CHAPTER 9 Guidelines for Design optimization

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General Guidelines - 1

 Wherever possible, take advantage of symmetry. Remember that the optimizer performs multiple analyses, so the smaller the model size, the better.

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General Guidelines - 2

 Avoid specifying density if it is not needed for the analysis. You will save the time needed to calculate the mass matrix.

 Make sure that the parametric model is valid for all possible values of the DVs. A sweep run with two sweeps per DV (minimum and maximum) may be a good idea.

 Save the optimization database to a “safe” file name at the end of each run. Keeping these databases will give you a wide array of potential designs that might come in handy some day.

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General Guidelines - 3

 Sometimes an optimization problem may converge to a local minimum. You can check for this and possibly arrive at a global minimum by first using the Sweep tool (or some other tool) and choosing the proper starting design(s).

OBJ Local minimum Written by Changhyun, SON DV Global minimum Chapter 9. Guidelines for Design Optimization - 4

Guidelines for DVs - 1

  Keep the number of design variables to a minimum: more than 20 is not recommended; fewer than 10 is preferred.

One way is to eliminate some DVs by expressing them in terms of others. For example, eliminate R3 below by expressing it in terms of R1 and T1. Similarly R4.

R2 R1 T2 T1 R3 Written by Changhyun, SON R4 Chapter 9. Guidelines for Design Optimization - 5

Guidelines for DVs - 2

 Choose DVs that permit several design configurations, but be aware of unrealistic or undesirable designs. Consider, for example, the weight optimization of a cantilever beam.

x 1 One DV, x 1 , will work, but it doesn’t permit a tapered or curved design.

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x 4 x 4

Guidelines for DVs - 3

x 3 x 3 x 2 x 2 x 1 Choosing 4 DVs x 1 -x 4 more flexibility… gives x 1 … but also allows local minima (unless otherwise constrained).

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Guidelines for DVs - 4

A better idea might be to choose height increments as DVs: dx 4 dx 3 dx 2 x 1 Written by Changhyun, SON Chapter 9. Guidelines for Design Optimization - 8

Guidelines for DVs - 5

 To specify discrete DVs, such as number of ribs or holes, use the NINT (nearest integer) function when building the model.

For example, if NRIBS represents the number of ribs, use NINT(NRIBS) to make copies of one rib, then declare NRIBS as a DV with the appropriate limits.  OR, you may need to use an if-then-else construct.

et,1,63 ! Shell element type *if,thk,lt,2.5/16,then thk=1/8 thk=1/4 ! Use 1/8 if thk < 2.5/16 *elseif,thk,gt,3.5/16,then ! Use 1/4 if thk > 3.5/16 *else thk=3/16 ! Otherwise use 3/16 *endif r,1,thk ! Define shell thickness

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Guidelines for SVs - 1

 Be sure to use the correct data. For example:  If a minimum first natural frequency is a state variable, be sure to retrieve the first non-zero frequency. The first frequency may be a rigid body mode.

 If the structure deflects in the -Y direction, and maximum Y deflection is a state variable, retrieve the maximum of absolute values or the minimum of real values.

 Typical state variables such as maximum stress (or deflection or temperature or ...) may occur at a different location in each loop.

In such cases, do not choose just one maximum (or minimum) for the entire structure. Doing so may result in poor quality approximations.

On the other hand, choosing a maximum in every element may result in a local minimum.

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Guidelines for SVs - 2

A compromise is to select a few key regions in which maximum stresses will be used as state variables.

For example, the maximum stress in each “bay” of the truss bridge below will give better results than just one maximum stress for the entire structure.

A1 A2 A3 SMX1 SMX2 SMX3 SMX4 H1 H2 Written by Changhyun, SON Chapter 9. Guidelines for Design Optimization - 11

Guidelines for SVs - 3

 Avoid tight bounds on two-sided state variables.

For example, a state variable limit of 500 to 1000 is better than 990 to 1000.

 If singularities exist, such as a point load or a re-entrant corner, the maximum stress will always be at that location.

Consider unselecting such regions before retrieving the maximum stress.

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Guidelines for SVs - 4

 To apply an equality constraint, such as first natural frequency = 256 Hz, use the bracketing technique:  Define freqA as an SV with upper limit of 257 Hz  Define freqB as an SV with lower limit of 255 Hz Both freqA and freqB represent the first natural frequency, but their limits bracket the desired value.

You may need to increase the number of successive infeasible designs in this case since a frequency value <255 or >257 will make the design infeasible.

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Guidelines for SVs - 5

 If too many infeasible designs are occurring, it is probably because a state variable approximation does not adequately represent the actual SV function.

Adding cross terms to the SV approximation (OPEQN) may overcome this problem.

Or you may need to use the first order method.

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Guidelines for OBJ

 Remember that ANSYS always minimizes the objective function.

To maximize an item, such as heat flow rate Q, specify 1/Q or CC-Q as the objective function (where CC is a constant larger than the highest expected value of Q).

 The OBJ should remain positive. Add a positive constant if needed to ensure this.

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