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Design optimization • 173
dimensions (such as thickness), shape (such as fillet radii), placement of
supports, cost of fabrication, natural frequency, material property, and so
on. Among many examples, the optimum design for a frame structure may
be the one with minimum weight or maximum frequency; in heat trans-
fer, the minimum temperature; or in magnetic motor design, the maximum
peak torque. Any ANSYS item that can be expressed in terms of parame-
ters is a candidate for design optimization. In many other situations mini-
mization of a single function may not be the only goal, and attention must
also be directed to the satisfaction of predefined constraints placed on the
design (e.g., limits on stress, geometry, displacement, heat flow).
5.2.1 DeSign oPTiMizATion TeRMinoLogy AnD
inFoRMATion FLoW
While working toward an optimum design, the ANSYS optimization rou-
tines employ three types of variables that characterize the design process:
design variables, state variables, and the objective function. These vari-
ables are represented by scalar parameters in ANSYS Parametric Design
Language (APDL). The use of APDL is an essential step in the optimiza-
tion process. The independent variables in an optimization analysis are
the design variables. To understand the terminology involved in design
optimization, consider the following problem:
Find the minimum-weight design of a beam of rectangular cross-sec-
tion subject to the following constraints:
• Total stress σ should not exceed σ max [s < s max ].
• Beam deflection Δ should not exceed Δ max [∆< ∆ max ].
• Beam height h should not exceed h max [h < h max ].
Design Variables (DVs): Independent quantities varied to achieve
the optimum design. Upper and lower limits are specified to serve as “con-
straints” on the DVs. These limits define the range of variation for the DV.
In the above beam example, width b and height h are obvious candidates
for DVs. Both b and h cannot be zero or negative, so their lower limit
would be b,h > 0.0. Also, h has an upper limit of h max . Up to 60 DVs may
be defined in an ANSYS design optimization problem.
State Variables (SVs): Quantities that constrain the design. Also
known as “dependent variables,” they are typically response quantities that
are functions of the DVs. A state variable may have a maximum and min-
imum limit, or it may be “single sided,” having only one limit. Our beam
example has two SVs: σ (the total stress) and Δ (the beam deflection). You
can define up to 100 SVs in an ANSYS design optimization problem.