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Over the past several decades, the finite element method has become a popular technique in civil engineering for predicting the response of structures and materials; however, until recently it was rarely used in the design of roadside hardware such as guardrails, bridge rails, and sign supports.In the finite element method, complex structures are divided into a large number of small elements whose stress-strain relationships are more easily approximated. Software programs then enforce the conditions of dynamic equilibrium and the boundary conditions on each of the thousands of elements. This allows the analyst to determine the displacements and stress associated with each element.
Roadside hardware is subjected to large impacting forces, applied very rapidly, which often results in the failure of the hardware. Such structures undergo large deformations, and nonlinear changes in material and geometric properties make it difficult to predict barrier response. Until the early 1980s, nonlinear finite element analysis techniques that would address these impact problems were not available for non-defense applications.
Beginning in the late 1970s, the Lawrence Livermore National Laboratory (LLNL) developed DYNA3D, an explicit, nonlinear finite element program, to solve explosion, blast, and high-velocity impact problems. (1) The analytical tools for solving impact problems evolved throughout the 1980s, but they required highly specialized analysts and super-computer processing power. Even with the most advanced super computers of the day, many relatively simple analyses would take days or even weeks to perform. Such computing resources were not available to roadside safety researchers. However, rapid improvement in the performance and cost of scientific workstations in the past several years and the civilian conversion of defense technologies have made nonlinear finite element analysis a feasible tool for evaluating and designing roadside hardware.
The Federal Highway Administration (FHWA) is the leader in using nonlinear finite element technology on motor vehicle collision problems. Researchers from FHWA, the National Highway Traffic Safety Administration (NHTSA), and LLNL are working together to develop common tools and techniques for crashworthiness research using analytical techniques such as nonlinear finite elements. These collaborators are sharing detailed finite element models of vehicles, anthropometric dummies, and roadside barriers to not only solve problems but to improve the capabilities of these analytical tools.
At FHWA, nonlinear finite element simulations are being integrated into the roadside hardware design-test-evaluate cycle. Figure 1 shows a photograph taken from a recent crash test at FHWA's Federal Outdoor Impact Laboratory and a similar finite element model of the same physical conditions. An 820-kilogram vehicle struck a 5.5 kilogram/meter flange-channel sign post at 9 meters/second. The 13,000-element vehicle model allows the analyst and designer to examine the collision sequence in much greater detail than is possible with a full-scale crash test as illustrated in figure 2. The state of stress of any vehicle or barrier component can be examined in detail to determine the actual failure mechanisms involved in the collision.
Figure 4 - Deformation of a post from a crash test and from a finite element simulation.Vehicle and post deformations, shown in figures 3 and 4, can be compared to the tested articles to gain confidence in the fidelity of the simulation model. A full-scale crash test would only show that the post tore along its center, whereas the finite element simulation can be used to show the initiation of the tear, how the crack propagates, and the stress and strain levels when failure occurs. The tear shown in the simulation plot in figure 4 can clearly be seen in the accompanying photograph. The simulation plot shows the levels of plastic strain experienced by the post as well as the regions where the strains were high enough to cause failure. Contoured plots of stress and strains in various vehicle and barrier components, as shown in figure 4, yield useful information about how materials deform and ultimately fail in collision events. The acceleration responses can also be compared as is shown in figure 5.
If the response of a finite element model is acceptable in comparison with full-scale tests, the designer can use the model to learn detailed information about the barrier that is not available in a full-scale test. For example, knowing the stresses and strains in a particular component is crucial for correctly sizing the member. A simulation will provide the required information directly, whereas the full-scale test could never provide this information.
While there are numerous benefits to using nonlinear finite element simulations, good correlation between simulations and tests requires well-understood, validated, and often complex models. While the plots in figure 5 are reasonably similar, improvement is still needed before the models can be used with confidence. This vehicle model is being carefully validated to ensure that the model response is a good predictor of actual vehicle kinematics.
In the past, roadside hardware was designed using intuition and basic engineering principles -- the only tools available at the time. A host of highly effective roadside hardware systems were developed, tested, and installed using these basic techniques. The roadside safety problems that have remained unsolved, however, are those that have resisted solution for decades. These are problems where proper understanding of the nonlinear dynamics of the impact is crucial. These persistent problems must be viewed in new, more analytically rigorous ways. Nonlinear finite element analysis is a technique that has drastically changed other fields in engineering. These techniques have great potential as a design tool for improving the effectiveness of roadside safety hardware.
Reference
(1) R. G. Whirley and J. O. Halquist. DYNA3D: A Nonlinear, Explicit, Three-Dimensional Finite Element Code for Solid and Structural Mechanics -- User Manual, Publication No. UCRL-MA-107254, Lawrence Livermore National Laboratory, Livermore, Calif., May 1991.Malcolm Ray is a senior engineer/analyst for AEPCO, Inc. Since 1993, he has been working as a lead analyst in AEPCO's Support Services contract to the FHWA's Turner-Fairbank Highway Research Center in McLean, Va. Dr. Ray has more than a decade of experience in roadside safety research, including crash testing hardware, simulating collision events, and formulating test and evaluation criteria and design. Dr. Ray, a registered professional engineer, received his doctorate in civil engineering from Vanderbilt University.
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