msc paper on composites
TRANSCRIPT
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*Copyright 2001 Lockheed Martin Corporation. All rightsreserved. Published by the MSC.Software Corporation withpermission.
1
Integration of External Design Criteria with MSC.Nastran Structural
Analysis and Optimization*
Paper No. 2001-15
D.K. Barker and J.C. Johnson
Lockheed Martin Aeronautics Company, Fort Worth, [email protected]
E.H. Johnson and D.P. Layfield
MSC.Software Corporation, Santa Ana, California
ABSTRACT
Lockheed Martin Aeronautics Company (LM Aero)
has partnered with MSC.Software Corporation to
implement enhancements in the core MSC.Nastran2001 software product. New features include
enhancements to the existing laminate modeling
capability, improved software integration methods(including the emerging MSC.Nastran Toolkit), and
the development of a new capability, external
responses for SOL 200. This paper describes the new
functional features of the core MSC.Nastran product,
demonstrates existing integration with LM Aero
structural analysis processes, and describes ongoing
integration with the new external response features.
Further, two example problems demonstrate the
benefit of new MSC.Nastran features, as well as,compare and contrast the fully stressed design (FSD)
and math programming (MP) design methodologies.
INTRODUCTION
The aerospace industry has traditionally relied on
regimented hand-stress analysis processes to perform
detail air-vehicle analysis and sizing. Automated
structural optimization methods have been
successfully used in the preliminary design arena to
develop fundamental laminate tailoring concepts to
satisfy certain system-level requirements, such as
aeroelastic effectiveness and roll performance (Refs
1-4). However, production drawing release demands
a rigorous assessment of detail strength analysis
criteria, which are not effectively accommodated
during the preliminary design cycle. Therefore,production air-vehicle programs devote significant
manpower to analyzing freebody loads developed
through finite element analysis (FEA), performing
detail structural analysis criteria checks, and
providing necessary increments to structural gages
where necessary.
LM Aero relies on a highly customized and
proprietary suite of analysis methods to assess
structural strength criteria including panel buckling
(Ref 5), local effects due to panel pressure (Ref 6),and fastener criteria (Ref 7). However, stress
analysts often spend a disproportionate amount of
time recovering and interpreting data from FEA toprovide input to the detail structural analysis utilities,
rather than actually performing and interpreting the
analysis criteria results.
As diagramed in Figure 1, the traditional detail struc-
tural analysis and sizing cycle consists of develop-
ment of the FEA internal loads data, assessment of
detail structural analysis criteria, and applying incre-
ments to structural gages as required. It is wellunderstood that changes to structural gage (i.e.,
structural stiffness) result in changes to the internal
load distribution, which may render the current
structural criteria analysis invalid. Therefore, addi-tional detail structural analysis and sizing cycles may
be performed in an attempt to account for redistribu-
tion of internal load. In some cases, when changes to
structural stiffness are significant, external loads are
recomputed to consider changes in aeroelastic be-
havior. Finally, the man-in-the-loop represents the
physical task of engineering data handoff between
processes and represents opportunities for data inte-
gration. Therefore, LM Aero has developed seamless
InternalLoads
Database
DetailStructuralAnalyses
UpdatedExternal
Loads
Structural
Sizing
InternalLoads
Database
DetailStructuralAnalyses
UpdatedExternal
Loads
Structural
Sizing
Figure 1. Hand Stress Analysis Consumes Time
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interfaces (using the MSC.Nastran Toolkit) between
its structural analysis criteria software and FEA result
data to automate the detail sizing tasks.
Similarly, LM Aero recognizes the benefit of incor-
porating detail structural analysis criteria early in
preliminary design and has long been a player in the
development and validation of FEA-based, multidis -
ciplinary design optimization methods (Refs 8-10).
The ability to consider detail structural analysis
criteria up front in the design process allows the
stress analysis community to have a voice in the de-termination of basic design concepts. For instance,
FEA-based, multidisciplinary design optimization
methods (such as MSC.Nastran SOL 200) provide
the means to acquire sensitivity of structural weight
to configuration-level criteria such as roll effective-
ness and structural weight to detailed structural
member criteria such as strength allowables. There-
fore, improved integration with SOL 200 was addi-
tionally sought by LM Aero and further led to thespecification and development of external response
criteria using the new DRESP3 capability.
MSC.NASTRAN ENHANCEMENTS
LM Aero has recognized the need for improved inte-
gration between its in-house detail structural analysis
criteria and FEA result data. In late 1999, LM Aero
partnered with MSC.Software Corporation to imple-
ment enhancements to the core MSC.Nastran soft-
ware product to accomplish this end. Specifically,
enhancements were implemented in three separate
areas simplified laminate modeling techniques forevolving structure, enhancements for improved inte-
gration with LM Aero in-house methods, and
development of external response criteria for SOL
200. The following paragraphs describe these
enhancements, which are available in MSC.Nastran
2001.
Laminate Modeling Enhancements
The primary motivation for the new PCOMP capa-
bility (Ref 11) is to support the use of composite
materials in a preliminary design stage where
stacking sequence effects are considered secondaryand would impede the development of high-quality
candidate design. This is particularly useful when the
composite description is used with an automated
design procedure such as SOL 200 in MSC.Nastran
or a client in-house procedure. Prior to version 2001,stacking sequence does impact the stiffness of the
laminate and, therefore, the results. In an automated
design context, it is often reasonable to assume the
effects on the results are small, especially for aircraft
structures since membrane effects typically dominate
the response in wing skins.
New laminate options have been provided on the
PCOMP entry (via the LAM field) to enable simpli-
fied laminate specification. The MEM option
neglects the stacking sequence effects since these
effects are only present in the bending terms. The
SMEAR option is a compromise solution that
includes the bending effects by assuming the plies are
uniformly distributed through the laminate and mem-
brane/bending coupling effects are ignored. TheSMCORE option is a further refinement allowing a
simple modeling of a frequently encountered sand-
wich panel design. The stacking sequence of the
plies in the face sheet are again ignored and a uni-
form distribution is assumed across two equivalent
face sheets, but now the offset due to the known core
thickness can be included. The BEND option is pro-
vided for completeness and can be thought to provide
a simple interface to situations where bending effectsdominate.
MSC.Nastran develops mass and stiffness data fromPCOMP input in a two-step process. First, PCOMP
input data are considered together with material data
referenced by MIDi attributes to produce
PSHELL/MAT2 combinations leading to the required
stiffness results and then the spawned data are used in
the actual stiffness and mass calculations. Currently,
the spawned PSHELL has four, nonblank MIDi
attributes, identifying the MAT2 entries to be used
for membrane, bending, transverse shear and mem-
brane bending coupling. The MEM, BEND, SM EARand SMCORE options are readily implemented in the
following manner.
MEM
The spawned PSHELL has MID1 (membrane) only
with the MID2, MID3, MID4, 12I/T**3 and TS/T
fields set as blanks.
BEND
In this case, the spawned PSHELL has MID2 (bend-
ing) only with MID1, MID3, MID4, 12I/T**3 and
TS/T fields set as blanks.
SMEAR
In this case, the spawned PSHELL has MID1=MID2
with MID3 and MID4 plus the 12I/T**3 and TS/T
fields set as blanks. This results in a bending term
given as:
IATB 12/][][3= (1)
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SMCORE
The SMCORE laminate is analogous to a sandwich
core laminate consisting of equivalent upper and
lower SMEARd face sheets separated by a core
thickness offset (Figure 2). Computation of the
membrane and bending stiffness matrices is
performed using the following derivation. Note that
membrane-bending coupling is ignored.
Definitions
Tface = T1 + T2 + + TN-1 (total thickness of
both SMEARd face
sheets) (2)
Tcore = TN (core thickness offset) (3)
SMEARd laminate
Thickness Offset
SMEARd laminate
SMEARd laminate
Thickness Offset
SMEARd laminate
Figure 2. Sandwich Core Laminate Defined Using
PCOMP LAM=SMCORE Option
Membrane Stiffness Matrix
The membrane stiffness matrix, [A], is computedusing method utilized by LAM=BLANK assuming
core stiffness (layer N) is zero.
Face Sheet Properties
[ ] [ ] 1AAI = (4)
11
12xy AI
AI= (5)
22
12
yx AI
AI= (6)
face
yxxy11
xt
0.1AE
= (7)
face
yxxy22
yt
0.1AE
= (8)
face
33xy
t
AG = (9)
Moment of Inertia
48
t
4
2ttt
II3
face
2
facecoreface
yyxx + +== (10)
This collapses to12
t3face if tcore is zero. (11)
Bending Stiffness Matrix
( )yxxyxxx
11 .1IE
D = (12)
( )yxxy
yyy22 .1
IED = (13)
x
yxy112112 E
EDDD
== (14)
xxxy33 IGD = (15)
0DDDD 32233113 ==== (16)
Improved Integration Methods
During the course of the development partnership,
LM Aero was given access to an emerging product,
MSC.Nastran Toolkit (Ref 12), to explore advanced
software integration techniques and provide feedback
to MSC.Software to improve the planned commercial
product. The MSC.Nastran Toolkit provides the
necessary tools (application programming interfaces)
to write customized, standalone applications that
communicate with the MSC.Nastran program using
client-server technology. The Toolkit provides themechanism to create standalone applications that can
access all of MSC.Nastran's functionality and com-
ponents (i.e., matrix operations, utilities, engineering
(FE) functions, and database management system)
and incorporate these into a modern software frame-
work as shown in Figure 3. This framework facili-
tates multitier architectures, Web-enabled applica-
tions, and the distribution of MSC.Nastran's func-
tionality across different host computers.
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User Written
Client Program
MSC-Supplied
Client Object Lib.
API
API
MSC.Nastran
Executable
MSC.Nastran
DMAP Library DATABASE
Figure 3. Framework of the MSC.Nastran Toolkit
LM Aero use of the MSC.Nastran Toolkit focused
primarily on access to data on the MSC.Nastran data-
base and interactive control and data transfer within a
DMAP sequence (i.e., DMAP breakpoint control).
As a result of LM Aero evaluation, many enhance-
ments were made to the Toolkit to improve speed andefficiency. In particular, datablock indexing was
implemented to enable partial recovery of a datablock
record (e.g., element results for a user-specified list
of element IDs, as an alternative to default recoveryof the entire record of all element result data). Addi-
tionally, enhancements were made to enable server
reconnect by a child process, rather than requiring
server restart.
In addition, evaluation of the MSC.Nastran Toolkit
highlighted the desire to recover element results
(stress, strain, and force) in the material coordinatesystem. MSC.Nastran has traditionally stored
element results in the element coordinate system and
placed the burden on downstream post-processing
utilities to perform the transformation from the
element coordinate system to the material coordinatesystem. To support useful and straightforward data
recovery, a new option has been provided that allows
users to specify element response quantities be pro-
duced in the material coordinate system. The new
capability is limited to CQUAD4, CTRIA3,
CQUAD8 and CTRIA6 for element force, stress and
strain responses, and provides output in the
coordinate system defined using the THETA/MCID
field on their associated bulk data entries. Both
element center and element corner results are output
in the material system.
The user specifies the desire to store results in the
material coordinate system by setting the PARAM
OMID equal to YES in the input bulkdata stream.
When the OMID parameter is activated, element
result data in material coordinate system are reported
in the standard output file, .f06, and are available
for direct recovery from the MSC.Nastran database.
External Responses for MSC.Nastran
The design optimization capability (SOL 200) in
MSC.Nastran has a preexisting feature allowing the
user to create a synthetic response (implemented
using the DRESP2 bulkdata entry). However, the
types of variables a synthetic response can use are
limited to the data available from MSC.Nastran. A
new external response feature (Ref 13) further
extends the synthetic response by allowing the user to
define a custom response using either in-house pro-
grams or any application programs written in Fortran,C, or other computer languages. Therefore, general
and proprietary responses can be used either as an
objective or a constraint in a design.
The external response feature is implemented in
SOL 200 with client server technology. The design
optimization module in SOL 200 is the client and
user-supplied routines form the server. Whenever the
optimization module requires the value of an externalresponse, it sends the request to the server. On re-
quest, the server invokes the user-supplied routines to
calculate the response and returns the value to theclient. The communication between the client and
server programs is established through the applica-
tion programming interface (API) routines. Figure 4
shows the implementation scheme for the external
response capability.
MSC.Nastran API Server2
Server1
Server i
ExternalCriteria
i = 1..10
MSC.Nastran API Server2
Server1
Server i
ExternalCriteria
MSC.Nastran API Server2
Server1
Server i
ExternalCriteria
i = 1..10
Figure 4. Scheme of the External Response
Capability
The implementation scheme for the external responsecapability can be accomplished in two parts. First,
the end-user must develop a functional criteria server,
which computes the intended response value based
on MSC.Nastran-supplied input. Second, the end-
user must define the external response functions
within the input bulkdata stream using the new
DRESP3 bulkdata entry. The DRESP3 bulkdata
entry identifies underlying model properties and re-
sponse quantities (either intrinsic or synthetic), which
are required by the external criteria server.
Additionally, the DRESP3 bulkdata entry provides a
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mechanism to specify user-defined parameters (e.g.,
nonmodeled parameters like panel dimensions,
fastener layout, etc.). Therefore, the implementation
scheme is general and supports integration of any
external criteria available to the user.
AUTOMATION OF DETAILED ANALYSIS
AND SIZING
LM Aero has developed an automated detail sizing
process called AS3 (Automated Sequential Sizing
System), which is essentially an extended fullystressed design (FSD) sizing methodology (Figure
5). FSD is a shorthand term that is used to refer to
the automated design technique that performs a re-
sizing based on the current design and the structural
response of that design. In its most basic manifesta-
tion, a structural member that exceeds a prescribed
allowable, such as stress, is increased in size while a
member that is below its allowable stress is decreased
in size. The assumption is that a limited number ofdesign cycles that use this technique will arrive at a
design wherein the response in each element is at its
allowable value. The AS3 sizing utility providesseamless interfaces to in-house structural strength
criteria procedures and has influenced implementa-
tion of basic FSD methodology in the core
MSC.Nastran product (Ref 14).
Execute NASTRAN Solution
Parse Input File
Evaluate Element Criteria
Evaluate Practicality Criteria
Update FE Bulkdata
Generate VIEW Results
Converged ?no
yes
Execute NASTRAN Solution
Parse Input File
Evaluate Element Criteria
Evaluate Practicality Criteria
Update FE Bulkdata
Generate VIEW Results
Converged ?no
yes
Figure 5. AS3 Process Flow
Many strength criteria options have been imple-
mented in AS3, including stress, strain, panel
buckling, panel pressure, and fastener criteria. How-ever, it would not be wise or practical to build a
structure where each of thousands of elements has
been individually sized to just meet an allowable.
Therefore, to generate a more practical design,
additional options have been implemented; such as,
minimum gage, property linking, ply percentage
criteria, and property drop-off criteria. Integration of
external strength criteria with the MSC.Nastran data-
base and implementation of practicality criteria are
discussed in the following paragraphs.
External Strength Criteria
The XSTREAM software module was developed to
enable seamless finite-element (FE) data Xtractionfor STRuctural Engineering Analysis Methods.
Using this capability, analysis methods driven by
ASCII input stream(s) can be directed to run with
data automatically recovered from one or more FE
result databases, as depicted in Figure 6. This
approach is different than traditional approaches
since the analysis method or application does not
require any modification. The analysis application
remains a stand-alone tool and the XSTREAM utilityprovides interfaces to the input and output files. A
significant benefit of this approach is that the analysis
application requires no knowledge of the FE model(element connectivity, property definition, results,
etc.). The XSTREAM utility recovers both required
FE result data and user-defined reference data and
provides the required information to the analysis
application through the ASCII input stream. The
BATCH packet concept is used to define a template
input file with imbedded data recovery commands.
Data recovery commands are replaced with the
requested data items to generate the desired input file.
Using the XSTREAM-generated input file, theanalysis application generates its standard output file,
which is then interpreted by the XSTREAM utility.
Input File
Detail Analysis
Tool
Output File
FE
Result
DBTemplate File
Batch File
GeneratorBuckling AnalysisConceptual Input
>>DBGET REFVAR
>>DBGET REFVAR
>>DBGET REFVAR
>>DBGET PROP
>>DBGET RESULT
>>DBGET RESULT
Title:Subtitle:
Material:
Panel Width:
Panel Length:
Panel Thick:
Load Case 1:
Load Case 2:
Elem. Set
Ref. Variables
Input File
Detail Analysis
Tool
Output File
FE
Result
DBTemplate File
Batch File
GeneratorBuckling AnalysisConceptual Input
>>DBGET REFVAR
>>DBGET REFVAR
>>DBGET REFVAR
>>DBGET PROP
>>DBGET RESULT
>>DBGET RESULT
Title:Subtitle:
Material:
Panel Width:
Panel Length:
Panel Thick:
Load Case 1:
Load Case 2:
Elem. Set
Ref. Variables
Figure 6. Seamless Integration of External
Strength Criteria
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Integration with the MSC.Nastran database is accom-
plished through the Batch File Generator (depicted
in Figure 6) and relies on the MSC.Nastran Toolkit
API to accomplish FEA data recovery. Using the
XSTREAM method, LM Aero has developed
standard interfaces for three in-house developed and
maintained structural strength criteria procedures:
panel buckling and strain optimization (TM1), local
effects due to panel pressure (PRESS), and fastener
criteria (IBOLT).
The TM1 procedure optimizes flat or curved panelssubject to any combination of membrane loads. The
procedure computes panel thickness as well as the
proper proportions of 0-deg, 90-deg, and 45-degplies to provide minimum panel weight without
violating strength or buckling constraints. Strength
constraints are based on the allowable lamina fiber
strains defined by the user or recovered from thematerial database. Buckling constraints are calcu-
lated using equations for buckling of a simply-sup-
ported rectangular, orthotropic plate.
The PRESS executable process calculates bending
moments, in-plane loads, strains, and the maximum
deflection of a flat laminated, rectangular panel
loaded with a uniform pressure distribution. The
element criteria function/interface recovers the
PRESS computed results, which capture the local
strain effects at the panel edges (boundary condi-tions) and panel center (maximum deflection). The
interface computes strain margins based on user-
specified or material database allowables and addi-
tionally computes the required panel thickness (andply percentages for orthotropic panel construction).
IBOLTs capabilities include the analysis of a rectan-
gular plate of known thickness and geometry with a
hole in its center. This configuration is subjected to
biaxial tension, off-axis bearing, and shear loads.
IBOLT also incorporates material type, operating
temperature, and moisture content into its analysis ofstiffness, strength and strain. This interface computes
fastener criteria margins and predicts required
element thickness increment for the combined effect
of in-plane load due to the statics FE solution and the
lateral pressure load. The previously described pro-cedure, PRESS, is used to compute the internal load
increment due to lateral pressure load.
Practicality Criteria
Practicality criteria are applied to the intermediate
properties defined by the previously evaluated
strength criteria, if specified by the user. Many prac-
ticality criteria options are available, such as mini-
mum gage, property linking, ply-percentage upper
and lower bounds, and maximum property drop-off
rate. Of these criteria, the property drop-off rate cri-
terion deserves further explanation.
The property drop-off rate between neighboringelements is evaluated according to the following
equation:
rate = (prop0 - prop1) / distance (17)
where, propi is element property value of the parent
(0) or adjacent (1) element and distance is computed
along element surfaces between adjacent centroids.
Figure 7 shows how this control is applied to ensure
that thickness changes occur at an acceptable rate.
Three contiguous 2-D elements are shown with initial
thicknesses and intermediate strength criteria incre-
ments. The edge view of the elements shows their
relative thicknesses along with an allowable property
drop-off rate indicated by a solid line. The actual
property drop-off rate moving from element 2 to
element 1 is less than the allowable drop-off rate, an
acceptable situation. The actual ply drop-off rate
moving from element 2 to element 3 is greater than
the allowable drop-off rate, an unacceptable situation.
In this case, AS3 would revise the thickness of
element 3 to meet the drop-off rate criterion as
shown. The property drop-off rate criterion can be
applied to any number of elements in a user-specifiedset. For any given element, AS3 checks all adjacent
elements (those sharing nodes with the given
element) for compliance with the ply drop-off rate
criterion. As AS3 continues to apply the criterion to
all elements in the element set, thickness changes that
were made to adjacent elements may then affect other
elements that are neighbors of the adjacent elements.
Thus, property drop-off criteria increments may
propagate over many elements to reduce a steep in-
termediate property gradient.
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Edge View of 2-D Element Strip
Plan View of 2-D Element Strip
Element Centroid
Allowable
Drop-Off
Rate
Actual Drop-
Off Rate
Allowable
Drop-OffRate
Revised Thickness
Initial Thickness
Intermediate Thickness
1 2 3
Actual Drop-
Off Rate
Edge View of 2-D Element Strip
Plan View of 2-D Element Strip
Element Centroid
Allowable
Drop-Off
Rate
Actual Drop-
Off Rate
Allowable
Drop-OffRate
Revised Thickness
Initial Thickness
Intermediate Thickness
1 2 3
Actual Drop-
Off Rate
Figure 7. Control of Property Taper Rate
Once all the strength criteria and practicality criteria
increments have been evaluated, an updated FE bulk-
data file is generated and a post-processing file is
developed, as depicted previously in Figure 5. If
property increments are small and satisfy the conver-
gence criteria, the automated detail sizing processconcludes. Otherwise, additional sizing iterations are
performed until convergence is reached or the maxi-
mum iterations have been performed.
FSD Demonstration Problem
The intermediate complexity wing (ICW) of
Figure 8 has been used by several automated design
procedures to demonstrate their utility. This demon-
stration applies the LM Aero automated detail sizing
utility, AS3, to size both composite wing skins and
metallic understructure simultaneously. The com-posite skins are modeled using the PCOMP
LAM=SMEAR option, include 0-deg, 45-deg and90-deg plies, and the 0-deg reference is oriented par-
allel to the box leading edge.
Skins 64 elements (4 layers/element)
Caps 110 elementsWebs 55 elements
Skins 64 elements (4 layers/element)
Caps 110 elementsWebs 55 elements
Figure 8. Intermediate Complexity Wing Model
Applied static loads for SOL 101 are summarized in
Table 1. The load envelope is predominantly posi-
tive wing bending with slightly different torsion for
each condition. A structural analyst would intuitively
suspect the upper skin to be subject to compression
and stability effects and the lower skin to be subject
to tension effects. Therefore, one would expect the
sized upper skin laminate to be dominated by a
combination of 0-deg plies, in order to satisfy com-
pression strain criteria, and 45-deg plies, to satisfypanel stability. Meanwhile, the upper 90-deg plies
should remain largely insignificant. However, one
would expect the sized lower skin to be dominated by
0-deg plies to satisfy the tension strain criteria, while
the 45-deg and 90-deg plies should remain largelyinsignificant.
Table 1. Applied Static Load Conditions
Condition
FZ
(103 lb)
MX*
(106 in-lb)
MY*
(106 in-lb)1 43.316 2.231 -1.027
2 42.533 2.211 - .447
*Moments summed about wing root at mid-chord.
Design criteria are shown in Table 2. Strength
criteria include strain and buckling criteria on the
wing skins, and stress criteria on the understructure
(spar/rib caps and webs). Additionally, practicality
criteria are applied to enforce minimum gage, ply
percentage, and property drop-off rate boundaries.
Table 2. Design Criteria (FSD Methodology)
Part Strength Criteria Practicality Criteria
Skins fiber strain
2200 tension2000comp.
panel stability
min. layer = 0.025 in.
min. ply % > 8%
max. ply % < 60%
drop-off rate < 0.02*
Caps axial stress
27 ksi tension
28 ksi compression
min. gage = 0.05 in.
drop-off rate < 0.015*
Webs max shear stress
24 ksi
min. gage = 0.025 in.
drop-off rate < 0.02*
*Drop-off rate defined by Equation 17.
Each element in the FE model (including each
laminate ply) is sized uniquely, resulting in 421
design variables. However, laminate torsion stiffnessis balanced by linking the +45-deg and 45-deg plies,
thereby reducing the total to 357 independent design
variables.
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To improve the design convergence, a design vari-
able move restriction is implemented using the
following equation.
Tenforced = (Trequired / Tinit ) Tinit (18)
where,
is the relaxation factorTinit is the initial property value
Trequired is property required by strength criteria
Tenforced is the enforced property value.
By enforcing only a fraction of the computed
sizing increment at completion of the design itera-
tion, the possibility of overshooting the actual re-quired increment is minimized. To demonstrate this
effect, three separate designs were achieved using
relaxation factors of 0.5, 0.75, and 1.00.
Each design solution was allowed to perform 10
design iterations. As shown in Figure 9, the total
design weight converges at different rates for each
design (as quickly as one iteration for =1.0 and upto 4 iterations for =0.5). Thus, in each case, theFSD methodology has demonstrated a total design
weight (representative of criteria applied) can be pre-
dicted rapidly and confidently in a minimal numberof iterations.
Objective Convergence
120
130
140
150
160
170
180
190
1 2 3 4 5 6 7 8 9 10
Iteration Number
TotalWeight(lb)
Alpha=0.50
Alpha=0.75
Alpha=1.00
Objective Convergence
120
130
140
150
160
170
180
190
1 2 3 4 5 6 7 8 9 10
Iteration Number
TotalWeight(lb)
Alpha=0.50
Alpha=0.75
Alpha=1.00
Figure 9. Objective Convergence Characteristics
(FSD Methodology)
However, as demonstrated in Figure 10, the design
criteria converges at a much slower rate, indicating
that the structural weight continues to be redistributed
for many iterations. For this demonstration problem,
criteria convergence requires 8 iterations if=0.5.
Critical Criteria Convergence
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
1 2 3 4 5 6 7 8 9 10
Iteration Number
MinMargin
ofSafety
Alpha=0.50
Alpha=0.75
Alpha=1.00
Critical Criteria Convergence
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
1 2 3 4 5 6 7 8 9 10
Iteration Number
MinMargin
ofSafety
Alpha=0.50
Alpha=0.75
Alpha=1.00
Figure 10. Criteria Convergence Characteristics
(FSD Methodology)
Further, negative margins of safety are still present in
the model even after 10 FSD sizing cycles. After the
tenth iteration, the most critical element has a margin
of safety of approximately 0.1 and is attributed
primarily to a single element. Element 261 (a ROD
element, which is the most inboard element on the
lower aft-spar cap) is the most critical element for
analyses 2 thru 10. The wing box root boundary is
simplistically modeled using a clamped boundary
condition and results in a load chasing effect,
which highlights a limitation of the FSD
methodology. A fundamental assumption of FSD is
that the internal load distribution remains constant asstructural properties (and, therefore, structural stiff-
ness) are redistributed. Therefore, the sizing process
is unable to detect that increasing the stiffness of
element 261 results in a nearly equivalent increase instructural load. As shown in Figure 11, the signifi-
cance of the localized effect is illustrated by exclud-
ing all ROD elements in the lower aft spar cap from
the criteria convergence assessment.
Critical Criteria Convergence
-0.5
-0.4
-0.3
-0.2
-0.1
0
1 2 3 4 5 6 7 8 9 10
Iteration Number
MinM
arginofSafety
All Elements
Lower Aft SparCap Excluded
Critical Criteria Convergence
-0.5
-0.4
-0.3
-0.2
-0.1
0
1 2 3 4 5 6 7 8 9 10
Iteration Number
MinM
arginofSafety
All Elements
Lower Aft SparCap Excluded
Figure 11. Criteria Convergence History (FSD
Methodology,=0.5)
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9
Having recognized this phenomenon, engineering
logic would certainly prevail in an actual application
and thickness would be artificially added to other
skin elements to reduce the localized stress concen-
tration. The computed laminate increment from
iteration 8 to 9 is displayed in Figure 12 and pro-
vides further insight into the load chasing effect. A
similar trend can be observed at each sizing iteration
thickness is added to the laminate aft of the center
spar, while thickness is removed from forward of the
center spar. The net result is that internal load is
slowly redistributed toward the aft portion of thewing and the sized structure has to continually adjust
to increasing internal load incurred at the aft portion
of the structure. Therefore, the analyst would likely
elect to artificially add a small increment to the
laminate forward of the center spar to counteract the
load chasing effect. Application of the artificial
laminate increment is merely identified as a likely
design strategy and is not demonstrated in this paper.
ABC
DE
FGH
IJK
L
MN
OPQ
R
-0.0055-0.0050-0.0045
-0.0040-0.0035
-0.0030-0.0025-0.0020
-0.0015-0.0010-0.0005
-0.0000
0.00050.0010
0.00150.00200.0025
0.0030
Increment (in.)
ABC
DE
FGH
IJK
L
MN
OPQ
R
-0.0055-0.0050-0.0045
-0.0040-0.0035
-0.0030-0.0025-0.0020
-0.0015-0.0010-0.0005
-0.0000
0.00050.0010
0.00150.00200.0025
0.0030
Increment (in.)
ABC
DE
FGH
IJK
L
MN
OPQ
R
-0.0055-0.0050-0.0045
-0.0040-0.0035
-0.0030-0.0025-0.0020
-0.0015-0.0010-0.0005
-0.0000
0.00050.0010
0.00150.00200.0025
0.0030
ABC
DE
FGH
IJK
L
MN
OPQ
R
-0.0055-0.0050-0.0045
-0.0040-0.0035
-0.0030-0.0025-0.0020
-0.0015-0.0010-0.0005
-0.0000
0.00050.0010
0.00150.00200.0025
0.0030
Increment (in.)
Figure 12. Upper Skin Laminate Increment
(iteration 8, =0.5)
Once the load chasing phenomenon is understood,
it is apparent that the best solution is certainly not the
last iteration. Since the critical design criteria
achieve convergence at iteration 8 (for =0.5), sub-sequent iterations are merely an opportunity to absorb
internal load in the aft structure (although the relaxa-
tion factor limits this effect). Evaluation of the sized
property contours for iterations 7 thru 10 confirm that
the model has essentially converged and, therefore,
iteration 8 is selected as the best design. The quality
of design iteration 8 is further illustrated in Figure
13, which displays a plot of critical criteria types andmargins of safety for each element in the upper skin.
All margins are close to zero and vary from a maxi-
mum margin of 0.181 to a minimum critical margin
of -.040.
Figure 13. Upper Skin Critical Criteria and
Margins of Safety (FSD Methodology)
The laminate total thickness contour for the upper
skin at iteration 8 is displayed in Figure 14. As
anticipated, the general characteristic is that the
thickness decreases as a function of span. Also, total
thickness tends to increase with chord (from fore to
aft). This result is consistent with the aft swept wing,
which tends to maximize wing-root bending moment
at the aft portion of the root boundary condition.
Also, the maximum laminate thickness does not
occur at the location of maximum wing bending
moment, but instead occurs at the third element out-
board of the aft -most wing-root element. Since ribspacing is reduced at the wing-root trailing edge, less
thickness is required to satisfy panel stability.
Figure 14. Upper Skin Laminate Thickness (FSD
Methodology)
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Laminate ply percentage contours for the upper skin
at iteration 8 are provided in Figure 15. Again, sized
physical properties are consistent with anticipated
results. The 0-deg plies and 45-deg plies are domi-nate throughout the laminate, while the 90-deg plies
remain at or near the minimum ply percentage
boundary of 8 percent. The concentration of 0-degplies is greatest at the aft portion of the wing root,
where wing-bending moment (and consequently 0-
deg fiber strain) is the greatest. In general, the con-
centration of 0-deg plies tends to decrease as a func-
tion of span and associated decrease in wing-bending
moment. Similarly, a significant concentration of
45-deg plies is required throughout the laminate inorder to provide panel stability. However, the re-
verse trend is observed for the 45-deg plies. In
general, the concentration of 45-deg plies tends toincrease as a function of increased span, which is
consistent with the transition from a 0-deg compres-
sion-dominate buckling mode (i.e., wing bending) atthe wing-root to a shear-dominate buckling mode(i.e., wing torsion) at mid-span.
A
BC
DEF
GH
IJK
L
5.0
10.015.0
20.025.030.0
35.040.0
45.050.055.0
60.0
Ply Percentage
0-degplies
90-degplies
45-degplies
A
BC
DEF
GH
IJK
L
5.0
10.015.0
20.025.030.0
35.040.0
45.050.055.0
60.0
Ply Percentage
A
BC
DEF
GH
IJK
L
5.0
10.015.0
20.025.030.0
35.040.0
45.050.055.0
60.0
Ply Percentage
0-degplies
90-degplies
45-degplies
Figure 15. Upper Skin Laminate Ply Percentages(FSD Methodology)
Lastly, the property drop-off criterion played only a
localized role in this demonstration problem. How-
ever, it did serve to smooth the local property build-
up as a result of the load chasing phenomenon de-
scribed previously. Recall that element 261 is the
most inboard element on the lower aft-spar cap.
Because of the local build-up in element 261, the
adjacent aft-spar cap element required a property
increment to satisfy the property drop-off criterion.
However, the overall effect is two-fold. First, as ini-
tially intended, the spar cap is enforced to maintain a
more gradual reduction in cross-sectional area and,
thereby, result in a more practical and manufactur-
able structural component. Second, by adding struc-
tural property increments around the local build-up,
the internal load concentration is likewise redistrib-
uted across a larger area and the peak internal load is
reduced. Therefore, for this demonstration problem,
the rate of the load chasing phenomenon is furtherreduced.
INTEGRATION WITH MSC.NASTRAN
OPTIMIZATION SEQUENCE
LM Aero is providing extended integration of its in-
house developed procedures to support multidiscipli-
nary, structural optimization using MSC.Nastran
SOL 200. Whereas the previously described integra-tion efforts rely on the more rapid FSD sizing meth-
odology to satisfy detail structural criteria (supports
engineering drawing release), integration with SOL200 math programming (MP) methodology provides
an opportunity to consider detail structural criteria
early in preliminary design. Specifically, system-
level trades such as aeroelastic performance as a
function of required structural weight can now be
more easily considered. The new DRESP3 external
response capability provides the mechanism to
include specialized in-house developed and main-
tained criteria (e.g., TM1, PRESS, and IBOLT)
within the optimization sequence. Additionally, thenew simplified laminate modeling techniques provide
an opportunity to define practicality criteria, such as
ply percentage constraints, which have previously
been difficult to define.
The MSC.Nastran Toolkit again plays a significant
role, as LM Aero intends to leverage the design
model definition already available through the in-
house developed AS3 input stream. Rather than
force the user to redefine design variables and struc-
tural design constraints through the MSC.Nastran
bulkdata file, LM Aero intends to define the design
model on the MSC.Nastran database during thecourse of the SOL 200 optimization sequence. Spe-
cifically, the MSC.Nastran Toolkit is being used to
define a breakpoint directly after the DMAP IFP
module, translate and append the AS3 design model
to any preexisting design data on the MSC.Nastrandatabase, then resume the SOL 200 optimization
sequence. In this fashion, detail structural strength
criteria and ply percentage criteria defined on the
AS3 input stream can be appended to aeroelastic
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criteria originally defined on the MSC.Nastran bulk-
data input file.
Integration of external strength criteria and imple-
mentation of ply percentage constraints are discussed
in the following paragraphs. Although intended inte-
gration is not complete prior to publishing this paper,
a prototype demonstration of these capabilities
further demonstrates the significance of the
MSC.Nastran 2001 enhancements.
External Response Servers and Strength Criteria
Integration with TM1, PRESS and IBOLT is straight-
forward and is accomplished in two parts. First, a
criteria server is required to interpret information
supplied by a DRESP3 entry, including model prop-
erties, response quantities, and user-specified
parameters (representing nonmodeled parameters
such as number of fastener rows and spacing). The
external criteria server must also call the main criteriafunction subroutine to generate the target response
and return the response value to the parent SOL 200
optimization sequence. Second, the design criteria,which are defined on the AS3 input stream, must be
translated to DRESP3 entries on the MSC.Nastran
database. This approach is taken to allow a common
input stream format for both structural sizing
approaches described in this paper.
A prototype criteria server has already been devel-
oped and demonstrated for the TM1 panel stability
and strain analysis procedure. The simplified imple-
mentation launches the TM1 procedure as a separatesystem command and recovers the response quantity
from an intermediate output file, relies on hardwired
parameters specific to the demonstration model, and
requires user specification of the driving DRESP3
entries directly in the MSC.Nastran input stream.
However, the prototype criteria server enables
demonstration of the DRESP3 entry described in the
following paragraphs.
In addition to integration of external criteria servers,
specialized synthetic strain criteria must be devel-
oped for SMEAR and SMCORE PCOMP entries.
The underlying assumption of the smearedlaminate is that all plies are uniformly distributed
throughout the thickness of the laminate, therefore,
the MSC.Nastran standard fiber strain criteria is not
correct. The standard fiber strain criteria uses strains
computed at the location of the ply, as defined by thePCOMP laminate stack, whereas the preferred con-
servative approach is to use upper and lower element
surface strains that are reoriented to the fiber coordi-
nate system to evaluate the fiber strain criteria. As
illustrated in Figure 16, a DEQATN entry can be
readily developed in the input bulkdata stream and
referenced by a DRESP2 entry to evaluate the syn-
thetic response. However, only the upper surface
synthetic fiber responses are shown. Therefore,
additional bulkdata entries are required to enforce
criteria on the lower laminate surface. Similar to the
external strength criteria, synthetic fiber strain criteria
will be automatically appended to design criteria on
the MSC.Nastran database as defined by entries on
the AS3 input stream.
$ SYNTHETIC FIBER STRAIN CONSTRAINTS
$ design constraints for fiber strain.
DCONSTR, 3, 201, -2000., 2200.
DCONSTR, 3, 202, -2000., 2200.
DCONSTR, 3, 203, -2000., 2200.
DCONSTR, 3, 204, -2000., 2200.
$ synthetic fiber strain responses (Z2)
$ (0, -45, +45, and 90 deg plies)DRESP2, 201, E1, 401
, DTABLE, A1
, DRESP1, 301, 302, 303
DRESP2, 202, E2, 401
, DTABLE, A2
, DRESP1, 301, 302, 303
DRESP2, 203, E3, 401
, DTABLE, A3
, DRESP1, 301, 302, 303
DRESP2, 204, E4, 401
, DTABLE, A4
, DRESP1, 301, 302, 303
$ intrinsic laminate strain
$ (Ex, Ey, and Exy) for top surface (Z2)
DRESP1, 301, EX, STRAIN, PCOMP, , 11, , 100DRESP1, 302, EY, STRAIN, PCOMP, , 12, , 100
DRESP1, 303, EXY, STRAIN, PCOMP, , 13, , 100
$ strain transformation equation.
DEQATN 401 thetar(theta,ex,ey,exy) =
theta * PI(1) / 180. ;
exfiber =
1.0e+6 *
(ex*cos(thetar)**2 +
ey*sin(thetar)**2 +
exy*sin(thetar)*cos(thetar))
$ table of constant parameters (ply angles).
DTABLE, a1, 0., a2, -45., a3, 45., a4, 90.
$ SYNTHETIC FIBER STRAIN CONSTRAINTS
$ design constraints for fiber strain.
DCONSTR, 3, 201, -2000., 2200.
DCONSTR, 3, 202, -2000., 2200.
DCONSTR, 3, 203, -2000., 2200.
DCONSTR, 3, 204, -2000., 2200.
$ synthetic fiber strain responses (Z2)
$ (0, -45, +45, and 90 deg plies)DRESP2, 201, E1, 401
, DTABLE, A1
, DRESP1, 301, 302, 303
DRESP2, 202, E2, 401
, DTABLE, A2
, DRESP1, 301, 302, 303
DRESP2, 203, E3, 401
, DTABLE, A3
, DRESP1, 301, 302, 303
DRESP2, 204, E4, 401
, DTABLE, A4
, DRESP1, 301, 302, 303
$ intrinsic laminate strain
$ (Ex, Ey, and Exy) for top surface (Z2)
DRESP1, 301, EX, STRAIN, PCOMP, , 11, , 100DRESP1, 302, EY, STRAIN, PCOMP, , 12, , 100
DRESP1, 303, EXY, STRAIN, PCOMP, , 13, , 100
$ strain transformation equation.
DEQATN 401 thetar(theta,ex,ey,exy) =
theta * PI(1) / 180. ;
exfiber =
1.0e+6 *
(ex*cos(thetar)**2 +
ey*sin(thetar)**2 +
exy*sin(thetar)*cos(thetar))
$ table of constant parameters (ply angles).
DTABLE, a1, 0., a2, -45., a3, 45., a4, 90.
Figure 16. Synthetic Fiber Strain Criteria for
Simplified PCOMP Laminates
Completion of this component of the integration
effort provides an equivalent set of strength criteria to
those presently available in the previously described
FSD-based sizing procedure.
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12
Practicality Criteria
The simplified PCOMP laminate options MEM,
SMEAR and SMCORE require a minimum number
of layers to define the desired laminate. For instance,
a smeared representation of a laminate comprised
solely of 0-deg, 45-deg, and 90-deg plies requiresonly four PCOMP layers. Therefore, synthetic plypercentage criteria boundaries are readily defined
using DRESP2 and DEQATN entries as shown in
Figure 17. Additionally, these criteria will be auto-
matically translated to the MSC.Nastran database as
directed by criteria defined on the AS3 input stream.
$ SYNTHETIC PLY PERCENTAGE CONSTRAINTS
$ design variable definition
$ (0, -45, +45, 90 deg plies)
DESVAR, 1, T1, 0.05, 0.025
DESVAR, 2, T2, 0.05, 0.025
DESVAR, 3, T3, 0.05, 0.025DESVAR, 4, T4, 0.05, 0.025
DVPREL1, 1, PCOMP, 100, T1
, 1, 1.
DVPREL1, 2, PCOMP, 100, T2
, 2, 1.
DVPREL1, 3, PCOMP, 100, T3
, 3, 1.
DVPREL1, 4, PCOMP, 100, T4
, 4, 1.
$ design constraints for ply % boundaries
DCONSTR, 2, 501, 8.0, 60.0
DCONSTR, 2, 502, 8.0, 60.0
DCONSTR, 2, 503, 8.0, 60.0
DCONSTR, 2, 504, 8.0, 60.0
$ synthetic ply percentage response
$ (0, -45, +45, 90 deg plies)
DRESP2, 501, PRCNT1, 402
, DVPREL1, 1, 2, 3, 4, 1
DRESP2, 502, PRCNT2, 402
, DVPREL1, 1, 2, 3, 4, 2
DRESP2, 503, PRCNT3, 402
, DVPREL1, 1, 2, 3, 4, 3
DRESP2, 504, PRCNT4, 402
, DVPREL1, 1, 2, 3, 4, 4
$ ply percentage formulation.
DEQATN 402 total(t1,t2,t3,t4,ti) =
(t1 +t2 +t3 +t4);
plyprcnt =
1.e2 * (ti / total)
$ SYNTHETIC PLY PERCENTAGE CONSTRAINTS
$ design variable definition
$ (0, -45, +45, 90 deg plies)
DESVAR, 1, T1, 0.05, 0.025
DESVAR, 2, T2, 0.05, 0.025
DESVAR, 3, T3, 0.05, 0.025DESVAR, 4, T4, 0.05, 0.025
DVPREL1, 1, PCOMP, 100, T1
, 1, 1.
DVPREL1, 2, PCOMP, 100, T2
, 2, 1.
DVPREL1, 3, PCOMP, 100, T3
, 3, 1.
DVPREL1, 4, PCOMP, 100, T4
, 4, 1.
$ design constraints for ply % boundaries
DCONSTR, 2, 501, 8.0, 60.0
DCONSTR, 2, 502, 8.0, 60.0
DCONSTR, 2, 503, 8.0, 60.0
DCONSTR, 2, 504, 8.0, 60.0
$ synthetic ply percentage response
$ (0, -45, +45, 90 deg plies)
DRESP2, 501, PRCNT1, 402
, DVPREL1, 1, 2, 3, 4, 1
DRESP2, 502, PRCNT2, 402
, DVPREL1, 1, 2, 3, 4, 2
DRESP2, 503, PRCNT3, 402
, DVPREL1, 1, 2, 3, 4, 3
DRESP2, 504, PRCNT4, 402
, DVPREL1, 1, 2, 3, 4, 4
$ ply percentage formulation.
DEQATN 402 total(t1,t2,t3,t4,ti) =
(t1 +t2 +t3 +t4);
plyprcnt =
1.e2 * (ti / total)
Figure 17. Synthetic Ply Percentage Criteria for
Simplified PCOMP Laminates
MP Demonstration Problem
The previous demonstration problem is repeated here,
but structural sizing is accomplished using the MP
optimization methodology. Applied design criteria
are the same as those identified previously in Table
2, with the exception that the property drop-off
criterion is not considered. Additionally, applying
the lessons learned from the FSD Demonstration
Problem, the wing skins are initially defined using a
[30%/60%/10%]0/45/90 constant laminate distribution
at 0.25 in. total laminate thickness. The torsion-
efficient initial laminate is intended to reduce the
load concentration at the lower aft-spar cap, as was
seen in the previous demonstration problem.
We anticipate MP methodology will achieve a
heavier design solution than that obtained by the FSD
methodology. Whereas the FSD methodology hasbeen shown to amplify inherent load-chasing effects,
the MP methodology determines the most effective
design strategy by computing design variable
gradients and sensitivities to the applied criteria.
Therefore, it is expected the MP methodology will
use thicker wing skins to reduce the internal load
through the substructure. As shown in Figure 18, the
MP methodology achieves an objective weight of 141
lb, which is approximately 20 lb heavier than the 121
lb previously achieved by the FSD methodology.
Objective Convergence
100.00
110.00
120.00
130.00
140.00
150.00
160.00
1 2 3 4 5 6
Iteration Number
TotalWeight(lbs
)
Objective Convergence
100.00
110.00
120.00
130.00
140.00
150.00
160.00
1 2 3 4 5 6
Iteration Number
TotalWeight(lbs
)
Figure 18. Objective Convergence History (MP
Methodology)
Figure 19 confirms that a feasible design has beenachieved at the fifth iteration. All design constraint
values are less than or equal to zero, including thecritical lower aft-spar cap.
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Critical Criteria Convergence
0.00
1.00
2.00
3.00
4.00
5.00
6.00
1 2 3 4 5 6
Iteration Number
MaxConstraintValue
Critical Criteria Convergence
0.00
1.00
2.00
3.00
4.00
5.00
6.00
1 2 3 4 5 6
Iteration Number
MaxConstraintValue
Figure 19 Design Constraint Convergence
History (MP Methodology)
To assess the distributed quality of the converged
solution, the LM Aero utility, AS3, was used to per-
form single iteration analysis to generate margins of
safety for the converged solution. The quality of the
converged solution is further illustrated in Figure 20,
which displays a plot of critical criteria types and
margins of safety for each of the elements in the
upper skin. As expected, most margins are close tozero and none are less than -.005. However, some
regions have been oversized as indicated by the large
positive margins of safety (ranging from 0.149 to
0.586). In particular, the inboard portion of the wing
skin has generally been oversized, probably in an
effort to reduce internal load through the substructure
and, thereby, satisfy stress criteria for critical compo-
nents such as the lower aft-spar cap.
Figure 20. Upper Skin Critical Criteria and
Margins of Safety (MP Methodology)
The laminate total thickness contour for the upper
skin is displayed in Figure 21. The general
characteristic is similar to the FSD solution since the
thickness decreases as a function of span. Also,
similar to the FSD solution, total thickness tends to
increase as a function of chord (from fore to aft).
However, as expected, the MP solution is generally
thicker than the FSD solution (up to 0.075 in. thicker
at the wing root), which is consistent with the margin
plot shown previously in Figure 20.
A
B
C
D
EF
GH
I
J
K
LM
0.200
0.225
0.250
0.275
0.3000.325
0.3500.375
0.400
0.425
0.450
0.4750.500
Thickness (in.)
A
B
C
D
EF
GH
I
J
K
LM
0.200
0.225
0.250
0.275
0.3000.325
0.3500.375
0.400
0.425
0.450
0.4750.500
Thickness (in.)
A
B
C
D
EF
GH
I
J
K
LM
0.200
0.225
0.250
0.275
0.3000.325
0.3500.375
0.400
0.425
0.450
0.4750.500
A
B
C
D
EF
GH
I
J
K
LM
0.200
0.225
0.250
0.275
0.3000.325
0.3500.375
0.400
0.425
0.450
0.4750.500
Thickness (in.)
Figure 21. Upper Skin Laminate Thickness (MP
Methodology)
Laminate ply percentage contours for the upper skin
are provided in Figure 22, which illustrates another
significant difference between the FSD and MP solu-tions. Whereas the FSD solution exhibits significant
transition from a bending-efficient design (up to 55
percent 0-deg plies) at the wing root to a torsion-
efficient design (up to 70 percent 45-deg plies) out-board of mid-span, the MP solution exhibits little
transition throughout the laminate, remains fairly
constant at [35%/50%/15%]0/45/90 and provides well-
balanced wing-bending and wing-torsion efficiency.While the 0-deg plies effectively reduce large wing
bending strains at the wing root, the 45-deg plieseffectively redistribute the internal load concentration
at the aft carry-thru boundary to other nodes along
the wing root boundary.
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ABC
DEF
GHI
JKL
5.010.015.0
20.025.030.0
35.040.045.0
50.055.060.0
Ply Percentage
0-deg
plies
90-deg
plies
45-deg
plies
ABC
DEF
GHI
JKL
5.010.015.0
20.025.030.0
35.040.045.0
50.055.060.0
Ply Percentage
ABC
DEF
GHI
JKL
5.010.015.0
20.025.030.0
35.040.045.0
50.055.060.0
Ply Percentage
0-deg
plies
90-deg
plies
45-deg
plies
Figure 22. Upper Skin Laminate Ply Percentages
(MP Methodology)
The improved laminate efficiency of the MP design
is further illustrated in Figure 23, which reports
reacted carry-thru bending moment for each of the
wing root upper/lower node pairs. As illustrated, the
MP design is able to reduce the reacted bending
moment at the aft most carry-thru locations (fuselage
stations (FS) 54.0 and 66.0) by increasing the bend-
ing moment in forward carry-thru locations (FS 18.0,30.0, and 42.0). The combined effects of improved
wing-torsion efficiency (to reduce reacted bending
moment at the aft carry-thru location) and increased
overall laminate thickness (to reduce internal load
through the substructure) satisfy stress criteria for the
lower aft-spar cap.
Carry-Thru Bending Moment Distribution
0
100
200
300
400
500
600
700
800
18 30 42 54 66
Fuselage Station (in.)
BendingMoment,MX
(100
0in-lbs)
FSD
MP
*Moments summed about wing root.
Carry-Thru Bending Moment Distribution
0
100
200
300
400
500
600
700
800
18 30 42 54 66
Fuselage Station (in.)
BendingMoment,MX
(100
0in-lbs)
FSD
MP
Carry-Thru Bending Moment Distribution
0
100
200
300
400
500
600
700
800
18 30 42 54 66
Fuselage Station (in.)
BendingMoment,MX
(100
0in-lbs)
FSD
MP
*Moments summed about wing root.
Figure 23. Comparison of Carry-Thru Bending
Moment Distributions
Finally, each element (and composite layer) was
sized uniquely in this demonstration problem. How-
ever, this is often impractical for a production-
quality, full-vehicle FEM, which can contain greater
than 100,000 elements. Since the MP methodology
becomes computationally impractical for optimiza-
tion problems containing more than approximately
1,000 design variables, elements must be effectively
grouped into coarse design regions. Therefore, the
MP methodology has been typically reserved for
conceptual/preliminary-quality FEM and the prelimi-nary design characteristics are established as mini-
mum structural requirements for the production-
quality FEM. Then additional property increments
are applied, as required, to satisfy the detail structural
analysis and practicality criteria (using procedures
such as AS3).
SUMMARY AND CONCLUSIONS
New functional features to the core MSC.Nastran
2001 software product were directed by LM Aero
and are now available to the MSC.Nastran usercommunity. New features include enhancements to
the existing laminate modeling capability, improved
integration methods, and the development of a new
capability, external responses for SOL 200. The new
functional capabilities have already enabled LM Aero
to provide improved integration with its in-house
structural analysis processes, while the new DRESP3
external response capability promises to provide a
mechanism to incorporate in-house criteria within the
SOL 200 MP optimization sequence.
Further, two example problems serve to demonstrate
the benefit of the new functional features available in
MSC.Nastran 2001, as well as, compare and contrast
the FSD and MP design methodologies. The first
demonstration problem uses the LM Aero utility,
AS3, to illustrate the rapid analysis/sizing character-
istics of the FSD methodology to perform structural
verification in support of production engineering
drawing release. Whereas the second demonstration
problem uses the MSC.Nastran SOL 200 optimiza-
tion sequence and provides insight toward the appro-
priate usage of the FSD and MP methodologies. Forinstance, although the FSD methodology can rapidly
achieve a nearly feasible design solution, it has been
demonstrated to amplify inherent load concentration
effects and, therefore, may require human interven-
tion and logic to achieve a truly feasible solution.However, although the MP methodology has been
demonstrated to achieve the optimum and feasible
design solution, it is computationally prohibitive for
large, production-quality FEM.
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Therefore, appropriate usage scenarios must be used
to effectively leverage the strengths of each design
methodology. Since the MP methodology is compu-
tationally prohibitive for large models, it has been
typically reserved for conceptual/preliminary-quality
FEM to establish the general physical characteristics
necessary to satisfy structural criteria (e.g., strength,
aeroelastic effectiveness, flutter). The general
physical characteristics established by the MP meth-
odology can be translated from the preliminary FEM
to the production-quality FEM and established asminimum structural requirements. The FSD method-
ology is readily suited to apply additional property
increments, as required, to satisfy detail structural
analysis and practicality criteria (using procedures
such as the LM Aero utility, AS3).
ACKNOWLEDGEMENTS
The work presented in this paper would not havebeen possible without the dedication of those who
implemented the MSC.Nastran enhancements.
Therefore, the authors would like to acknowledge theoutstanding efforts of the following individuals:
Xiaoming Yu PCOMP enhancements Shenghua Zhang DRESP3 development Vinh Lam and Steve Wilder MSC.Toolkit
enhancements.
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