
MSC 1987 World Users' Conference
Proceedings-Volume I
The conference proceedings
for the 1987 World Users' Conference are now available on-line in Adobe
Acrobat PDF format. (The Adobe Acrobat Reader software is available for
free download from Adobe's web site at
www.adobe.com.) When printed, these PDF files will produce a better
quality image than the one shown on your computer screen.
STATUS
OF MSC PRODUCTS, 1987 (Acrobat 2.08MB) #0287, 44 pgs.
M.A. Gockel--MSC.Software Corporation
ABSTRACT: MSC provides
a series of software products and services useful to the engineering
community. The status of these products and services is discussed here.
(The text below is intended to accompany the figures attached at the
end, which will be used for presentation at the 1987 MSC World Users
Conference.)
OPTIMIZATION
AND FINITE ELEMENT ANALYSIS: THE STEP FROM ANALYSIS TO DESIGN
(Acrobat 1.95MB) #0387, 21 pgs.
Garrett N. Vanderplaats--University of California Santa Barbara, California
ABSTRACT: The process
and prospects of coupling finite element analysis with numerical optimization
is discussed. The general history of these two technologies is first
reviewed to identify the present state of the art. General concepts
of optimization are then outlined to identify both the methodology and
the generality of these methods. The finite element method is then discussed
in its simplest form and the features that make it particularly amenable
to optimization are identified. The concept of using approximation techniques
is then introduced as a means of dramatically reducing the number of
detailed finite element analyses used by optimization. Examples are
offered to demonstrate the power of optimization when coupled with finite
element analysis. Finally, the present effort to incorporate optimization
directly into the MSC/NASTRAN program is described. References are provided
for further reading. It is concluded that optimization is a powerful
design tool whose time has come.
STRESS
ANALYSIS OF PLANET GEARS WITH INTEGRAL BEARINGS; 3-D FINITE ELEMENT MODEL
DEVELOPMENT AND TEST VALIDATION (Acrobat 1.95MB) #0487, 14 pgs.
Raymond J. Drago and
Ravi N. Margasahayam--Boeing Vertol Co., Philadelphia
ABSTRACT: The load-carrying
capacity of helicopter planetary transmissions depends to a great extent
on the strength of thin-rimmed, roller-supported, hollow planet gears
with integral bearings. Thick-rim analogy forms the basis for planet
strength evaluation in the conventional method now used. Such methods
lack accuracy as the rim thickness decreases, both in the prediction
of location as well as the magnitude of maximum stress. Therefore, more
accurate design tools are necessary to improve the reliability of lightweight
planetary gears.
This paper presents an analytical
technique for the evaluation of planet gear strength based on the three-dimensional
finite-element method (FEM). Full-gear tooth-rim models were developed
from 8-noded CHEXA elements and were superimposed with CONROD's to simulate
test placement of strain gages. Reasoning for a circumferential model
comprising 3,000 to 5,000 elements, together with a brief review of
related FEM effort, are presented to provide a case for full-gear three-dimensional
models, especially for planet gears.
The finite-element-model-predicted
shape of the stress distribution around the gear is used to evaluate
the magnitude and location of maximum stress for two planet gears. A
comparison of FEM-calculated stresses and those from full-scale quasistatic
tests for the two planet gears indicated good correlation. The FEM technique
was then extended to determine the strength of an existing designs in
the absence of full-scale test data.
The effect of planet gear
support on the overall gear strength, not fully addressed by the conventional
method, has been demonstrated as an important factor in the design of
planet gears. The ability of the present FEM analytical tool to accurately
identify and evaluate alternative designs is pointed out. Finally, the
applicability of three-dimensional modeling in the design optimization
of planet gears with integral bearings is noted.
STRUCTURAL
AND OPTICAL ANALYSIS OF A LANDSTAT TELESCOPE MIRROR (Acrobat 1.11MB)
#0587, 14 pgs.
Thomas E. Wolverton and John J. Brooks--Santa Barbara Research Center,
California
ABSTRACT: Finite element
techniques were employed to determine distortions and subsequent image
characteristics of the primary telescope mirror in a LANDSAT scanning
spectral radiometer. Mirror deformations due to gravity and the presence
of friction loads in kinematic mirror mounts were determined using the
static analysis capabilities of MSC/NASTRAN. Displacement results were
then postprocessed by PDF/PATRAN to create optical pseudo-spot diagrams
indicating image degradation. These focal plane spot diagrams provide
a convenient graphical method for quickly identifying critical load
cases and predicting results of optical testing.
ANALYSIS
OF AUTOMOTIVE AXLE CARRIER ASSEMBLY AND COMPARISON WITH TEST DATA (Acrobat
2.27MB) #0687, 26 pgs.
A.A. Herbert and A.O. Currie--Compumod Pty. Ltd.
W. Wilson--Borg Warner, Australia
ABSTRACT: This paper
describes the analysis of an axle carrier manufactured by Borg Warner
Australia for the Pontiac Firebird. The aims of the analysis were to
model the separation of the crown and pinion gears under drive and coast
load and to produce reasonably accurate stress information for the axle
carrier shell. It was also intended to gain confidence in the modelling
techniques so that they could be used in the design of future components.
Deflections test data was
available for the actual carrier. The paper shows that good correlation
(within the accuracy of the test) was achieved between the model and
the results.
This paper also discusses
several other points of interest in the analysis. These include the
use of solid modeling to define complex surface geometry, the use of
solid modelling to define complex surface geometry, the use of inclined
planes to model gear tooth interaction, modelling of bearing stiffness
and support conditions and the use of thermal expansion to model an
interference fit.
STRUCTURAL
REANALYSIS SYSTEM (SRS) FOR THE PHILLIPS PETROLEUM GROUP'S "MAUREEN"
TSG PLATFORM USING MSC/NASTRAN SUPERELEMENT DATA BANK AND DMAP PROCESSING
(Acrobat 1.56MB) #0787, 21 pgs.
D.R. Hummel--Phillips Petroleum Co., Ivory Coast
ABSTRACT: The Maureen
Platform Structural Reanalysis Sytem (SRS), based on MSC/NASTRAN Superelement
Data Bank and DMAP processing, provides a rapid and low cost computer
analysis of structural integrity in the event of damage to primary steel
works.
This paper describes the
main components of the system and how it is used in case of structural
damage.
The system is composed of:
- the "as built"
MSC/NASTRAN structural model of the platform (24,000 DOFs subdivided
into 5 superelements)
- the structural Data Bank,
including all the input/output data relevant to the NASTRAN analyses
performed on the intact structure
- a set of DMAP routines
to manage the Data Bank and interactive software devoted to quick
selection, sorting and visualization of data included in the Data
Bank
- a set of operating manuals
to guide the structural reanalysis.
The actions to be performed
by the SRS in case of damage are:
- automatic identification
of the structural area sensitive to the damage (critical area)
- automatic identification
of the loading conditions from 200 combined loading cases that induce
the maximum stresses in the elements of the critical area.
- automatic generation of
a reduced structural model (i.e. damage model) in NASTRAN format,
including load vectors for the critical loading conditions and relevant
boundary conditions for the reduced model.
- structural reanalysis
and checks of the elements in the reduced model
- visualization on a graphic
screen of the required parameters (displacements, forces, safety factors,
etc.) for each desired portion of the structure.
A team of engineers and computer
scientists then analyze the results and reach conclusions regarding
the structural integrity of the platform.
The SRS System allows all
these operations to be performed in less than 24 hours, a process which
in the past has taken weeks, even months to be performed.
AUTOMATED
FINITE ELEMENT MODELING: HOW CLOSE IS IT? (Acrobat 1.15MB) #0887,
10 pgs.
Mark S. Shephard--Rensselaer Polytechnic Institute
ABSTRACT: This paper
gives a brief overview of the progress that has been made on the development
of automated finite element modeling procedures. It then gives an indication
of how users may view such systems.
ASSUMPTIONS
AND ACCURACIES ASSOCIATED WITH THE MSC/NASTRAN ROD, BAR, AND QUAD4 ELEMENTS
(Acrobat 1.56MB) #0987,28 pgs.
ABSTRACT: A number
of scattered references regarding certain MSC/NASTRAN finite elements
are united in this paper to give the program user a convenient single
source for the assumptions involved when modeling typical aerospace
structures. Items such as mass and stiffness matrix element assumptions,
implicit when using the ROD, BAR, and QUAD4 elements, are presented.
In addition, the accuracies associated with their common usage are also
summarized.
These elements are then used
in various combinations to model a stiffened circular cylinder with
features typical of many semi-monocoque structures. Finite element free
vibration results are then compared with closed-form analytical solutions
for both an isotropic and orthotropic thin cylindrical shell formulation
to further substantiate the overall accuracy possible when modeling
aerospace type structures with the above cited elements.
FINITE
ELEMENT SIMULATION OF COUPLED AUTOMOBILE ENGINE DYNAMICS (Acrobat
672K) #1087, 14 pgs.
David N. Herting, David F. Bella, and Patty A. Kimbrough--MSC.Software
Corporation
ABSTRACT: A procedure
has been developed to simulate engine dynamics and determine displacements
and forces in the reference frames of the moving components. The method
is based on a harmonic domain representation of displacements and forces
and the coupling between harmonics at component interfaces. A processor
generates the required coupling matrices and inertial loading vectors
for each harmonic. A DMAP Alter assembles the matrices, solves for the
harmonic displacements and provides plots of the displacements and forces
over the two revolution period of the engine. A comparison is made between
an analytic solution for a rigid component engine and the simulation
procedure with both rigid and flexible components.
ANALYSIS
OF SPACE STATION DYNAMICS USING MSC/NASTRAN (Acrobat 1.80MB) #1187,
27 pgs.
John P. Raney--NASA Langely Research Center, Virginia
M. Kaszubowski and J. Kirk Ayers--PRC Kentron, Inc, Virginia
ABSTRACT: The Space
Station Office at the NASA Langely Research Center is responsible for,
among other things, conducting and coordinating analyses and trade studies
which focus on Space Station structural dynamics and attitude control
(station pointing). During the now-completed preliminary design phase,
Phase B, of the Space Station project several studies were performed.
One study, led by Structures
Division, focused on determining truss bay size by examining the relative
merits of a 9 foot and a 5 meter bay size from the standpoint of station
attitude control. In another study, the dynamics of a proposed Space
Station precursor experiment using protoflight hardware were examined
, while a companion study determined the structural effects of firing
the Orbiter's primary reaction control system jets with a large structure
attached.
In a more recent study, the
vibration characteristics and attitude control qualities of the Space
Station were determined for critical configurations during assembly
and buildup. The purpose of this paper is to highlight the methodology
and results of Reference 4 and, coincidentally, to discuss the environment
within which MSC/NASTRAN is utilized at the Langley Research Center.
EMPLOYMENT
OF MSC/STI-VAMP FOR DYNAMIC RESPONSE POST-PROCESSING (Acrobat 1.75MB)
#1287, 25 pgs.
Robert N. Coppolino and David F. Bella--MSC.Software Corporation
ABSTRACT: Employment
of MSC/STI-VAMP as an interactive dynamic response post-processor for
MSC/NASTRAN is outlined. A new modification to SOL 3 (Normal Modes Analysis)
provides for determination of quasi-static residual vectors, base motion
excitation matrices and other modal quantities required by the post-processor.
The general operation of a MSC/STI-VAMP dynamic response post-processor
is demonstrated for frequency, transient and random response calculation.
EXPERIENCES
WITH OPTIMIZATION USING ADS/NASOPT AND MSC/NASTRAN FOR STRUCTURAL DYNAMICS
(Acrobat 1.39MB) #1387, 15 pgs.
Warren C. Gibson--CSA Engineering, Inc., California
ABSTRACT: ADS/NASOPT
is an optimization code which works with MSC/NASTRAN to produce optimal
structural designs. The user creates a design model which defines design
variables (element properties), constraints (limits on displacements,
stresses, natural frequencies, buckling loads,or weight), and an objective,
a function to be minimized. This paper describes experiences in using
ADS/NASOPT in optimizing a complex structure to weight and frequency
constraints.
DYNAMIC
RESPONSE OPTIMIZATION USING MSC/NASTRAN (Acrobat 2.16MB) #1487, 24
pgs.
M. Chargin and H. Miura--NASA Ames Research Center, California
G. Clifford--Cray Research, Inc., Minnesota
ABSTRACT: Numerical
optimization techniques are used to modify the dynamic response at a
specified point(s) of a structure due to a steady state narrow band
excitation. Calculation of steady states vibration amplitude is reduced
to the solution of linear equations with complex coefficients. The sensitivity
of the dynamic amplitudes with respect to the structural parameter perturbations
can be computed with the same technique as the one used in the static
displacement sensitivity without requiring eigenvector sensitivity.
Approximate models for critical structural responses are created based
on the sensitivity data to reduce the amount of computational effort
and to enable the design of structures of practical scale and complexity.
This approach is general in that it accommodates static, dynamic, and
frequency constraints simultaneously as long as their computational
models are available. It can be used in optimizing mass distribution
as well as stiffness modifications of practical structures.
Two example problems are
solved to demonstrate the capability of these techniques. One is a simply
supported beam subjected to a rotating force and static gravity load.
The other example is an engine support structure which possesses significant
size and complexity. It is loaded by static gravity loads and forces
due to rotating mass unbalance.
THE SHAPE
OF THINGS TO COME (Acrobat 832K) #1587, 19 pgs.
P.A. Zelenski--MSC.Software Corporation
ABSTRACT: The development
of engineering software tools is a very specialized and complex field
of endeavor. MSC has long been a leader in the development of Engineering
analysis tools and has now embarked on a growth path to include an integrated
interactive graphics system into its successful and capable repertoire
of software products.
This paper suggests the principles
involved in the design and development of such a system. The concept
of "form follows function" leads to a discussion of the attributes
that good engineering software ought to have and the mechanisms that
software developers may use to build those attributes into the software.
Programming techniques involving
rapid prototyping, artificial intelligence, new programming languages
and the "object oriented" approach are discussed.
The conclusion of this presentation
is the realistic and critical observation that all stages of the development
activity must be done with the end user in mind. All capabilities added
to the system and all techniques used in its developments must bring
out the primary premise that "the User is King."
OPTIMIZATION
OF THE BUCKLING STRENGTH OF CARBON-REINFORCED CYLINDERS (Oral Presentation)
#1687
ABSTRACT: This paper
summarizes H. Zimmerman's doctoral dissertation offering an organized
approach to optimizing the buckling strength of carbon-reinforced cylinders.
Also included are observations on the current and future applicability
of composite materials in the European aerospace industry.
PARALLEL STATIC SOLUTION
IN FINITE ELEMENT ANALYSIS (Acrobat K) #1787, 7 pgs.
Louis Komzsik--MSC.Software Corporation
ABSTRACT: The availability
of parallel supercomputers created some expectations for easy and inexpensive
improvements in finite element analysis. It is true that the most time
consuming numerical modules of finite element analysis systems can be
executed in parallel; however the conversion is not easy because sometimes
new algorithms are required, which are suitable for parallelization.
In the following sections
we discuss the major theoretical issues of converting finite element
code to a parallel machine:
- measurement of performance
gain
- the level of parallelization
- interaction with vectorization
- portability
The results presented are
from benchmarks executed on CRAY/XMP and IBM 3090 computers with multiple
processors.
A TOTAL
FINITE ELEMENT MODELING SYSTEM FOR THE MSC/NASTRAN USER (Acrobat 392K),
#1887, 3 pgs.
Gil White--Intergraph Corporation
ABSTRACT: The modern
structural analyst is often confronted with a multitude of CAD/CAE systems
that offer solutions to the problems of finite element model construction,
analysis, and results interpretation or postprocessing. The history
of computer-aided design and analysis has followed a path that provided
for the quickest method for automating specific functions. This evolution
has created islands of automation. Various attempts have been made to
link segregated databases and form cohesive systems. Some attempts have
proven successful but their efficiency is limited. Recent developments
in both hardware and software have opened the door to systems of fundamental
new design. The industry is now seeing the development of fully standalone
workstation platforms that provide new and exciting opportunities for
the MSC NASTRAN user.
EFFECTIVE
USE OF MSC/NASTRAN PARABOLIC TETRAHEDRAL ELEMENTS (Acrobat 1.02MB),
#1987, 8 pgs.
B. William Rudd and David Tompkins--SDRC CAE International, Ohio
ABSTRACT: Tetrahedral
elements have traditionally had little use for a number of reasons:
- The linear tetrahedron
is clearly to stiff for practical structural analysis applications.
- Traditional mesh generators
can not easily generate the elements
- More tetrahedral elements
are required to model a give geometric region than hexahedra, and
each node typically has more tetrahedral elements attached to it (hence
increasing analysis time).
- There are no natural planes
of nodes within a tetrahedral model. This makes it difficult to perform
certain checks and to review the analysis results.
In spite of the limitations,
modern free mesh generation techniques that can generate models with
tetrahedral elements very quickly for complex geometries have brought
renewed interest in using these elements. There are certainly modeling
advantages, but most users are concerned about the analysis results.
Since the linear tetrahedron element has a bad reputation, users are
understandably wary of using the new parabolic tetrahedron element.
MSC has added a parabolic
tetrahedron element to NASTRAN. Although this element has given excellent
results, there is a relatively small base of experience. SDRC has had
good success in applying it in structural and heat transfer applications,
and some of these experiences are documented here.
INTERACTIVE
LAMINATE POSTPROCESSING OF NASTRAN STRUCTURAL ANALYSES
(Acrobat 1.46MB) #2087, 15 pgs.
Keith J. Meyer and Steven Rahmann--PDA Engineering, California
ABSTRACT: The analysis
of laminated composite structures requires significant ply stress and
strain data recovery to determine margins-of-safety. If obtained in
batch mode for a large number of plies even a modest structural model
will produce boxes of printout. An interactive laminate postprocessing
feature in PATRAN was used to recover ply data for an aircraft access
door cutout analysis in which several PCOMP directives were used to
model increases in laminate thickness around the cutout. Both ply stresses
and strains were recovered and the stresses are the same as those (fiber
dominated) recovered by NASTRAN. The interlaminar shears differ only
in the off-axis or angle plies where a known problem exists. The paper
also presents margins-of safety for ply failure analyses based on the
Tsai-Wu criteria in graphical format. These enhanced postprocessing
features increase significantly the utility of NASTRAN for laminated
composite structural design.
MSC/NASTRAN
IN A HIGH PERFORMANCE COMPUTER ENVIRONMENT (Acrobat 914K) #2187, 9
pgs.
Ian A. Taylor and John Huseby--Floating Point System
ABSTRACT: MSC/NASTRAN
has been available on high-speed computers, such as the FPS M64 Series
of Minisupercomputers, for sufficiently long enough to enable the collection
of a substantial body of performance results. These results indicate
that elapsed job time can be significantly affected by such factors
as CPU clock rate, memory and I/O bandwidth, mass memory device utilization,
software constructs, and general system parameters.
We examine the performance
of a typical MSC/NASTRAN job, in the context of Amdahl's Law, under
varying conditions and approaches on the FPS M64 Series. Important conclusions
are reached indicating that raw CPU power is not sufficient to guarantee
high performance that CPU LOAD and SYSTEM I/O must be balanced, and
that judicious application of system software parameters can produce
impressive results.
ACCESSING
AND DISPLAYING MSC/NASTRAN RESULTS USING A RELATIONAL DATABASE
(Acrobat 789K) #2287, 6 pgs.
Asbjorn Melo, Jim Ross, Richard Russell and Paul McDonald--SDRC CAE International,
Ohio
ABSTRACT: Many
graphical pre- and post-processing systems allow generation of specific
model types and review of specific, predefined results from MSC/NASTRAN.
Few if any allow the flexibility to get at the full spectrum of analysis
capabilities in MSC/NASTRAN. This paper discusses a flexible approach
to generating, accessing, manipulating and displaying data using a relational
database. The database is an integral part of the SDRC I-DEAS Supertab®
pre-post-processing software. The relational database allows the user
to modify the type of model generated, add additional data to the input
deck, access and review virtually any result and perform additional
calculations for results understanding. A number of examples, such as
creating the CHBDY convective heat boundary element, accessing frequency
response data and performing fatigue life estimates, are used to illustrate
application of the I-DEAS relational database with MSC/NASTRAN.
NASTRAN
NONLINEAR ANALYSIS OF STIFFENED WING PANELS (Acrobat 621K) #2387,
6 pgs.
E. Chow--Douglas Aircraft Company--Long Beach
ABSTRACT: MSC/NASTRAN
nonlinear analysis capability has been studied by many investigators.
In this paper, Solution 66 of MSC/NASTRAN Version 64A is used to analyze
stiffened panels of the wing in a large transport aircraft. Material
nonlinear buckling results, obtained from Solution 66 and its DMAP Alter
for nonlinear eigenvalue extraction, shows substantial agreement with
the experimental test data of stiffened panel under compression. The
paper also addresses the application of nonlinear analysis of MSC/NASTRAN
in material evaluation and selection of structures.
PRESSURE
FOLLOWER MATRIX FOR GEOMETRIC NONLINEAR FINITE ELEMENT ANALYSIS
(Acrobat 1.16MB) #2487, 23 pgs.
David N .Herting--MSC.Software Corp.
Gernot W. Haggenmacher--Consultant
ABSTRACT: The variation
of pressure loads due to displacement variations in nonlinear geometric
analysis is developed in terms of a tangent finite element matrix. This
so-called follower force matrix is significant relative to the normal
geometric tangent matrices for many problems and improves the convergence
of the nonlinear solution. The effects of the follower force matrices
are also important for analyzing problems of instabilities and dynamics
under pressure, such as containers and tires where an accurate tangent
matrix is required. Special finite elements are implemented in MSC/NASTRAN
to represent the tangent stiffness of pressure loads on surfaces. Results
shown for buckling solutions and normal mode analysis, indicate dramatic
improvement in the results.
USE OF
MSC/NASTRAN FOR THE THERMAL ANALYSIS OF THE SPACE SHUTTLE ORBITER BRAKING
SYSTEM (Acrobat 1.59MB) #2587, 19 pgs.
James Shu and David McCann--Lockheed-EMSCO, Texas
ABSTRACT: The MSC/NASTRAN
thermal capabilities are being employed to calculate the space shuttle
orbiter braking system thermal margins and to analytically verify the
current beryllium brake hardware improvements and the new structural
carbon brake design.
MSC/NASTRAN thermal capabilities,
transient thermal (SOL.89) and linear stress analysis (Sol. 24), are
being used to conduct thermal transient and thermal stress analysis
of this complex system. Three finite element models have been created
to investigate the spacial and temporal temperature variations in the
brake stators and the complete brake system, and to determine thermal
and mechanical stress distributions in the brake stator during the braking
process.
During the course of this
investigation, the thermal capabilities of MSC/NASTRAN have truly been
put to a thorough test. Man modeling difficulties have had to be overcome
and several deficiencies in the program were discovered. This paper
discusses the modeling techniques, solution methods, analytical results,
comparisons with SINDA results, and experience gained in using solutions
89 and 24 for this type of application.
THE USE
OF MSC/NASTRAN TO DETERMINE THE IMPACT RESPONSE OF A REACTOR CORE DUE
TO SEISMIC LOADING (Acrobat 1.16MB) #2687, 13 pgs.
R.G. Hill--Advanced Nuclear Fuels Corp., Washington
ABSTRACT: The finite
element analysis methodology used to determine the nonlinear mechanical
response of pressurized water reactor (PWR) fuel assemblies is described.
The models include nonlinearities such as impacting among the various
structural components and permanent deformation of fuel assembly spacer
grids during impact loading. The primary results obtained are fuel assembly
impact forces and spacer grid crushing loads. The fuel assembly is modeled
using a modal synthesis simulation. A combination of finite element
representation of the fuel assembly and experimental results is used
to develop this model. The synthesized fuel assembly is then combined
with nonlinear spacer grid models to form the overall core response
model for evaluation with MSC/NASTRAN. The applicability of this finite
element analysis methodology is demonstrated by evaluation of a Nuclear
Regulatory Commission (NRC) standard problem.
A STUDY
OF THE THERMO-ELASTIC BEHAVIOR OF A CONTROLLED THERMAL EXPANSION MODULE
USING LINEAR FINITE ELEMENT THEORY IN MSC/NASTRAN (Acrobat 5.61MB)
#2787, 43 pgs.
F.W. Palmieri--Palmier Consulting Company, Inc.
ABSTRACT: Due to the
mismatch in the coefficients of thermal expansion of leadless chip carriers
and printed wire boards, cyclic changes in ambient temperature create
thermal strains in solder joints which lead to premature fatigue failures.
One method of precluding these failures is to manufacture electronic
modules which consist of printed wire boards laminated to low expansivity
metal sheets, known as controlled thermal expansion modules. It was
the purpose of this study to utilize finite element techniques to qualify
the relative advantage of various design alternatives by investigating
the effect of variations in two design parameters (i.e., bond and face
sheet thickness). Analysis of test results show good correlation of
finite element predictions and experimental results.
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