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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.
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