the end of the collapse when the whole structure is collapsed and the crash force rose quickly as radiation. In the structure impact study, the former peak value is mainly considered, which has important significance to structural failure and respectively less effect to the energy absorbing ability. Mean Crash Force m P . The mean crash force is the mean value of crash force curve vs. collapse displacement, which indicates the whole energy of the thin-walled sections absorbed. Design Parameters The energy absorbed and the mass of structure are determined by the section dimension and thickness of the thin-walled sections. So the design parameters are the following (Figure 1): Figure 1. Design Parameters of the Thin-walled Sections Section dimensions: 3 2 x x < Thickness of the front segment: 1 t Thickness of the rear segment: 2 t Design Constraints To assure the rear segment not collapsing before the front segment of the thin-walled sections, the thickness of rear segment must be larger than the front segment. That is 3 2 x x < (3) The maximum crash force can not be above 100KN, that is KN Pmax 100 < (4) DESIGN OF EXPERIMENT (DOE) FOR STRUCTURAL CRASHWORTHINESS When constructing RSM for the thin-walled sections crashworthiness, the appropriate DOE are adopted to calculate the coefficients of RSM, acquiring enough observation value of response parameters and making RSM constructed easily. From the experiment scheme with minimum experiment points, the number of experiment points should be equal to the number of coefficients in the RSM. This experiment program is named saturation experiment program, which has fewer freedoms. So the experiment program with residual freedoms is adopted generally, which is the number of experiments N larger to the number of coefficients in the RSM. For example to the quadratic RSM (see equation Simulation Technology (2) 7 International LS-DYNA Users Conference 9-44 6), the number of the coefficients is ( )( ) 2 2 1 1 2 + + = + + + = n n C n n q n . To construct the quadratic RSM, the number of experiments is not less than q . In the RSM design, even if the design parameters are fewer, the full-factors experiment is not adopted generally for the residual freedoms are larger. So the experiment design such as the orthogonal design, central combination design and equal square design can be adopted generally. Code Transformation In the RSM design, the variety range of every design parameters may be different, even for some parameters with large variety. To deal with them easily, the linear transformation, named code transformation is adopted properly to the value of design parameters and the corresponding relationships between the parameters level and codes are built. The code transformation makes the range of factors transforming to the cube with its center at origin and overcome the difficult of different dimensions in the design and analysis. Three design parameters are a , 1 t , 2 t and every parameter has two levels. The levels of design parameters are showed in table 1. Three design parameters are transformed as the following formulation correspondingly: 10 90 1 − = a x 5 0 5 1 1 2 . . t x − = 5 0 5 1 2 3 . . t x − = (5) Central Combination Design The central combination design is consists of n 2 factor design points with two levels, n 2 axial points and c n central points. Among them the axial points are distributed symmetrically on n coordinate axles with the origin point as central. The distance between the axial points and the central points is named axial arm γ and γ is a coefficient determined by the orthogonality of DOE. The central points are points when every design parameters are taken as 0 level and the experiments of the central points can be done once or more repeatedly (TIEMAO, 1990). For code variable, the coordinates of experiment points are showed in table 2. The numeric experiments are processing by the central combination design matrix D . The results of DOE are showed in table 3.                       