Multidisciplinary Design Optimization of a Full Vehicle with High Performance Computing

18 Pages·2001·0.87 MB·English

by  Yang, R. J.

AIAA-2001-1273
MULTIDISCIPLINARY DESIGN OPTIMIZATION OF A FULL VEHit2LE
WITH HIGH PERFORMANCE COMPUTING I
R. J. Yang, L. Gu, C. H. Tho
Ford Motor Company
2101 Village Road, MD2115-SRL, Dearborn, MI 48124
Phone: [phone]
Email:
Jaroslaw Sobieszczanski-Sobieski
NASA Langley Research Center
MS 139, Hampton, VA 23681
Phone: [phone]
Email: [email protected]
evolution and development of theoretically sound,
ABSTRACT
robust and efficient FEMs for the simulation of
Multidisciplinary design optimization (ME)O) of a nonlinear structural dynamics have advanced computer
full vehicle under the constraints of crashworthiness, aided vehicle design to the point where the results are
NVH (Noise, Vibration and Harshness), durabil;ty, and trusted with a high degree of confidence.
other performance attributes is one of the imperative The resulting surge in super computing is
goals for automotive industry. However, it is often revolutionizing the way vehicles are designed. The
infeasible due to the lack of computational resources, application of crashworthiness optimization to vehicle
robust simulation capabilities, and efficient design has drawn significant attention and interest in
optimization methodologies. This paper intends to automotive industry over the past few years [1-6].
move closer towards that goal by using parallel Recently, Yang et al. [5] developed a nonlinear
computers for the intensive computation and combining response surface based safety optimization and
different approximations for dissimilar analyses in the robustness process, which has been successfully applied
MDO process. The MDO process presented in this to the vehicle safety design. They investigated four
paper is an extension of the previous work reported by + nonlinear response surface methods for different crash
Sobieski et aL In addition to the roof crush, two full modes of large-scale systems as well as occupant
vehicle crash modes are added: full frontal impact and restraint system. Sobieski et al. [7] investigated the
50% frontal offset crash. Instead of using an adaptive multidisciplinary design optimization for a car body
polynomial response surface method, this paper structure under constraints of VH and roof crush. This
employs a DOE/RSM method for exploring the design study extends the previous work to include two more
space and constructing highly nonlinear crash functions. crash modes: full frontal impact and 50% frontal offset
Two MDO strategies are used and results are compared. crash. A 512-cpu SGI Origin 2000 computer is used for
This paper demonstrates that with high performance computation as opposed to a 256-cpu one as in [7]. In
computing, a conventionally intractable real world full addition, an alternative optimization strategy is
vehicle multidisciplinary optimization problem investigated to compare the results.
considering all performance attributes with large All the crash simulations are performed on NASA
number of design variables become feasible. AMES SGI Origin 2000 machines: LOMAX (512
processors, 300 MHZ) and STEGER (256 processors,
INTRODUCTION 250 MHZ). The nonlinear explicit finite element
commercial software, RADIOSS, is used for crash
Continuous demands on efficient design of vehicle simulations while MSC/NASTRAN is used to perform
safety, NVH, durability, and other attribute performance NVH analyses. The conservative Taylor Series
have increasingly emphasized on the analysis of the approximation [8] is used to approximate the NVH
vehicle structural designs as well as occupant restraint performance functions.
systems. Numerical computation methods have been
widely employed for this purpose. The most popular VEHI(_LE MODELS AND, DESIGN TARGETS;
and flexible computation method for vehicle design is
the finite element methods (FEM). Over the past ten Vehicle safety design is one of the major attributes
years, tremendous increase in computer speed and rapid in car product development. The vehicle structure must
Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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be designed to absorb enough crash energy through during impact
structural deformation and attenuate the impact force to (t:-tJ is within 36ms
a tolerable level when crash events occur. In the real
world, all crash modes need to be considered If the occupant P,o,_ is equal to or less than 10%, it
simultaneously for crash analysis and optimization. In is graded as 5-star, which is the highest rating in
this paper however, only full front crash impact, 50% NCAP star-rating, with 50% confidence interval
frontal offset impact, and roof crush are considered, as calculated from student t-distribution, as shown in
the main scope of this research is to demonstrate the Figure 2. The finite element model is shown in Figure
state-of-the-art MDO methodologies with high 3.
performance computing. In addition to the safety
Roof Crush Model
attributes, the vehicle NVH performance measures are
also included in this study. Vehicle roof crush is a federal mandatory
requirement intended to enhance passenger protection
Full Frontal Crash Model
during a rollover event. The test procedure is defined in
The full front car crash finite element model used FMVSS 216. The finite element roof crush model for
in this study contains about 100,000 elements. It this study is converted from a NVH model, as shown
crashes into a rigid 90 degree fixed barrier with the in Figure 4.
speed of 35 MPH. The key safety performance measures The explicit finite element dynamic software
in the full frontal crash include occupant Head Injury RADIOSS is used for crush simulation. Unnecessary
Criteria (HIC) and Chest G, which are calculated from parts in the NVH model are deleted and some missing
the MADYMO analysis with importing the crash pulse parts are added in the roof crush model, e.g., very
from RADIOSS crash analysis. The MADYMO is a detailed side doors were added and the glasses are
commercial multi-body occupant simulation product refined. The total number of elements for roof crush is
from TNO. The process is shown in Figure 1. about 120,000. A 72 inches by 30 inches rectangular
The full frontal crash is commonly used to design ram is added to perform the' roof crush as specified by
and validate the vehicle front structures. Federal Motor the FMVSS 216. The longitudinal axis of the ram (see
Vehicle Safety Standards 208 (FMVSS) specifies the Figure 4) is at a forward angle (side view) of 5 degrees
safety regulations and test configuration. The regulation below the horizontal, and is parallel to the vertical
states that the HIC and Chest G injury numbers have to plane through the vehicle's longitudinal centerline. The
be within 1000 and 60g, respectively. The explicit lateral axis is at a lateral outboard angle, in the front
finite element dynamic software RADIOSS is used to view projection, of 25 degrees below the horizontal.
perform crash simulations throughout this study. The The lower surface is tangential to the surface of the
design targets for the full frontal impact in this study vehicle and initial contact point is on the longitudinal
are to satisfy both FMVSS 208 regulation and centerline of the lower surface of the ram and 10 inches
corporate guidelines with occupant HIC and Chest G from the forward most point of the centerline. In roof
targeted within 450 and 45g, respectively. Note that the crush simulation, the ram normal speed is set to be 7.5
numbers may not be realistic, as they are solely used MPH.
for proving this methodology. Another design As described in the FMVSS 216, the force
requirement is the New Car Assessment Program generated by vehicle resistance must be greater than
(NCAP) star-rating criterion, proposed by the National 5,000 Ibs (22,240 N) or 1.5 times the vehicle weight,
Highway Traffic Safety Administration (NHTSA) in w_r is less, through 5 inches of ram
1994. The NCAP star-rating criterion is derived from displacement. In this study, the roof crush resistant
the total injury probability criteria combining the force is set to be larger than 6,000 lbs (-- 27kN). The
occupant HIC and Chest G numbers. The total occupant door thickness and material yield stresses are chosen as
probability of severe injury is given by: the design variables.
50% Frontal Offset Crash Model
p,o,., = I- (1- PhylaJ,1- _h,,, )
where In addition to full frontal crash and roof crush, a
1 50% offset frontal impact mode is also considered in
Phead = l+e" ............. ' the optimization process. The vehicle finite element
model is exactly same as the front crash model. The
1
only difference isthe barrier. In this model, the vehicle
l+e" ................. ' crashes into a 90 degree fixed rigid wall with 50%
-- 2.5 offset (Figure 5). The impact velocity is 40 mph. The
HIC = 1 " adt (t: - tI)_ RADIOSS is used for the simulation. The key output
from the frontal offset impact is the toeboard intrusion.
The design target for toeboard intrusion is set to be less
where a is a multiple of G's than 10 inches. The design variables used for 50%
tt, t2is expressed in second and measured
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frontal offset crash is same as those used for full front Db = displacement at local point = 0.9mm
crash.
Roof Crush Constraints:
NVH Model
Crush distance (D) < 5"
In car product development process, different NVH Critical peak load (P,.r) > 27kN (=60001b)
models are used for different purposes so that the
quality of the NVH is high and the cost is at Full Frontal Impact Constraints:
minimum. A car body called Body-In-Prime (BIP) is Head injury criteria < 450
used for this study. The BIP is a trimmed body Chest G < 45g
without all the closures (door, hood, deck lid) and other Plo_a_< 10 % (i.e. 5-star NCAP rating)
sub-systems (steering column, fuel tank, and seats) and where P,o_l= Total probability of severe injury
trim items (carpeting, battery, etc.). A trimmed body
structure may be thought of as a vehicle without the 50% Frontal Offset Crash Constraints:
suspension and powertrain sub-systems. The BIP can Toe board intrusion < 10"
also be thought as the "Body-In-White" with glass. The
BIP plays an important role in determining the In the multidisciplinary design optimization
dynamic characteristics of the vehicle.
problem, there are 10 global (system) thickness design
The BIP normal modes, static bending and static variables including windshield, roof panel, roof rail,
torsion analyses were conducted using the roof cross members and pillars. The total number of
MSC/NASTRAN. The full scale NVH finite element
design variables for the NVH model is 19, including I0
model is shown in Figure 6. The total number of shell
for backlite glasses and sheet metal thickness, 9 for the
elements is close to 68,000. The total number of nodes
stiffness of connection between the backlite glass and
is about 69,000. The normal modes were calculated
structures. The thickness design variables contain floor
under the free-free condition. The static bending panels, jacking/towing on quarter panel, backlite glass,
analysis was conduced with front (yz and z) and rear (xz
shotgun and radiator support. There are 5 subsystem
and xyz) shock towers constrained while for the static
thickness design variables for full frontal and 50%
torsion rear shock tower supports (xz and xyz) and a frontal offset crash models, namely rails and subframe.
mid point of the lower radiator support (z) were As for the roof crush, 3 thickness and 7 material yield
constrained. The bending stiffness calculated using a stress local design variables are taken into account for
load applied at the front rocker locations was 4,551 consideration.
N/mm while the torsion stiffness calculated using a
torque applied at the front shock tower locations was
M-DO PROCEDURE
8726 N-m/Deg. The free-free normal mode analysis
showed that the overall torsion at 26.5Hz and overall The multidisciplinary .... design optimization_
bending at 38.9 Hz. procedure is based on the previous work by Sobieski et _ _
The torsion frequency for the BIP free-free normal -'al' [7], as shown in Figure 7. The difference in this "_
mode is set to increase by 5% from 26.5 to 27.8 Hz. paper is that instead of using an adaptive polynonial
The upper bounds for static torsion and static bending response surface approximation, a DOE/RSM (Design
displacements are chosen as 3.4 mm and 0.9 mm, of Experiments/Response Surface Method) method is _
respectively, i.e., 10% improvement from the initial employed to construct the approximation models for :"
design. crash performance functions. Among the various
methods for DOE and RSM, the optimal Latin _
MDO PROBLEM Hypercube Sampling method is employed to explore
the design space uniformly to capture the nonlinear
The multidisciplinary design optimization problem behavior of crash functions, while the stepwise
is to minimize the total vehicle weight subjected to regression method is used to construct the nonlinear
design constraints of NVH and 3 safety crash modes: response surfaces based on the computer experimental
roof crush, full frontal impact, and 50% frontal offset
points. The NVH responses are approximated by the
crash. The problem is formulated as following: conservative Taylor Series Approximation (TSA) as in
[7].
Minimize: Vehicle weight Two optimization strategies are employed to
Subject to: perform the inner loop within the MDO process. The
VII Constraints:
first takes advantage of the design senitivity analysis
2"I.SHz< J3 <-29.3Hz
capability in MSC/NASTTRAN [7] and the second
Static torsion " Dt takes advantage of both the sensitivity and the
Static bending -- Db optimization capabilities.
where fi = 3'_frequency In the first strategy, the NVH sensitivities are
Dt = displacement at local point = 3.4mm extracted from the MSC/NASTRAN output and
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approximations are constructed using TSA. In addition one predictor, which provides the best fit. The second
to the three crash mode responses approximated by the independent predictor to be added to the regression
quadratic order of stepwise regression, the MDO model is the one that provides the best fit in
problem is solved by an SQP optimizer. As the NVH conjunction with the first predictor. Given the other
model is less expensive to run in this case, the NVH predictors already in the model, further optimum •
design variables are updated and the analysis is repeated predictors are then added at each step in a recursive
in MCS/NASTRAN for several times (3 in this study) fashion. Alternatively, backward elimination can be
while keeping the crash approximation models used. Atter certain predictors have been added in the
unchanged. After three NVH inner loops, all design model, the predictors are dropped one at a time_ The
variables are updated and reflected on the NVH and predictor that has the least effect on the fit of the model
crash models. Simulations are then performed to. is dropped at the stage. The stepwise regression model
conform the results from the first MDO cycle. The is built by combining the techniques of forward
crash approximation models are updated and then selection with backward elimination.
continue to perform the next MDO cycle if necessary. In this paper, the second order polynomial for the"
The move limits of the design variables for VII regression is employed to construct the nonlinear
approximation using the TSA are selected to be 20%. response surfaces for all crash modes (full frontal, 50%
The second strategy for the inner loop optimization frontal offset, and roof crush) except the vehicle weight, "
is to take advantage of the design optimization where a linear basis function is selected. •
capabilities in MSC/NASTRAN. Instead of exporting
the NVH sensitivities and performing inner HIGH PERFORMANCE COMPUTING
optimization loop manually for three iterations, the
The primary computational cost is in performing
optimization process for each MDO cycle is completed
the RADIOSS finite element analysis for the sample set
entirely in the MSC/NASTRAN by imposing the crash
performance constraints using the DEQATN and of design points corresponding to each of the 3 crash
modes in section 2. The optimal Latin Hypercube
DRESP2 cards for the explicit crash equations provided
from the stepwise regression approximations._ The sampling method that is used in generating an initial
advantage of this strategy is that the inner loop can be set of design points for frontal and offset frontal crash
and the multilevel orthogonal arrays are for roof crush
completed without any human intervention. However,
the approximated crash functions needs to be inputed as in reference [7]. The computational details of the
number of sample points and the elapsed computational
explicitly.
times are provided in Table 1. It is important to note i
Optimal Latin Hypereube Sampling (LHS) that the RADIOSS analysis for the baseline and Sample--_
In this research, the optimal Latin Hypercube set (3*N) designs can be performed concurrently on a 7_
multiprocessor machine thereby reducing the elapsed
Sampling method [9] is employed to explore the design
space for constructing the response surfaces for crash time. The two confo.__ation analyses correspond to the
models. The LHS is chosen due to the absence of a verification analyses on the optimal designs obtained
prior knowledge of the parametric form of the model. Most RADIOSS crash simulations were performed
The experimental design is directed to minimize the on NASA Ames LOMAX machine (SGI Origin 2000,
bias part of the Mean Square Error (MSE) by 512 processors, 300 MHZ). Each simulation used 4 _!
distributing the sample points uniformly over the entire processors. Based on numerical experience, running the
design region. The number of runs in LHS is crash simulation with 4 processors using RADIOSS
determined by the total number of factors including code can achieve an approximate speedup of 3, :t
control variables and noisy variables. The minimum- compared to a simulation with a single processor. Ond
number of runs is selected to be 3N in this paper, where _ cycle of the MDO process can be completed in 70 hours
N is the total number of design variables. or approximately 3 days with the 512-cpu LOMAX
computer running simultaneously. It may require 938 :a
Stepwise Regression (SR)
days to complete if it were executed on a single
Among the various response surface methods processor. The 938 days estimate is based on the
(RSM), the stepwise regression method is used to following formula: (46*60+46*65+25*70)*3 = 22,500
construct the response surface functions for its hours = 937.5 days (details see Table 1). In other
simplicity and accuracy for structural crash problems words, a total speedup of 321 (22,500 hrs/70 hrs) can
[5]. The regression analysis techniques have widely be achieved. Note that the two conformation runs are
been used and a detailed description of stepwise not counted, as they can only be executed after the
regression procedures can be found in [10]. In general, previous MDO cycle. In Reference [7], a similar MDO
the stepwise regression model is constructed recursively problem, involving NVH and roof crush, was able to be
by adding or deleting the independent predictions one completed in one day while it required 257 days of
at a time. When the model is built up, the procedure is elapsed computing time for a complete solution on a
known as forward selection. The first step is to choose single processor of an Origin 2000 server. Reference
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[6] reportedanevenbetterspeeduupsinga more
t !
advancecdomputearnda MessagPeassingInterface A(_KNOWLEDGMENT_ [_1C5_ c, :
(MPI)basevdersionofRADIOSS. The study was performed by collaboration of the/, _"
Computational AeroSciences Team of the High
This study shows that with high performance Performance Computing and Communication Program
computing, conventional intractable vehicle design and Ford Research Laboratory. The authors
problems now become feasible. acknowledge Mr. J. Chang of NASA Ames NAS
Computing facility for his assistance. The authors
would like to express their appreciation to D. Johnson
NUMERICAl,, RESULTS
and F. Maillet of RADIOSS Consulting Corporation
The initial design is started from an infeasible for providing RADIOSS software license for crash
region, as shown in Table 2. The constraints of the simulation. The authors also acknowledge Drs. T. Tyan
third mode frequency, torsion and bending and M. Jayasuriya of Ford Motor Company for
displacements, HIC and toe-board intrusion are all" providing the crash and NVH models and consultation.
violated. The design variables, their lower bounds and
upper bounds are in Table 3. REFERENCES
After two MDO cycles, all constraints are satisfied
1. R. J. Yang, L. Tseng, L. Nagy and J. Cheng,
and it is shown that the two MDO strategies yield
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by 14.8kg and 15.6kg, _respectively. The objective and
2. M. Chargin, H. Miura, Computer Aided
the maximum constraint histories are shown in Figure
Engineering for Improved Vehicle Crashworthiness,
8. The design histories for the two strategies are
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summarized in Tables 2. The design variables for both
Canada, 1999.
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3. N. Stander, Crashworthiness Technology Using
(P,o,a_vs. weight) and offset crash (maximum intrusion
Response Surface Methodology and Massively
vs. weight) are shown in Figures 9 and 10,
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respectively. It is observed that significant design
Optimization in Industry-II, Banff, Canada, 1999.
improvements for both strategies are achieved, after two
4. U. Schramm, D. Schneider and H. Thomas,
complete cycles. In frontal crash, the Ptotal (total
"Structural Optimization in Occupant Safety and
probability of severe injury) is improved from 10% to
Crash Analysis", Proceedings of Conference
8.0% and 7.5%, respectively. While in the offset crash,
Opticon '99: Optimization Sofware, Methods and
the maximum toe-board intrusion is successfully
Applications, Newport Beach, California, October
controlled within 10 inches, while reducing vehicle _.
14-15, 1999.
weight. The roof crush performance constraint is
5. R. J. Yang, L. Gu, L. Liaw, C. Gearhart, C.H. Tho,
insignificant as all designs are feasible before and after
X. Liu, and B. P. Wang, "Approximations for
the optimization process. All NVH targets are also met,
Safety Optimization of Large Systems,"
i.e. improving the torsion and bending stiffness by
Proceedings of ASME Design Engineering
10% and increasing the third mode frequency by 5%.
Technical Conferences, September, Baltimore,
CONCLUSIONS Maryland, 2000.
6. S. Kodiyalam, R. J. Yang, L. Gu, C. H. Tho,
This research has successfully demonstrated the
"Large-Scale, Multidisciplinary Optimization of a
feasibility and benefits of the multidisciplinary design
Car Body in a Scalable, High Performance
optimization methodology with high performance
Computing Environment", Submitted to ASME
computing. The results showed that the MDO/HPC _
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certification of new vehicle designs while satisfying the
September 9-12, 2001.
functionality requirements.
7. J. S. Sobieski, S. Kodiyalam, and R. J. Yang,
Two optimization strategies were employed to
"Optimization of Car Body under Constraints of
perform the MDO process and they produced Noise, Vibration, and Harshness (NVH) and Crash",
comparable results. Optimal designs were achieved with
AIAA, 2000-1521, April, Atlanta, GA, 2000.
significant reduction of vehicle weight in both
8. J. H. Starnes, R. T. Hattka, Preliminary Design of
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side impact, rear impact etc.) with a larger number of
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process in the future to solve a real world problem.
Ylvisaker, "Bayesian Prediction of Deterministic
Function, with Applications to the Design and
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American Institute of Aeronautics and Astronautics
Analysisof Computer Experiments," Journal of the 10. P.R. Krishnaiah, "Selection of Variables
American Statistical Association, Vol 86, pp. 953- under Univariate Regression Models," Handbook of
963. Statistics, Vol. 2, 1982.
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American Institute of Aeronautics and Astronautics
Extract
crash
Injury
numbers
• HIC I
• Chest G I
Figure 1. CAE Process for Frontal Crash Problem
1400
J
1200
1000
800
G00
400
20O
20 30 40 50 GO 70
Chest G
Figure 2. NCAP Star-Rating Curve
Figure 4. Roof Crush FE Model
Figure 3. Frontal Crash FE Model
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Figure 5. 50% Frontal Offset Crash Model
Figure 6. NVH FE Model
_" System+Analysis (NVH, Crash)]
Concurrent Processing using
I C51ra2shproRcSessoCronstrSuGctIionO/Uringdinates2000 ]
_-( NVH Analysis & Smsitivities ]
Multidisciplinary Optimizati_on _ NVH SensitivityMbnadesledApproximation J
j, Crash Response SMuorfdaecle Approximation ]
,nnevLoon( Update Variables (NVH, Crash) ]
Outer Loon ]
Figure 7. MDO/HPC Flow Chart
1745 0.15
Original (v_ight) [
N._ - - IF - Alternative (weight)l 0.10
1740
t,x _ -- A-- -Original (Gmax) [
0.05
1735 o
0.00
1730
-0.05 ¢g
1725
-0.10
1720 -0.15
Initial 1 2
Number of Cycles
Figure 8. MDO Design History
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20 _ I Unfav°rable regi°n
4-
151t i
/ I I . I ii Baseline / '
_1°}1:y .....,._..... ,.,. ,.,..,
." ".
I Favorablereg'on Ii
0 i c i
1720 1730 1740 1750 1760
Weight (Kg)
Figure 9. DOE Matrix for Frontal Crash (P,ot,Z vs Weight)
i Unfavorable region
_" 1146t ....... _:- i .........t.......
12 ri 4'_ 9 • **_' t • •
-3" r....... _-* ......... * ..........._'""'_ ....................o...._.....................
,_ L> ,
'_' ' II _,vorab,oreI g,on
81 , ,. ,
1720 1730 1740 1750 1760
Weight (Kg)
Figure 10. DOE Matrix for Offset Crash (Maximum Intrusion vs Weight)
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Table 1.Computational Requirements for Safety Disciplines
Crash Modes Number of Design Number of RADIOSS Total Elapsed Time
Variables (N) simulations
(using 4 CPU/simulation)
on Origin 2000 machine
Frontal Crash 10 (system) + 3*N + 1(baseline) + 60 * 48 = 2,880 hrs
5(local) 2 (conformation) = 48
Offset Crash 10 (system) + _3*N+ 1(baseline) + 65 * 48 = 3,120 hrs
5(local) 2 (conformation) = 48
Roof Crush 10 (system)'+ L24 + 1(baseline) + 70 * 27 = 1,890 hrs
I0 (local) 2 (conformation) = 27
Total 7,890 hrs
Table 2. MDO Design History
Attribute Performance Baseline Target Original* Alternative**
.... Cycle 1 Cycle 2 Cycle 1 Cycle 2
3_ frequency (Hz) 26.5 27.8 < fi < 29.3 29.3 29.3 27.8 27.8
NVH Forsion disp. 1(mm) 3.8 < 3.4 3.4 3.4 3.4 3.4
I'orsion disp. 2 (mm) -3.8 > -3.4 -3.4 -3.4 -3.4 -3.4
Bending disp. (ram) -0.97 > -0.9 -0.9 -0.87 -0.9 -0.9
[-IIC 500 _<450 356 411 411 357
Frontal 2hest G 42 < 45 38 39 42 39
Ptot,t(%) 10 < 10 7.3 8.0 9,2 7.5
Roof Resistance force (kN) 34.7 _>27 30.5 31.2 31.4 31.3
Intrusion 1(in.) 11.2 < 10 9.7 9.9 10 9.9
Intrusion 2 (in.) 10.8 < 10 9.4 10 9.7 9.8
Offset intrusion 3 (in.) 10.9 < 10 9.4 10 10 9.8
Intrusion 4 (in.) 10.1 < 10 8.9 9.4 9.5 9.4
Intrusion 5 (in.) 10.5 < 10 9.3 9.8 9.9 9.6
Weight'(Kg) _.i_::_ 1740.5 M,n,_iz_"_ ._1726.6. _1725.7 1727.2_L172.4_,
* 3 iterations for NVH loop
** 5 iterations for NVH loop in NASTRAN
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