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Visualizing cross section forces
Comput. & Graphics, Vol. 19, No. 3, pp. 475480, 1995 Copyright CD1995 ElsevierScienceLtd Printed in Great Britain. All rights reserved 0097-8493/95 $9.50+ 0.00
oo!v-8493(95)ooo19-4
Short Technical Note
VISUALIZING
CROSS SECTION
FORCES
JOHN D. REID Department of Mechanical Engineering, University of Nebraska, Lincoln, NE 685880656, U.S.A. Abstract-A visualization technique is presented that can signiticantiy advance the comprehension of the forces and moments that exist throughout a structure during a crashevent. This is made possible through colored, scaled vector display of the forces at individual cross sections. Animating the deformed geometry while displaying cross section forces gives the analysts a detailed view of what is happening in the structure. This deeper understanding can be used to help design a structure for optimum crashworthiness performance. 1. INTRODUCTION
crosssectionforcesand momentsis a very effective tool in the designingof structures undergoing impact conditions.This analysiscan be usedto increaseunderstanding of system behavior, verify model accuracy, understand and control pitch, quantify inertia relief, perform subsystemmodeling, and develop reducedordered models.This analysis, however, is currently done through analyzing numericaldata. The goal of this paperis to introduce a visualization technique that can significantly advance the comprehension of the forces and momentsthat exist throughout a structure during a crashevent. Analyzing
In this research, LS-DYNA3D is used as the simulationtool. Thus, its implementationof calculating cross sectional information will be discussed. Additionally, discussion will be limited to forcessince they are our primary concern.However, momentsare calculated similarly and their visualization (as describedin the next section) are the sameas for forces. Crosssectionsare definedby specifyingthe nodes of the crosssection and the elementsto be usedto calculate the forces at thosenodes.The sign of the forces transmitted are determinedby which side of the nodesthe elementslie on. In general,the load is comprisedof two components:elementstiffnessand massinertia. The equilibriumequationof a node on a crosssectioncanbe written usingNewton’s2nd Law:
2. CROSS SECITON FORCES
F+f=
Crosssection analysisis well suited to analytical tools rather than experimentalmethods.The reason for this is that it is very difficult, if not impossible,to position load cells within a deforming structure without altering its stiffness. Sectionforces and momentscan be usedto get an overall view of how a structure is performing.At any point in time, the split of forces betweenthe main structural pieces(e.g., the upper rail, midrail and engine cradle on a typical passengercar) can be compared, as well as how those forces compare to surroundingstructure (e.g., the barrier on a frontal barrier test). Additionally, individual components can be analyzed to seehow and when they transmit loads, and absorbenergy throughout an event [l]. Typical nonlinearf&rite elementcodes,suchasLSDYNA3D [2] and PAM-CRASH [3], allow the engineer to define cross sectionsthrough various parts of the structure. Both codes calculate the transmission forces through these defined cross sections.Additionally, LS-DYNA3D calculatesthe moments,the centroid location, and the areaof each cross section. All quantities mentioned above are functions of time, including centroid location and area.
mass* acceleration,
(1)
whereF= nodal force due to the stresses in the cross sectionelements,f= interface forces. Equation 1 can be usedto solve for the interface forces (alsoknown as transmissionforcesor section forces). Accelerationsfor eachnode and stresses for eachelementare calculatedthroughout a simulation, thus computingcrosssectioninformation is relatively inexpensive.This equation is a vector, resulting in global X, y and z forces (as opposed to a local coordinate system). Mass is allocated by LS-DYNA3D to ensureequal and opposite forces when choosingelementson onesideof the nodesversusthe other side. Section output from the simulation can easily be graphedas functions of time. The objective of this researchis to extend the functionality of this section analysisthrough visualization. The next sectionwill detail this extension.
475
3. GRAPHICAL DISPLAY
Cross section plots are very useful for section analysis,however, it is still hard to actually visualize the forcesgoing through the structure over time. For
476
J. D. Reid
this reason, a method for displaying the cross section forces directly on the deforming geometry was created. The idea is to display 3-D vectors representing the force through the cross section. For each cross section a scaled vector is displayed at all nodes defming the section. In addition to being scaled, the vectors are also colored to indicate magnitude. This can be done for all sections, a subset of sections and/ or just portions of individual sections. The visualization is available for any desired time throughout the crash event. Since graphical programs used to post-process simulations currently do not support this functionality, methods were developed to “trick” the software into displaying the desired information. This process has been done with three separate graphical packages, HyperMesh [4], I-DEAS [5] and LSTAURUS [6]. Each implementation was slightly different but the end results were all satisfactory. Here we describe the HyperMesh implementation, but will use IS-Taurus output for figures because they make more suitable hardcopy. The general process for visualizing cross section forces is as follows: (1) Include appropriate information in the model. l Degne desired cross sections. 0 Save section forces at 10 pts per ms. l Save the deformed geometry at desired intervals during the crash (usually between 2 and 5 ms> (2) Run the simulation. (3) Convert the deformed geometry into suitable format for the post-processor. (4) Process the section force file. l Filter the section data. l Sample the section data at the same interval the deformed geometry was saved. s Save the processed section data. (5) Relate section forces to defined cross sections. l For each cross section For each node in each cross section For each time step Assign the appropriate section forces 6, Y, z, n=gnitude). l Save this data in the appropriate vector format. (6) Run the post-processor. l Read in the initial model. l Read in the deformed geometry. l Read in the force vector data. l Display the deformed geometry while displaying the vector information at a desired time. The key in this process is the vector format and display steps listed above. In HyperMesh, the user has access to vectors that represent displacements. By placing force vector information into displacement vector slots we can then display these “displacement” vectors, obtaining the desired force visualization.
The display can actually be done in a sequence, providing an animation of the simulation while at the same time visualizing how the forces change magnitude and direction throughout the crash event.
4. APPLICATION
I-VEHICLE
STRUCTURR
One application that this visualization technique has been found to be useful is in vehicle crashworthiness. As a vehicle crushes during an accident it is critical that the kinetic energy be absorbed efficiently by the structure. In addition to absorbing energy, the frame structure also helps control the pitch of the vehicle. Efficient energy absorption and controlled pitch are keys to avoiding occupant injury. Therefore, the design of the structure must be thoroughly investigated to ensure good crash performance. One of the keys to this understanding is to know the load path through the vehicle as it undergoes a crash event, Figure 1 shows a quarter vehicle model used to predict the vehicle performance in a frontal collision, This type of collision is a regulated requirement for all passenger vehicles (FMVSS 208 [7]). During collision the load has multiple paths to be carried. Primary paths for many vehicles include the frame structure load path, the engine load path and the cradle load path. The frame structure load path generally absorbs the most energy and is the one studied in this project. Six cross sections were made in the quarter vehicle model as shown in Fig. 2. These cross sections consist of two slices through the structure. Each slice is broken into three sections, one each for each component of the structure. Those being, the midrail, wheelhouse and upper rail. The forces and moments are calculated during the simulation as described previously. Using the results, we apply the visualization technique in order to increase understanding of the crash event. Results of the visualization at 35,45,55 and 65 ms are shown in Fig. 3. From the visualization we can readily determine the following: (1) The midrail is the major load carrying component of the structure during the time period of iuterest. (2) The midrail load drops considerably during plastic deformation. (3) The load through the midrail is primarily along the direction of the vehicle. (4) The load varies considerably throughout the crush. (5) The load through the wheehouse is angled, meaning that its load partially comes from “bleed-off” of the midrail. (6) The load through the upper rail section is relatively minor. This could indicate a deficiency in the vehicle being able to control pitch of the vehicle.
Visualizing cross section forces
Upper Rail
Ise
Lower Tie-Bar Fig. 1. Vehicle side structure.
cs 5
CS - Cross Section Fig. 2. Defined cross sections.
5. APPLICATION
D-GUARDRAIL
DESIGN
Another application of the load path visualization technique dealswith a redesignof a turned-down guardrail. There are many different types of guardrails, one particular type installedon many highways in severalstatesiswhat is known asthe turned-down guardrail. Theseguardrailswere designedand tested usingall recommendedtestingproceduresat the time of their development. Unfortunately, a recent problem hasbeendiscoveredthat wasunforeseenduring development.When a smallvehicle rides up the end of the guardrail, there is a potential for the rail to stay firmly attached to the poststhat hold it up. This in turn can causea small vehicle to roll-over, The smaller sixed vehicles were uncommon during the developmentof the original turned-down guardrail.
Detailed background on this guardrail can be found in ref. [8]. Figure 4 depicts a simulation of a small vehicle riding up a guardrail. The objective is to develop a retrofit to the existing guardrail without totally removing the current ones and without excessive costs. Previously, guardrail design has been done usingsimplehand calculationsand a lot of physical testing.The computersimulationof this type of event is relatively new. The root causeof the guardrail failing to behave properly was determined through simulation, By examiningcrosssectionsin the rail before and after post 1 it was possibleto determinethe forces and momentsthat were holding the rail up. The cross sectionanalysisshowedthat during the impact, the
418
J. D. Reid
Visualizing cross section forces
Turned-Down
Post 2
Post 1
Total rail includes 13 posts Fig. 4. Small vehicle riding up a turned-down guardrail.
Forces at 200 ms
Forces at 225 ms
ucctar
Forces at 250 ms
n
I
valuer B.BBBE+BB 7.0BeIE+Em 1.4EaE+01 2.100E+m 2. meE+el 3.5eeE+Bl 4.20EK+01
Forces at 275 ms
Fig. 5. Guardrail forces during impact: at Post 1
J. D. Reid
480
rail is forced both downward and towards the post. Figure 5 shows selected views of the forces in question. The force towards the post is caused by the turned guardrail geometry and the angle of the rail as it approaches post 1. Due to back-up plates on the posts (used to connect the rail to the post) being the same shape as the rail, the force towards the post resists the downward force, thus preventing the release of the rail. For larger vehicles the downward force is large enough to overcome the inward force. The section analysis, and specifically, the new visualization technique, provided this key information which was needed to proceed with redesign of the guardrail system. 6. CONCLUSIONS
Visualizing cross section forces can be a very valuable tool in determining the behavior of a structure during a crash event. This is made possible through colored, scaled vector display of the forces at individual cross sections. Animating the deformed geometry while displaying cross section forces gives the analysts a detailed view of what is happening in the structure. This information can be used to help design the structure for optimum crashworthiness performance.
author expresses his thanks to LivermoreSoftwareTechnologyCorporation(LSTC) for providingLS-DYNA3DandLS-TAURUScodes,to Tony Lee from LawrenceLivennoreNational Laboratory for providingthesmallvehiclemodel.andto KenBonellofrom GeneralMotors for providingthe initial vehiclestructure. model Acknowledgements-The
REFERENCES
I. J. D. ReidandM. Y. Sheh,Loadpathanalysis in vehicle crashworthiness, Crashworthiness and Occupant Protection in Transportation Systems, ASME, AMD 169,91104(1993). 2. J. 6. HaIIquist,D. W. StiIlman,and T. Lin, L9 DYNA3D User’s Manual. LiverrnoreSoftwareTechnology Corporation(1993). 3. PAM-CRASH User’s Manual,ESI,Version11.1(1990). 4. HyperMesh User’s Manual,Altair Computing (1994). 5. I-DEAS Master Series, StructuralDynamicsResearch Corporation(1994). 6. D. J. Wynn and J. 0. HaIIquist,LS-TAURUS: An Interactive Post-Processor. Livermore Software Techno-
logy Corporation(1993).
7. National Highway TratEc Safety Administration, Federal Motor VehicleSafetyStandardNo. 208. 8. R. K. Faller, J. C. Holloway, B. T. Rosson, B. G. Pfeifer, and J. K. Luedlce, Safety Evaluation on the Nebraska Turned-Down Approach Terminal Section, Transportation Report No. TRP-O3-32-92, Final Report to the Nebraska Department of Roads, Civil Engineering Department, University of Nebraska-Lincoln (October 1992).
oo!v-8493(95)ooo19-4
Short Technical Note
VISUALIZING
CROSS SECTION
FORCES
JOHN D. REID Department of Mechanical Engineering, University of Nebraska, Lincoln, NE 685880656, U.S.A. Abstract-A visualization technique is presented that can signiticantiy advance the comprehension of the forces and moments that exist throughout a structure during a crashevent. This is made possible through colored, scaled vector display of the forces at individual cross sections. Animating the deformed geometry while displaying cross section forces gives the analysts a detailed view of what is happening in the structure. This deeper understanding can be used to help design a structure for optimum crashworthiness performance. 1. INTRODUCTION
crosssectionforcesand momentsis a very effective tool in the designingof structures undergoing impact conditions.This analysiscan be usedto increaseunderstanding of system behavior, verify model accuracy, understand and control pitch, quantify inertia relief, perform subsystemmodeling, and develop reducedordered models.This analysis, however, is currently done through analyzing numericaldata. The goal of this paperis to introduce a visualization technique that can significantly advance the comprehension of the forces and momentsthat exist throughout a structure during a crashevent. Analyzing
In this research, LS-DYNA3D is used as the simulationtool. Thus, its implementationof calculating cross sectional information will be discussed. Additionally, discussion will be limited to forcessince they are our primary concern.However, momentsare calculated similarly and their visualization (as describedin the next section) are the sameas for forces. Crosssectionsare definedby specifyingthe nodes of the crosssection and the elementsto be usedto calculate the forces at thosenodes.The sign of the forces transmitted are determinedby which side of the nodesthe elementslie on. In general,the load is comprisedof two components:elementstiffnessand massinertia. The equilibriumequationof a node on a crosssectioncanbe written usingNewton’s2nd Law:
2. CROSS SECITON FORCES
F+f=
Crosssection analysisis well suited to analytical tools rather than experimentalmethods.The reason for this is that it is very difficult, if not impossible,to position load cells within a deforming structure without altering its stiffness. Sectionforces and momentscan be usedto get an overall view of how a structure is performing.At any point in time, the split of forces betweenthe main structural pieces(e.g., the upper rail, midrail and engine cradle on a typical passengercar) can be compared, as well as how those forces compare to surroundingstructure (e.g., the barrier on a frontal barrier test). Additionally, individual components can be analyzed to seehow and when they transmit loads, and absorbenergy throughout an event [l]. Typical nonlinearf&rite elementcodes,suchasLSDYNA3D [2] and PAM-CRASH [3], allow the engineer to define cross sectionsthrough various parts of the structure. Both codes calculate the transmission forces through these defined cross sections.Additionally, LS-DYNA3D calculatesthe moments,the centroid location, and the areaof each cross section. All quantities mentioned above are functions of time, including centroid location and area.
mass* acceleration,
(1)
whereF= nodal force due to the stresses in the cross sectionelements,f= interface forces. Equation 1 can be usedto solve for the interface forces (alsoknown as transmissionforcesor section forces). Accelerationsfor eachnode and stresses for eachelementare calculatedthroughout a simulation, thus computingcrosssectioninformation is relatively inexpensive.This equation is a vector, resulting in global X, y and z forces (as opposed to a local coordinate system). Mass is allocated by LS-DYNA3D to ensureequal and opposite forces when choosingelementson onesideof the nodesversusthe other side. Section output from the simulation can easily be graphedas functions of time. The objective of this researchis to extend the functionality of this section analysisthrough visualization. The next sectionwill detail this extension.
475
3. GRAPHICAL DISPLAY
Cross section plots are very useful for section analysis,however, it is still hard to actually visualize the forcesgoing through the structure over time. For
476
J. D. Reid
this reason, a method for displaying the cross section forces directly on the deforming geometry was created. The idea is to display 3-D vectors representing the force through the cross section. For each cross section a scaled vector is displayed at all nodes defming the section. In addition to being scaled, the vectors are also colored to indicate magnitude. This can be done for all sections, a subset of sections and/ or just portions of individual sections. The visualization is available for any desired time throughout the crash event. Since graphical programs used to post-process simulations currently do not support this functionality, methods were developed to “trick” the software into displaying the desired information. This process has been done with three separate graphical packages, HyperMesh [4], I-DEAS [5] and LSTAURUS [6]. Each implementation was slightly different but the end results were all satisfactory. Here we describe the HyperMesh implementation, but will use IS-Taurus output for figures because they make more suitable hardcopy. The general process for visualizing cross section forces is as follows: (1) Include appropriate information in the model. l Degne desired cross sections. 0 Save section forces at 10 pts per ms. l Save the deformed geometry at desired intervals during the crash (usually between 2 and 5 ms> (2) Run the simulation. (3) Convert the deformed geometry into suitable format for the post-processor. (4) Process the section force file. l Filter the section data. l Sample the section data at the same interval the deformed geometry was saved. s Save the processed section data. (5) Relate section forces to defined cross sections. l For each cross section For each node in each cross section For each time step Assign the appropriate section forces 6, Y, z, n=gnitude). l Save this data in the appropriate vector format. (6) Run the post-processor. l Read in the initial model. l Read in the deformed geometry. l Read in the force vector data. l Display the deformed geometry while displaying the vector information at a desired time. The key in this process is the vector format and display steps listed above. In HyperMesh, the user has access to vectors that represent displacements. By placing force vector information into displacement vector slots we can then display these “displacement” vectors, obtaining the desired force visualization.
The display can actually be done in a sequence, providing an animation of the simulation while at the same time visualizing how the forces change magnitude and direction throughout the crash event.
4. APPLICATION
I-VEHICLE
STRUCTURR
One application that this visualization technique has been found to be useful is in vehicle crashworthiness. As a vehicle crushes during an accident it is critical that the kinetic energy be absorbed efficiently by the structure. In addition to absorbing energy, the frame structure also helps control the pitch of the vehicle. Efficient energy absorption and controlled pitch are keys to avoiding occupant injury. Therefore, the design of the structure must be thoroughly investigated to ensure good crash performance. One of the keys to this understanding is to know the load path through the vehicle as it undergoes a crash event, Figure 1 shows a quarter vehicle model used to predict the vehicle performance in a frontal collision, This type of collision is a regulated requirement for all passenger vehicles (FMVSS 208 [7]). During collision the load has multiple paths to be carried. Primary paths for many vehicles include the frame structure load path, the engine load path and the cradle load path. The frame structure load path generally absorbs the most energy and is the one studied in this project. Six cross sections were made in the quarter vehicle model as shown in Fig. 2. These cross sections consist of two slices through the structure. Each slice is broken into three sections, one each for each component of the structure. Those being, the midrail, wheelhouse and upper rail. The forces and moments are calculated during the simulation as described previously. Using the results, we apply the visualization technique in order to increase understanding of the crash event. Results of the visualization at 35,45,55 and 65 ms are shown in Fig. 3. From the visualization we can readily determine the following: (1) The midrail is the major load carrying component of the structure during the time period of iuterest. (2) The midrail load drops considerably during plastic deformation. (3) The load through the midrail is primarily along the direction of the vehicle. (4) The load varies considerably throughout the crush. (5) The load through the wheehouse is angled, meaning that its load partially comes from “bleed-off” of the midrail. (6) The load through the upper rail section is relatively minor. This could indicate a deficiency in the vehicle being able to control pitch of the vehicle.
Visualizing cross section forces
Upper Rail
Ise
Lower Tie-Bar Fig. 1. Vehicle side structure.
cs 5
CS - Cross Section Fig. 2. Defined cross sections.
5. APPLICATION
D-GUARDRAIL
DESIGN
Another application of the load path visualization technique dealswith a redesignof a turned-down guardrail. There are many different types of guardrails, one particular type installedon many highways in severalstatesiswhat is known asthe turned-down guardrail. Theseguardrailswere designedand tested usingall recommendedtestingproceduresat the time of their development. Unfortunately, a recent problem hasbeendiscoveredthat wasunforeseenduring development.When a smallvehicle rides up the end of the guardrail, there is a potential for the rail to stay firmly attached to the poststhat hold it up. This in turn can causea small vehicle to roll-over, The smaller sixed vehicles were uncommon during the developmentof the original turned-down guardrail.
Detailed background on this guardrail can be found in ref. [8]. Figure 4 depicts a simulation of a small vehicle riding up a guardrail. The objective is to develop a retrofit to the existing guardrail without totally removing the current ones and without excessive costs. Previously, guardrail design has been done usingsimplehand calculationsand a lot of physical testing.The computersimulationof this type of event is relatively new. The root causeof the guardrail failing to behave properly was determined through simulation, By examiningcrosssectionsin the rail before and after post 1 it was possibleto determinethe forces and momentsthat were holding the rail up. The cross sectionanalysisshowedthat during the impact, the
418
J. D. Reid
Visualizing cross section forces
Turned-Down
Post 2
Post 1
Total rail includes 13 posts Fig. 4. Small vehicle riding up a turned-down guardrail.
Forces at 200 ms
Forces at 225 ms
ucctar
Forces at 250 ms
n
I
valuer B.BBBE+BB 7.0BeIE+Em 1.4EaE+01 2.100E+m 2. meE+el 3.5eeE+Bl 4.20EK+01
Forces at 275 ms
Fig. 5. Guardrail forces during impact: at Post 1
J. D. Reid
480
rail is forced both downward and towards the post. Figure 5 shows selected views of the forces in question. The force towards the post is caused by the turned guardrail geometry and the angle of the rail as it approaches post 1. Due to back-up plates on the posts (used to connect the rail to the post) being the same shape as the rail, the force towards the post resists the downward force, thus preventing the release of the rail. For larger vehicles the downward force is large enough to overcome the inward force. The section analysis, and specifically, the new visualization technique, provided this key information which was needed to proceed with redesign of the guardrail system. 6. CONCLUSIONS
Visualizing cross section forces can be a very valuable tool in determining the behavior of a structure during a crash event. This is made possible through colored, scaled vector display of the forces at individual cross sections. Animating the deformed geometry while displaying cross section forces gives the analysts a detailed view of what is happening in the structure. This information can be used to help design the structure for optimum crashworthiness performance.
author expresses his thanks to LivermoreSoftwareTechnologyCorporation(LSTC) for providingLS-DYNA3DandLS-TAURUScodes,to Tony Lee from LawrenceLivennoreNational Laboratory for providingthesmallvehiclemodel.andto KenBonellofrom GeneralMotors for providingthe initial vehiclestructure. model Acknowledgements-The
REFERENCES
I. J. D. ReidandM. Y. Sheh,Loadpathanalysis in vehicle crashworthiness, Crashworthiness and Occupant Protection in Transportation Systems, ASME, AMD 169,91104(1993). 2. J. 6. HaIIquist,D. W. StiIlman,and T. Lin, L9 DYNA3D User’s Manual. LiverrnoreSoftwareTechnology Corporation(1993). 3. PAM-CRASH User’s Manual,ESI,Version11.1(1990). 4. HyperMesh User’s Manual,Altair Computing (1994). 5. I-DEAS Master Series, StructuralDynamicsResearch Corporation(1994). 6. D. J. Wynn and J. 0. HaIIquist,LS-TAURUS: An Interactive Post-Processor. Livermore Software Techno-
logy Corporation(1993).
7. National Highway TratEc Safety Administration, Federal Motor VehicleSafetyStandardNo. 208. 8. R. K. Faller, J. C. Holloway, B. T. Rosson, B. G. Pfeifer, and J. K. Luedlce, Safety Evaluation on the Nebraska Turned-Down Approach Terminal Section, Transportation Report No. TRP-O3-32-92, Final Report to the Nebraska Department of Roads, Civil Engineering Department, University of Nebraska-Lincoln (October 1992).