Msc Paper on Composites

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*Copyright 2001 Lockheed Martin Corporation. All rightsreserved. Published by the MSC.Software Corporation withpermission.

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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


Server1

Server i

ExternalCriteria


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.


Webs max shear stress

24 ksi

min. gage = 0.025 in.


*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


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


-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.


-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


-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)


9/15

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)


10/15

10

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


11/15

11

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.


12/15

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.


, 2, 1.


, 3, 1.


, 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


, DVPREL1, 1, 2, 3, 4, 2


, DVPREL1, 1, 2, 3, 4, 3


, 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


, 1, 1.


, 2, 1.


, 3, 1.


, 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)


, DVPREL1, 1, 2, 3, 4, 1


, DVPREL1, 1, 2, 3, 4, 2


, DVPREL1, 1, 2, 3, 4, 3


, 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.


100.00

110.00

120.00

130.00

140.00

150.00

160.00

1 2 3 4 5 6

Iteration Number

TotalWeight(lbs

)


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.


13/15

13


0.00

1.00

2.00

3.00

4.00

5.00

6.00

1 2 3 4 5 6

Iteration Number

MaxConstraintValue


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.


14/15

14

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.


0

100

200

300

400

500

600

700

800

18 30 42 54 66


BendingMoment,MX

(100

0in-lbs)

FSD

MP


0

100

200

300

400

500

600

700

800

18 30 42 54 66


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.


15/15

15

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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