A new method for designing automobile bumpers provides an optimized structure in a matter of days compared to weeks or even months that are required using traditional methods. Normally, engineers build intricate finite element models, which typically take several days to determine the viability of each design concept. The new approach involves using a computerized engineering handbook, which can provide a fairly accurate estimate of the viability of each concept in less than an hour. Using this method, engineers are able to quickly evaluate a large number of alternate approaches and only use finite element analysis to validate the final design.

Structured Solutions is an engineering consulting firm that specializes in structural analysis work for automobile companies and other manufacturers. The company is a leader in the design of bumpers, having completed eight such projects in the past year and a half. In a bumper design project, the automobile OEM typically provides the vehicle mass, package space, allowable rail loads and mass and cost targets. Frequently, the automobile OEM will also supply line data for their first concept bumper system.

The normal assignment for the engineering firm is to develop a bumper within these specifications that will experience limited damage to the bumper system and none to the rest of the vehicle. It should be noted that current government regulations specify a 2.5 mph barrier standard but all major North American manufacturers are currently designing to the more stringent 5 mph standard. Normally, the engineering consultant begins with the OEM's concept, or if it wasn't supplied, develops his or her own. This concept is then subjected to analysis with a high-end dynamic finite element code such as LS-DYNA3D, PAM-CRASH and ABAQUS. Developing the finite element model normally takes weeks. In most every case, the initial concept does not meet requirements which means the consultant must repeat this process, often up to a dozen times, until they have found an acceptable design.

The new approach begins with a series of quick studies to quickly determine whether or not the initial design concept is viable. The consultant begins by estimating the amount of kinetic energy that will be absorbed by the energy absorbers. The amount of energy transmitted to the bumper depends on the type of energy absorber used and is typically 20% to 30% of the total. The total energy of the crash is equal to 1/2 MV2 where M is equal to the mass of the vehicle and V is equal to the velocity at impact. Then engineering calculations are performed with a hand calculator or on a spreadsheet to determine the required stiffness of the beam.

The next step is the hardest: determining whether the beam under consideration has the required stiffness. The stiffness of a beam is equal to CEI/L3 where L is the length of the beam, E is the modulus of elasticity of the material used in the beam, I is the moment of inertia, and C is a dimensionless constant (which is a function of the boundary conditions) whose value is typically taken as between 70 and 100. The difficult part of solving the equation is, of course, determining the moment of inertia of the prospective bumper section.

This is virtually impossible with hand calculations because post-buckling stress will render a certain portion of the cross-section ineffective, resulting in a classic "chicken-and-egg" scenario. For example, the moments of inertia are needed to calculate the stress conditions under applied load to determine the effective width of each segment, which is required to determine the moments of inertia. This means that an extremely tedious and time-consuming series of calculations are required to iterate to a solution despite the fact that the equations involved are straight-forward.

Recently, a computer program has been developed that automates the process of determining effective properties of sections with arbitrary shapes. The program, called Geometric Analysis of Sections (GAS), uses an iterative procedure to compute the stress distribution and corresponding effective properties until the results converge. The effective properties of the section are computed using effective width calculation results. The effective width calculations are based on the Cold-Formed Steel Design Manual and Automotive Steel Design Manual published by the American Iron & Steel Institute. To facilitate the effective property calculation for coldformed steel cross sections, the Auto/Steel Partnership (A/SP) and The American Iron and Steel Institute (AISI), Southfield, Michigan, sponsored the development of GAS and its integration into the AISI Computerized Application and Reference System (AISI/CARS), a computerized version of the Automotive Steel Design Manual. The software was developed by Desktop Engineering Int'l Inc., Woodcliff Lake, New Jersey.

In the AISI Automotive Steel Design Manual, the effective width concept is used to account for the post-buckling strength of a thinwalled section. The post-buckling strength is the additional load carried by portions of the cross section, after they have buckled locally, by means of a redistribution of stress. Under the effective width concept, only certain portions of the section width are considered to be effective in carrying loads after exceeding the local buckling stress and the nonuniformity of stress distribution in the section is accounted for by replacing the actual section width by a reduced effective width such that the total area under the stress distribution curve is the same. The effective width of a cross section area is a function of a number of parameters such as boundary condition, stress state, material and width to thickness ratio, etc. The stress distribution cannot be computed until the cross section property is calculated. Therefore, it is necessary to assume a certain stress distribution and compute the associated effective property. This process can be an iterative process, which is shown in the examples in the Automotive Steel Design Manual.

The GAS program performs these iterative calculations and determines the moment of inertia of the section. First, the consultant selects the material properties from the program's database. Then, he or she defines the geometry of the section and it's thickness. The program then analyzes the section and determines its moment of inertia. The entire process generally takes less than a minute. Since the consultant knows the moment of inertia that is required to meet the collision standard, he or she can quickly evaluate different thicknesses to determine the minimum thickness that will provide the desired stiffness. Often, the thickness that is required to meet the stiffness requirement will cause the bumper to exceed the weight requirement. In that case, it is generally necessary to try another section. The key advantage of this approach is that in an hour the consultant knows whether or not the section design will work, compared to weeks with the old approach.

The new approach makes it possible to evaluate a much wider range of alternatives and in this way optimize the design rather than simply meeting the specifications. For example, the consultant can consider a stamped C section versus a rollformed W section as two different options and provide the OEM with required thicknesses for either approach to allow for an objective comparison. Sometimes the beam that is not the optimum from a structural standpoint is preferable for other reasons. For example, in one new vehicle the OEM is storing a washer fluid bottle in a C section. But, in any case, having complete information leads to better design decisions.

It's important to note that the computerized engineering handbook is used as a filter rather than a replacement for full-blown finite element analysis. The bumper beam that is selected using the handbook is still subjected to the complete analysis for validation. While the results are typically quite close, finite element analysis requires fewer assumptions and thus provides more accurate results. It's important to note that, because of the complexity of finite element analysis, it's possible for an analyst to make an error that could lead to seriously misleading results. The upfront handbook analysis providing a verification step that virtually eliminates this danger.

This new approach has been a key factor in the success of Structured Solutions in the automotive engineering market. Many of its competitors burn up time by rushing to the computer to do a full-blown analysis while the company can accomplish far more in a shorter period of time using a computerized handbook. A key advantage of the handbook approach is that it exercises basic engineering skills, which keep the engineer in closer touch with the fundamentals of the design. Applying this approach to bumper design is a key reason that the company has been awarded 8 different bumper programs by automotive OEMs in the last 18 months.