handbook engineering section12 transportation ch83

7/31/2019 Handbook Engineering Section12 Transportation Ch83

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Khalil, T. B. Safety Analysis

The Engineering Handbook.

Ed. Richard C. Dorf

Boca Raton: CRC Press LLC, 2000

1998 by CRC PRESS LLC


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83Safety Analysis

83.1 Mathematical ModelsLumped Parameter Models Hybrid Models Finite Element Models

83.2 Summary

Tawfik B. KhalilGeneral Motors Corp.

Safety of transportation systems, including land, water, and space vehicles, can be defined as theability of the vehicle structure to provide sufficient protection to mitigate occupants' harm and to

reduce cargo damage in the event of a crash. This goal is typically achieved by a combination of

structural crashworthiness to manage the crash energy and by a system of restraints within the

passenger compartment to minimize the impact forces on the human body during the second

collision. Crash energy management is viewed here as absorption of the crash kinetic energy of the

vehicle while maintaining sufficient resistance to sustain the passenger compartment

integrity.

Safety studies for land motor vehicles, the subject discussed in this chapter, are accomplished by

a combination of experimental and analytical techniques. Experimental techniques involve sled

tests, in which mechanical surrogates of humans (anthropomorphic test devices, or "dummies")

are subjected to dynamic loads similar to a vehicle decelerationtime pulse to study occupant

response, in either frontal or lateral impact modes. The measured dummy kinematics and

associated loads (moments) provide a measure of the impact severity and the effectiveness of the

restraint system in reducing loads transferred to the occupant. Another type of test typically run to

ensure total vehicle structural integrity (crashworthiness) and compliance with

government-mandated regulations is the full-scale frontal vehicle to barrier impact. In this test a

fully instrumented vehicle with a dummy in the driver seat is launched to impact a rigid barrier

from an initial velocity of 30 mph. Other tests include side impacts, rear impacts, and rollover

simulations.

Such experimental studies are not only time consuming but also expensive, particularly at the

early stages of design, where only prototype vehicles are available. The need to simulate the crashevent by an analytical procedure is obvious. This chapter addresses the use of analytical techniques

in design of transportation systems, with particular emphasis on motor

vehicles.



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Developing mathematical models for structural crashworthiness and occupant response to impact is

conceptually easy; it involves solving a set of partial differential equations that govern the response

of structures to dynamic loads, subject to initial and boundary conditions. In practice, however, the

problem is complicated due to the following factors:

The crash process is a dynamic event persisting for a short duration of approximately

100200 milliseconds.

Vehicle structures are typically complex in geometry, manufactured from metallic and

composite shell components, and assembled by various fastening techniques.

Biomechanical simulation of human or mechanical surrogates to impact requires extensive

knowledge of human anthropometry, biological tissue properties, and human tolerance to

impact.

The governing equations are highly nonlinear due to large deformations, large rotations,

buckling, elastic-plastic rate-dependent material response, and contact and folding in the shell

structures.

Given the aforementioned factors, it is not surprising that analytical simulations of vehicle

collisions and occupant response to impact have been evolving over the last 25 years. Three types

of models are used in safety simulations: lumped parameter models (LP), hybrid models (HM),

andfinite element (FE) models.

Lumped Parameter Models

The first vehicle structure LP model was developed [Kamal, 1970] by using lumped spring-mass

components. It simulated the vehicle response to frontal impact into a rigid wall by a

unidimensional model consisting of three masses, which represented the inertia of the vehiclebody, engine, transmission, and drive shafts. The masses are interconnected by nonlinear springs to

simulate the compliance of the vehicle structure. The force-deformation characteristics of the

springs are determined by quasi-static crush of vehicle components, which incidentally require

significant experience on the behavior of thin sheet metal structural components subject to large

deformations and various end conditions (e.g., fixed, hinged, or free). This type of model is still

widely used by crash engineers because of its simplicity and surprisingly relative accuracy in

comparison with test data. In fact, this modeling approach has been extended to simulate side

impact collisions between two vehicles. It is important to note, however, that developing such

models relies on experimental data and extensive experience on structural behavior in crash

environments. Further, translating model parameters into design data is not immediately

obvious.

Two-dimensional and three-dimensional LP models [Prasad and Chou, 1989] are also developed

to simulate occupant response to deceleration pulses generated by vehicle structures. These models

consist of a group of masses that simulate the inertia and CG locations of anthropomorphic

dummies used in crash testing. The dummy segments are connected by joints with appropriate

moment-rotation and force-deformation characteristics to represent biomechanical human

articulation. Interactions between the dummy model and the passenger interior compartment are

achieved by specifying force-deformation curves between the dummy segment and the potential

83.1 Mathematical Models



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contact target. Figure 83.1shows an example of a three-dimensional average size dummy model

used in crash simulations. Similar to LP models of vehicle structure, the occupant models are

relatively simple to develop and not computationally demanding. In fact, all LP models can be run

in minutes on an engineering workstation or a personal computer.

Figure 83.1 Three-dimensional LP model of a seated dummy, represented by ellipsoidal rigid bodiesinterconnected by appropriate joints.

Hybrid Models

Hybrid models were developed to remedy the limitations inherent in the LP spring-mass models.

The modeling technique, simply, recommended calculation of the force-deformation component

response from structural mechanics equations, instead of testing, which would subsequently beused as the spring property in the LP model. The recommended components initially were generic

S-shaped hollow beams built from thin sheet metal [Ni, 1981]. Two beams typically represent the

lower or mid-rails (also referred to as torque boxes ) of the vehicle and represent the main

longitudinal load-path carriers from the bumper to the vehicle body. The analysis was

accomplished by a finite difference solution, which treated the shell structure by a series of beams

with appropriate geometry and material models. Plastic behavior at the hinges was accomplished



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by a moment-rotation curve, derived experimentally. Although the component response can be

calculated in three dimensions, due to the inability of the LP technology to superimpose

path-dependent plastic deformations, the analysis allowed only uniaxial deformations. Further, the

boundary conditions at the spring ends cannot be accurately represented. These limitations

rendered the technique approximate. Yet, it is commonly used in vehicle design due to itssimplicity and to its low requirements of computer resources.

Finite Element Models

There are two types of FE models, discussed in the following sections, that are used in structural

crashworthiness:

Heuristic Beam Models

Heuristic models (semianalytical models) are formulated by complementing the equations of

mechanics with experimental data and empirical information. These models are developed to

provide design guidelines for vehicle structure at the early stages in vehicle conception. Four typesof models are constructed and analyzed in parallel to investigate the synergy between the major

collision modes, namely, front, rear, side, and rollover impacts. At the early stage in vehicle

design, crashworthiness is considered in parallel with other design requirements, such as

packaging, vehicle dynamics, noise and vibrations, and so on. Accordingly, a computationally

efficient scheme along with a fast process to build models is necessary. This led to the

development of FE beam models [Mahmood and Paluzeny, 1986], which define all major

components of the vehicle skeleton by means of beam elements. With skill and experience, the

influence of connecting panels can be included in the analysis.

The basic building blocks of these models are structural members that are referred to as columns

when subjected to uniaxial compression and as beams when subjected to bending deformations. In

either case these components are manufactured from stamped thin sheet metal. Column membersare typically exposed to axial or slightly off-angle loads, which can produce progressive

(accordion) crush, as shown in Fig. 83.2 . This type of progressively stable collapse, highly desired

in energy absorption, requires a compressive load smaller than the Euler buckling load and larger

than the plastic yield of the column plates. Unstable column collapse, which can include some

folding, is less efficient in absorbing energy.



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Beam bending is the dominant mode of collapse in many vehicle structures, due to its need for

the least amount of energy. Collapse by pure bending is rare. In most vehicle crashes, structural

deformations involve a combination of axial compression, bending, and torsion. Component

collapse will initiate where the compressive stress exceeds the material yield/local-buckling

strength by forming a plastic hinge. The structure cannot continue to support an increasing load at

the hinge and stress redistribution occurs, followed by the formation of more plastic hinges. This

continues until eventually the structure evolves into a kinematically movable framework, as shown

inFig. 83.3. Therefore, it is important that the model captures the plastic hinge formations and

subsequent linkage kinematics effects.

Figure 83.2 Schematic of axial compression of a straight column, showing progressive formation ofaccordion folds.



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Approximate formulas, based on a force method or a displacement method, are derived

[Mahmood and Paluszny, 1986] to determine the peak and average crush loads on the basis of

local buckling and plastic yielding of thin-walled columns and beams. The component geometry is

subdivided into plate elements, which are joined by nodes. A computer program is developed to

determine the maximum load-carrying capacity of vehicle structures and subsequent energy

absorption following large deformation collapse of the structure. The computation can account for

compression and biaxial bending deformations.

Analytically Based FE Models

All previously cited models require some prior knowledge of the potential failure mechanism of

the structure, in addition to experimental data as input to the model. It has always been the desire

of safety engineers to develop analytically based models for vehicle crash and occupant dynamics

simulations. These models should be based on the physical process involved in the crash

eventgeometry of the structure, basic stress-strain response of the material, initial conditions of

impact and boundary/constraint conditions. This type of analysisknown in mechanics as

initial-boundary value problemrequires the solution of a nonlinear, coupled system of partial

differential equations that can only be applied to extremely simple geometries. Accordingly,

classical closed form solutions are nearly inapplicable to real-world structural mechanicsproblems.

FE technology was introduced in the early 1960s for linear structural analysis, in which the

geometry of the structure can be discretized into a set of idealized substructures, called elements.

Several Fortran computer codes were developed, for both research and commercial applications.

Application of the FE technology to crashworthiness analysis did not gain serious momentum until

the mid-1980s, due to accelerated advances in explicit time-integration nonlinear FE technology

Figure 83.3 Schematic of S-rail bending deformations, showing plastic hinge formations and subsequent

linkage-like kinematics.



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[Liu et al., 1986] and due to the development of FE codes with reduced integrated elements for

spatial discretization and versatile contact algorithms [Goudreau and Hallquist, 1982]. In addition,

the introduction of supercomputers provided the necessary impetus for applying the technology to

practical problems.

FE crash codes are based on updated Lagrangian mechanics. The equations of motion areobtained from stating the balance of linear momentum in an integral form and introducing spatial

discretization by linear isoparametric elements. The semidiscretized second-order set of equations

of motion can be written as

Ma = P(x; t) Q(x; t)

where M is the diagonal mass matrix, a is the acceleration vector, P is the external force vector,

Qis the nodal internal force vector,x is a spatial coordinate, and tis time. The solution of the

previous set of equations in time is accomplished by the explicit central difference technique. The

integration scheme, though conditionally stable, has the advantage of avoiding implicit integration

and iterative solution of the stiffness matrix.Initially, this technology was applied to analyze generic components (columns and S-rails) with

emphasis on analytically capturing the plastic hinge formation, peak load, sustained collapse load,

and associated energy absorption. Following this, a number of simulations modeled structural

components manufactured from thin sheet metal and assembled by spot welding [Khalil and

Vander Lugt, 1989].Figure 83.4shows the initial and deformed configurations of the front-end

structure of an experimental vehicle launched to impact a rigid wall from an initial velocity of 50

km/h. The model simulated the structure by predominantly quadrilateral shell elements, which

allows for both bending and membrane deformations. Elastic-plastic material properties with

appropriate strain hardening and rate effects were assigned to the shell elements. Constraint

conditions were used to tie the shell nodes where spot welds were used. A single-surface contact

definition was specified for the frontal part of the structure to allow for sheet metal stacking

without penetration. The predicted peak force from this impact was 250 kN, which agreed quite

well with test data.



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After advances in the ability of FE technology to simulate subsystem impact response, the

methodology was extended to simulate full-scale vehicle collisions. Current simulations include

frontal vehicle collision with a rigid barrier, commonly conducted for compliance with federal

safety standards.Figure 83.5shows an FE model of a vehicle structure before and after impact

with a rigid barrier from an initial velocity of 50 km/h [Johnson and Skynar, 1989]. Other models

of vehicle structures simulate a movable deformable barrier impacting the side of a stationary

vehicle. Also, simulations of vehicle-to-vehicle frontal impact as well as rear impact have been

successfully attempted.

Figure 83.4 FE model of a vehicle structure front end, launched to impact a rigid barrier from an initial

velocity = 50 km/h.



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Figure 83.5 FE model of frontal vehicle collision with a rigid barrier, initial velocity = 50 km/h.



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Recently, the technology has been extended to simulate air bag inflation and deployment of

driver-side and passenger-side air bags.Figure 83.6shows an isolated, folded driver-side air bag in

its initial configuration and its shape subsequent to inflation. Of particular interest here, from the

FE simulation point of view, is the technology's ability to simulate the bag fabric material, which

can sustain tension and no compression; the gas dynamics and their interaction with the bag toallow for pressurization and controlled leakage; and, finally, the contact and interactions among the

bag layers, which should allow for deployment without penetration.

Figure 83.6 FE simulation of driver-side air bag inflation.

The limitation of using LP models in simulating occupants has been recognized for some time.

With the success demonstrated in simulating vehicle structures, analysts were encouraged to

extend FE analysis to simulate occupant interactions with interior passenger compartments [Khalil

and Lin, 1991].Figure 83.7shows an FE model of a dummy used to simulate an occupant in crash

testing.



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83.2 Summary

Several analytical techniques are used in safety analysis to simulate vehicle structural response and

occupant behavior in a crash environment. Early models include lumped-parameter, hybrid, and

FE heuristic beam models. These models are characterized by gross geometric approximations,

and, consequently, they are quick to develop and require minimum computer resources that can be

provided by a PC. In the past seven years, detailed representations of vehicle structures by FE

models have evolved in size and complexity from geometries represented by 2800 shell elements

with one or two material models to current models simulated by over 50 000 shell, solid, and beamelements. These models also include several material representations for metallic and nonmetallic

components. Currently, vehicle models exist in the open literature for frontal, side, and rear-impact

simulations. Also, modeling of occupant interactions with inflatable restraint systems has recently

been published and discussed. It is anticipated that in the near future (within five years) system

models representing vehicle structures, occupants, and restraint systems will be in the

neighborhood of 100 000 elements and will become a routine design tool in the transportation

Figure 83.7 FE representation of a seated dummy with three-point belt harness.



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industry. However, this increase in model sizecoupled with demands for lighter vehicles

manufactured from materials such as aluminum and compositeswill require new developments

in FE technology and hardware architecture to allow for reducing model development effort and

computation time.

Defining Terms

Anthropomorphic: Describes a mechanical manikin that possesses geometric, inertial, and

material characteristics similar to a human's.

Crashworthiness: The ability of a vehicle structure to absorb mechanically energy resulting from

collision with another object while maintaining integrity of the passenger compartment.

Heuristic model: A model formulated from discrete deformable elements with built-in empirical

knowledge.

Hybrid model: A lumped parameter model in which the discrete springs are replaced by

deformable components.

Lumped parameter model: A mechanical system model that represents a continuum structureby discrete masses, springs, and dampers.

References

Goudreau, G. L. and Hallquist, J. O. 1982. Recent developments in large-scale finite element

Lagrangian hydrocode technology. Comp. Methods Appl. Mech. Eng. 33: 725757.

Johnson, J. P. and Skynar, M. J. 1989. Automotive crash analysis. In Crashworthiness and

Occupant Protection in Transportation Systems, ed. T. B. Khalil and A. I. King, p. 2733.

AMD-Vol. 106, BED-Vol. 13. ASME, New York.

Kamal, M. M. 1970. Analysis and simulation of vehicle to barrier impact. SAE.

700414:14981503.Khalil, T. B. and Lin, K. H. 1991. Hybrid III thoracic impact of self-aligning steering wheel by

finite element analysis and mini-sled tests. In 35th Stapp Car Crash Conference

Proceedings. Paper No. 912894. SAE, Warrendale, PA.

Khalil, T. B. and Vander Lugt, D. A. 1989. Identification of vehicle front structure

crashworthiness by experiments and finite element analysis. In Crashworthiness and

Occupant Protection in Transportation Systems, ed. T. B. Khalil and A. I. King, p. 4153.

AMD-Vol. 106, BED-Vol. 13. ASME, New York.

Liu, W. K., Belytschko, T., and Chang, H. 1986. An arbitrary Lagrangian-Eulerian finite element

method for path-dependent materials. Comp. Methods Appl. Mech. Eng. 58: 227245.

Mahmood, H. F. and Paluzeny, A. 1986. Analytical technique for simulating crash response ofvehicle structures composed of beam elements. In Sixth International Conference on Vehicle

Structural Mechanics. Paper No. 860820. SAE, Warrendale, PA.

Ni, C. M. 1981. A general purpose technique for nonlinear dynamic response of integrated

structures. In Fourth International Conference on Vehicle Structural Mechanics. SAE,

Warrendale, PA.

Prasad, P. and Chou, C. C. 1989. A review of mathematical occupant simulation models. In



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Crashworthiness and Occupant Protection in Transportation Systems, ed. T. B. Khalil and

A. I. King, p. 95113. AMD-Vol. 106. ASME, New York.

Further Information

ASME Winter Annual Meeting Proceedings: published annually by the Applied Mechanics

Division.

Vehicle Structures Mechanics Conference: published biannually by the Society of Automotive

Engineers (SAE).

U.S. Department of Transportation, International Conference on Experimental Safety Vehicles:

published biannually by the National Highway Traffic Safety Administration.

Stapp Car Crash Conference: published annually by the Society of Automotive Engineers (SAE).

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