B.5 Scaling of Design Variables and Constraints 787
Table B.1 Summary of Some Structural Optimization Packages
Software system Source Capabilities and
(program) (developer) characteristics
ASTROS (Automated
STRuctural
Optimization System)
Air Force Wright Laboratories
FIBRA
Wright-Patterson Air Force
Base, OH 45433-6553
Structural optimization with
static, eigenvalue, modal
analysis, and flutter
constraints;
approximation concepts;
compatibility with
NASTRAN; sensitivity
analysis
ANSYS Swanson Analysis Systems,
Inc.
P.O. Box 65
Johnson Road
Houston, PA 15342-0065
Optimum design based on
curve-fitting technique to
approximate the response
using several trial design
vectors
MSC/NASTRAN
MacNeal Schwendler
Corporation/NAsa
STRuctural ANalysis)
MacNeal-Schwendler Corpo-
ration
15 Colorado Boulevard
Los Angeles, CA 90041
Structural optimization
capability based on static,
natural frequency, and
buckling analysis;
approximation concepts
and sensitivity analysis
NISAOPT Engineering Mechanics
Research Corporation
P.O. Box 696
Troy, MI 48099
Minimum-weight design
subject to displacement,
stress, natural frequency
and buckling constraints;
shape optimization
GENESIS VMA Exngineering Inc.
Manderin Avenue, Suite F
Goleta, CA 93117
Structural optimization;
approximation concepts
used to tightly couple the
analysis and redesign
tasks
B.5 Scaling of Design Variables and Constraints
In some problems there may be an enormous difference in scale between variables
due to difference in dimensions. For example, if the speed of the engine (n) and the
cylinder wall thickness (t) are taken as design variables in the design of an IC engine,
nwill be of the order of 10^3 (revolutions per minute) andtwill be of the order of
1 (cm). These differences in scale of the variables may cause some difficulties while
selecting increments for step lengths or calculating numerical derivatives. Sometimes
the objective function contours will be distorted due to these scale disparities. Hence it
is a good practice to scale the variables so that all the variables will be dimensionless
and vary between 0 and 1 approximately. For scaling the variables, it is necessary to
establish an approximate range for each variable. For this we can take some estimates
(based on judgment and experience) for the lower and upper limits onxi(ximinand
