Structural optimization has been available to the structural analysis community as a tool for many years. The popular use of displacement method finite-element techniques to analyze linearly elastic structures has resulted in an ability to calculate the weight and constraint gradients inexpensively for numerical optimization of structures. Here, recent experiences in the investigation and use of structural optimization are discussed. In particular, experience with the commercially available ADS/NASOPT code is addressed. An overview of the ADS/NASOPT procedure and how it was implemented is given. Two example problems are also discussed

Love, Mike H.

Mcconnell, J. C.

Paul, B. K.

English

NASA Technical Reports Server

RECENT EXPERIENCES USING FINITE-ELEMENT- 
BASED STRUCTURAL OPTIMIZATION 
B. K. Paul, J. C. McConnell, M. H. Love 
General Dynamics 
Fort Worth Division 
Fort Worth, Texas 
58 1 
https://ntrs.nasa.gov/search.jsp?R=19890015806 2020-03-20T01:50:07+00:00Z
I OUTLINE 
Structural optimization has been available to the structural 
analysis community as a tool for many years. The popular use of 
displacement method finite-element techniques to analyze linearly 
elastic structures has resulted in an ability to calculate the 
weight and constraint gradients inexpensively for numerical 
optimization of structures. 
In this presentation, recent experiences in the investigation and 
use of structural optimization will be discussed. In particular, 
experience with the commercially available ADS/NASOPT (Reference 
1 )  code is addressed. An overview of the ADS/NASOPT procedure 
and how it was implemented will be shown. Two example problems 
will also be discussed. 
1 
58 2 
4 BACKGROUND 
0 PROGRAM FORMAT 
TYPICAL INPUTS 
0 BUCKLING EXAMPLE 
0 CANOPY PROBLEM 
SOFTWARE GOAL 
The goal of our structural optimization software investigation 
was to develop a production level finite-element-based system for 
aircraft design and resizing. The tools available from vendors 
are diverse. Optimization methods range in mathematical 
programming techniques and optimality criteria with various types 
of sensitivity analyses, design variable 'linking options, 
materials capabilities and disciplines. The use of existing 
finite-element models was also an important consideration. The 
OPTDES-BYU (Reference 2 )  and GD-GIFTS, an in-house finite- 
element program, were combined into an application specific 
finita-element optimization package using the combined databases 
from each program. Difficulty arose in making this program 
generic enough in terms of sensitivity analysis and structural 
geometry. The ADS/NASOPT program was selected and used in the 
following applications with favorable results. Since our in- 
house pre and post finite-element processors communicate with 
MSC/NASTRAN (Reference 3 ) .  ADS/NASOPT minimizes changes to 
existing finite-element models. In addition, we had prior 
knowledge of ADS (reference 4 ) .  
TO DEVELOP A PRODUCTION LEVEL FINITE 
ELEMENT BASED STRUCTURAL OPTIMIZATION 
SYSTEM FOR AIRCRAFT DESIGN AND RESIZING 
TOOLS 
I MSWNASTRAN I I ADS-NASOPT I 
58 3 
OUTLINE OF ADS/NAGOPT 
The ADS/NASOPT procedure uses a structural finite-element model 
as the starting point in an analysis cyc1e;thenittranslates this 
into a design model through NASOPT. The program then optimizes 
using the ADS optimization program and returns to the structural 
model to update the data if so chosen by the user. A combination 
of approximation techniques, sensitivity analysis and 
optimization algorithmsallows the user to minimize his objective 
function (such a3 weight) subject to constraints(such as stress 
allowables, buckling load factors, or displacements). 
STRUCTURAL MODEL 4 
MSC/NASTRAN 
PROBLEM W 
TYPICAL MODEL REQUIREMENTS 
The structural finite-element model includes the MSC/NASTRAN bulk 
data information such as control cards, grid points, elements, 
materials, . properties, loads, and boundary conditions. 
ADS/NASOPT is limited in the variety of elements that can  be 
resized as design variables; however, the finite-element model may 
contain unlimited types of elements available in the MSC/NASTRAN 
element library. 
MATERIAL 
CARDS 
P-CARDS 
ELEMENTS 
BOUNDARY 
GRIDS CONDITIONS 
LOADS CONTROL 
CARDS 
58 5 
TYPICAL ADS/NASOPT INPUT 
The ADS/NASOPT program requires some additional input in the form 
of NASTRAN data card images. These data include design variable, 
and constraint definitions, design variable upper, lower bounds, 
move limits, and method of optimization. A typical i n p u t  
sequence also requires NASOPT instructions or job control 
language. ADS/NASOPT is run in phases each performing a specific 
function in the optimization task. Phase 1 sets up the database 
by reading the NASTRAN and design data. Phase 2 prepares the 
NASTRAN sensitivity analysis data after screening the analysis 
results. Phase 3 reads sensitivity results, prepares the 
appropriate model and calls ADS to perform the optimization. 
Phases S and A call MSC/NASTRAN to execute the desired solution 
sensitivity solution sequences 51,53,55 (for phase S )  and 
analysis solutions 2 4 , 6 1 , 6 3 , 6 5  (for phase A). 
Generation of the extra data cards to convert a MSC/NASTRAN 
finite-element model to an ADS/NASOPT design model can be tedious 
for large models. Work station procedures included as a part of 
the finite-element pre-processors facilitate routine use of 
programs such as ADS/NASOPT. 
L 
OPTCOM 
MOVLIM 
L 
DVPROP 
JCL 
PLAT€ BUCKLING EXAMPLE - NASTRAN MODEL 
The first example represents a typical section from an aircraft 
structure. This particular section was extracted from a fuselage 
keel beam and loaded with combined shear/biaxial displacements. 
The hole typifies routing requirements of plumbing, electrical, 
and fuel considerations. 
58 7 
PLATE BUCKLING EXAMPLE - PROBLEM INPUTS 
Material properties were selected for a typical aluminum alloy. 
In the case of this illustration, only two design variables were 
selected, Physical linking of the finite-element thicknesses was 
incorporated as shown in the figure. Although two design 
variables may be a crude definition of the design space, for 
manufacturing reasons, the design of such structure may often 
requiie this definition, And, the problem illustrates 
interesting results. 
MATERIAL PROPERTIES 
E = 10. 0 E7 
DENSITY 0.1 LB/CU INCH 
POISSON'S RATIO 0.3 
DESIGN CONSTRAINTS 
BUCKLING EIGENVALUE => 1.5 
INITIAL DESIGN 
THICKNESS VARIABLE 1 0.1 
THICKNESS VARIABLE 2 = 0.1 
OBJECTIVE FUNCTION 
MINIMUM WEIGHT 
DESIGN 
VARIABLE 1 
DESIGN 
VARIABLE 2 
DESIGN HISTORY OF PLATE BUCKLING EXAMPLE 
WEIGHT 
THICKNESS UPPER 
THICKNESS LOWER 
BUCKUNG LOAD FACTOR 
The pertinent results from the ADS/NASOPT run are shown in both 
tabular form and graphically. The table displays weight, 
thickness (the two design variables), and the buckling load 
factor. The procedure was run for eight optimization iterations. 
The weight and buckling load factor are both displayed with 
respect to the vertical axis of the graph. 
INITIAL 1 2 3 4 5 6 7 8 
0 lWD0 0 12500 0 15S25 0 19511 0 11494 0 11183 0 15116 0 19544 0 15211 
0 IOWO 0 12500 0 15825 0 0511 024414 020145 ,024061 02005l 024115 
0282W 044200 0 69010 101910 l31MO I 16440 I 12280 I 13580 I20000 
201000 zzuw 251210 184190 302580 z 8 s s i o  2 9 ~ 0  2 m a o  29i200 
The first observation of note is that after eight iterations, the 
process failed to satisfy the buckling load factor constraint. 
The second observation is that the buckling load factor steadily 
increased along with the design thickness through iteration 3. 
At iteration 4, the thicknesses began to separate, and the 
buckling constraint attained its highest point. During the 
remaining iterations, the thicknesses flip/flop and the buckling 
constraint actually decreased. 
A s  best as w e  could determine, the design process seemed to be 
confused. ADS/NASOPT incorporates linear approximations, and 
between the few number of design variables, nonlinearity of 
buckling, and the choice of move limits, satisfactory results 
were obtainable. 
We attribute our lack of success in this example to problem 
complexity and user inexperience. 
3.5 
3.0 
2.5 
2.0 
1.5 
1 .o 
0.5 
0.0 
FACTOR 
0 WEIGHT 
2 3 4 5 6 7 0 9  
ITERATION 
PLATE BUCKLING PROBLEM DESIGN VARIABLE VALUES 
589 
590 
SINGLE PIECE CAST CANOPY FRAME - NASTRAN MODEL 
A canopy bow frame model was optimized to test the functionality 
of the ADS/NASOPT software. A modern fighter aircraft canopy is 
primarily constructed of a polycarbonate transparency mounted in 
an aluminum frame. The frame is typically fabric.ated from various 
castings, extrusions, plate and sheet stock. This design is a 
labor intensive subcomponent to the canopy assembly. To replace 
the design with a single piece casting would represent a cost 
savings provided the additional tooling costs could be offset by 
the reduced labor costs. 
The finite~element model of 1140 grid points and 5 8 8  bending 
elements was developed to represent the behavior of the 
structure. The NASTRAN mpdel was adapted from the production 
finite-element model of the F-16 canopy frame with changes 
minimized to guarantee acc'!rate comparisons in results. 
DESIGN AND ANALYSIS MODELS - INITIAL SIZING 
Eighty-eight design variablesrepresentingthe canopy frame were se- 
lectedfromthebending elements available with 84 given initial 
thickness of 0.2 gauge size. The remaining 4 design variables 
representing the bow hoops, external covers, transparency, and 
tension ties were given "fixed sizes" to maintain their assembly 
requirements. These design variables were used mainly to allow 
stress constraints related to these elements to be applied and 
influence the design process. It seemed that ADS/NASOPT allows 
the user to constrain element behavior only if the element is 
labeled as a design variable. Regardless, this incident 
highlighted the need to consider neighboring structure in an 
optimization design setting. 
88 VARIABLES REPRESENTING GAUGE THICKNESS FOR 
VARIOUS PARTS OF THE CANOPY FRAME 
SIZE CONSTRAINTS 
COMPONENT 
CANOPY FRAME 
EXTERNAL COVERS 
BOW HOOPS 
TRANSPARENCY 
TENSION TIE 
SIZE CONSTRAINTS 
0.080 e t e 0.500 inch 
0.100 e t e 0.100 inch 
0.250 e t e 0.250 inch 
0.700 e t 0.700 inch 
0.150 e t e 0.150 inch 2 
591 
DESIGN AND ANALYSIS MODEL - LOADING CASES 
59 2 
Two symmetric loading cases were selected representing ultimate 
cabin pressure and a balanced ejection condition. The ejection 
condition was balanced by inertia loads at the latching mechanism 
location along the length of the frame. Boundary conditions of a 
plane of symmetry along the aircraft were accounted for with 
reaction points at the tension tie locations. These loading 
cases represent typical production loading configurations. 
The candidate materials used were A 3 5 7  alloy f o r  the frame which 
is a high strength heat treatable Al-Si-Mg alloy that is 
relatively inexpensive to manufacture. Other materials were kept 
as the current design exists. 
LOADING CONDITIONS 
CASE 1 10.2 PSI CABIN PRESSURE 
CASE 2 PILOT EJECTION 
BOUNDARY CONDITIONS 
3 HOOK LATCHES 
1 PIVOT 
CENTERLINE SYMMETRY 
MATERIALS 
FRAME, CAST A357 
EXTERNAL COVERS, BOW HOOPS, AI 2024 
TRANSPARENCY, POLYCARBONATE 
PIVOT FITTING TENSION TIE, PH13-8 STAINLESS STEEL 
SINGLE PIECE CAST CANOPY FRAME - STRESS CONSTRAINTS 
The canopy frame consists of bending elements representing 
flanges and webs. These elements were sized using a 26250 psi von 
Mises maximum stress. The bow hoops and external covers are 
loaded in tension with a required stress level between 40000 psi 
and 50000 p s i  for principal stresses. The polycarbonate 
transparency was held to a maximum 2000 psi von Mises stress. 
Finally the tension ties are loaded in tension, and the members 
were sized using 75000 psi as a maximum axial stress. 
COMPONENT 
CANOPY FRAME 
BOW HOOPS, 
EXTERNAL COVERS 
TRANSPARENCY 
TENSION TIE 
STRESS CONSTRAINTS 
VON MISES e 26250 PSI 
40000 e PRINCIPAL e 50000 PSI 
VON MISES e 2000 PSI 
AXIAL e 75000 PSI 
593 
S I N G L E  P I E C E  CAST CANOPY FRAME - I N I T I A L  S I Z I N G  
The finite-element results for the initial sizing show large 
regions of low stress as expected. 
_ _ ~  
STRESS 
CONTOURS 
(MIDDLE) 
‘HETA- 0. 
HENKY-VON MISES 
A 0. 
B 1350. 
C 2700. 
D 4050. 
E 6400. 
F 6750. 
0 8100. 
H 9450. 
I 10800. 
J 12150. 
K 13500. 
L 14850. 
M 16200. 
N 17550. 
0 18900. 
P 20250. 
R 22950. 
S 24300. 
T 25650. 
U 27000. 
Q 21600. 
STRESS 
CONTOURS 
[MIDDLE) 
‘HETA- 0. 
HENKY-VON MISES 
A 0. 
B 1360. 
C 2700. 
D 4060. 
E 6400. 
F 0760. 
G 8100. 
H 9460. 
I 10800. 
J 12160. 
K 13600. 
L 14860. 
M 16200. 
N 17660. 
0 18000. 
P 20260. 
Q 21600. 
R 22950. 
S 24300. 
T 25060. 
U 27000. 
~ ._ ~~ 
LOADING CASE 1 
LOADING CASE 2 
CANOPY FRAME INITIAL SIZES 
SINGLE P I E C E  CAST CANOPY FRAME - WEIGHT RESULTS 
A comparison of two optimization methods was achieved f o r  designs 
derived from load case 1, the ultimate cabin pressure case. Path 
1 used 4 ADS steps using the Modified Method of Feasible 
Directions algorithm, while path 2 used 1 fully stressed design 
analysis and 3 ADS cycles. The FSD path also took less CPU time 
when run on the CRAY. 
SINGLE-PIECE CANOPY FRAME 
WEIGHT HISTORY LOAD CASE 1 
199.5 
1 go 
1 ea 
170 
INITIAL 1 2 3 4 
ITERATION NUMBER 
176.36 
173.27 
59 5 
SINGLE P I E C E  CAST CANOPY FRAME - STRESS RESULTS 
The final stress results for load case 1 the ultimate pressure 
case, show areas of high stress concentration near the tension 
ties. The optimized structure was sized predominantly to minimum 
gauge with the exception of the tension tie points and canopy 
latch hooks. 
Although, it seems in hindsight that the problem was trivial as 
a built-up frame structure, the design was complex. T h i s  
exercise demonstrated the functionality of ADS/NASOPT as a 
preliminary design tool because all aspects of the structure were 
included simultaneously in the structural sizing. 
STRESS 
CONTOURS 
(MIDDLE) 
THETA- 0. 
HBNKY-VON MISES 
A 0. 
B 1360. 
C 2700. 
D 4080. 
E 5400. 
P 6750. 
0 8100. 
Ii 9450. 
I 10800. 
J 12150. 
K 13500: 
L 14880. 
M 16200. 
N 17660. 
0 18900. 
P 20280. 
Q 21600. 
R 22860. 
S 24300. 
T 25650. 
u 27000. 
JOB: CANOPY 
8-338-88 
18: 18:33 
LOADINQ CASE 1 
k i \ 
I 
wz 
STRESS 
CONTOURS 
(MIDDLE) 
0. 
HENKY-VON MISBS 
A 0. 
B 1360. 
C 2700. 
D 4060. 
E 6400. 
P 6750. 
Q 8100. 
H 9450. 
I 10800. 
K 13600. 
L 14860. 
M 16200. 
N 17650. 
0 18900. 
P 20260. 
Q 21600. 
R 22960. 
S 24300. 
T 26650. 
U 27000. 
HETA- -
J iai60. 
597 
SUMMARY 
In summary, our studies have provided four significant lessons 
learned. First it is evident that effective use of optimization 
techniques in design requiresarobust-expert preprocessor as part 
of a basic finite-element preprocessor. Second, as in the 
example of the buckling problem, the design problem must be well 
posed both in a practical design sense and a numerical sense. 
The third observation to be made relates back to the problem 
definition. In particular, although neighboring elements to a 
design model may not be subject to resizing, their behavior may 
impose constraints on the design model. These constraints may be 
imposed through the use of larger models or formal decomposition 
methods. ADS/NASOPT provides functional use of MSC/NASTRAN as a 
preliminary design optimization tool. 
LARGE DESIGN MODELS REQUIRE ' PREPROCESSORS 
0 ADSINASOPT REQUIRES EXPERIENCED USAGE 
J DESIGN MODELS 
J ALGORITHM 
SENSITIVITY OF NEIGHBORHOOD S I R  
ESSENTIAL 
J DECOMPOSITION 
J LARGE MODELS 
JCTURE IS 
@ ADSINASOPT PROVIDES FUNCTIONAL USE OF 
MSCINASTRAN 
REFERENCES 
1. Gibson, W.C., Miura H., ADS/NA SOPT User's ManuaL, version 1.00 
Rev A. Palo Alto: CSA Engineering, Inc, Sept 1986. 
2 .  OPTDES - BYU : A Soft  ware System f or Optimal E naineerins Des ian 
User's Manual vers ion 3.1 , Brigham Young University, Provo Utah, 
1986. 
3. MacNeal-Schwendler Corporation, MSC/NASTRAN Linear Static 
Analysis Manual version 65, Los Angeles: MacNeal Schwendler 
Corp., 1987. 
4. Vanderp1aats.G. N., g P S  - FORTRAN Proaram f o r  Automatea 
gesian Synthesis. Version l.lQ, Santa Barbara: EDO, Inc, 1985. 
CRAY IS A REGISTERED TRADEMARK OF CRAY RESEARCH INC. 
NASTRAN I S  A REGISTERED TRADEMARK OF NASA. MSC/NASTRAN I S  
AN ENHANCED PROPRIETARY VERSION DEVELOPED AND MAINTAINED BY 
THE MACNEAL SCHWENDLER CORPORATION. 
599 


Recent experiences using finite-element-based structural optimization

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