Page 199 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

186 • using ansys for finite eLement anaLysis
from loop to loop. Also avoid the other extreme, which would be to
choose the stress in every element as a state variable. The preferred
method is to define the stresses at a few key locations as state variables.
• For the subproblem approximation method, if possible, choose SVs
that have a linear or quadratic relationship with the DVs.
• If a state variable has both an upper and lower limit, specify a rea-
sonable range of limit values. Avoid very small ranges, because
feasible designs may not exist. A stress range of 500 to 1,000 psi,
for example, is better than 900 to 1,000 psi.
• If an equality constraint is to be specified (such as frequency =
386.4 Hz), define two state variables for the same quantity and
bracket the desired value, illustrated as follows:
*GET,FREQ,ACTIVE,,SET,FREQ ! Parameter FREQ
= calculated
frequency
FREQ1=FREQ
FREQ2=FREQ
/OPT
OPVAR,FREQ1,SV,,387 ! Upper limit on FREQ1 =
387
OPVAR,FREQ2,SV,386 ! Lower limit on FREQ2 =
386
• Avoid choosing SVs near singularities (such as concentrated
loads) by using selecting before defining the parameters.

5.2.5.3 Choosing the objective Function

The objective function is the quantity that you are trying to minimize or max-
imize. Some points to remember about choosing the objective function are:

• The ANSYS program always tries to minimize the objective func-
tion. If you need to maximize a quantity x, restate the problem and
minimize the quantity x1 = C − x or x1 = 1/x, where C is a number
much larger than the expected value of x. C − x is generally a bet-
ter way to define the objective function than 1/x because the latter,
being an inverse relationship, cannot be as accurately represented by
the approximations used in the subproblem approximation method.
• The objective function should remain positive throughout the opti-
mization, because negative values may cause numerical prob-
lems. To prevent negative values from occurring, simply add a
sufficiently large positive number to the objective function (larger
than the highest expected objective function value).