METBD 450 Lecture Notes

Text: Building Better Products with FEA,
by V. Adams & A. Askenazi, (Read pp. 355-374)

Reference:  ANSYS Advanced Analysis Techniques

• Chapter 1: Design Optimization
• Chapter 2: Topological Optimization
• Chapter 3: Probabilistic Design

Design Optimization:

• Phase 1 Opt = good, old-fashioned brainstorming
  • explore design concepts with:
    • coarse models
    • broad assumptions
• example (p. 358) winch mounting bracket:
  • concept restrictions/limitations (p. 358)
  • assumptions (p. 359)
• Sensitivity Study - vary design parameters ±1 % to see their effect on the critical design responses (stress, deflection, frequency, etc.)
• Global Sensitivity - system response to varying a design parameter through its entire range of possible values
  
• Phase 2 Opt = fine tuning
  • refine to produce the best performance for the lowest cost
  • re-evaluate geometry, assumptions, loads and constraints
  • set REALISTIC goals, limits, and part parameters
  • In ANSYS: Main Menu > Design Opt
• Phase 2 Opt GOALS:
  • minimize weight, volume, cost, etc.
  • cost is more difficult to describe for a manufactured part or assembly
  • In ANSYS: this is called the OBJECTIVE FUNCTION
• Phase 2 Opt LIMITS:
  • allowable stress, deflection, force, weight, frequency, etc.
  • (these are usually calculated results of the FEA analysis)
  • In ANSYS: these are called STATE VARIABLES (SV's)
• Phase 2 Opt PART PARAMETERS:
  • from the Phase 1 Opt study = dimensions, materials, b.c.'s, etc.
  • In ANSYS: these are called DESIGN VARIABLES (DV's)
  • Use as FEW as possible to describe the Opt problem
  • "false" minimums can occur, but better designs still are produced

In ANSYS:

• Build your model in terms of parameters (which will be your DV's).  See: Utility Menu > Parameters > Scalar Parameters
• Solve
• Extract parameters from the results (which will be your SV's).  See: Utility Menu > Parameters > Get Scalar Data (*GET Command)
• Under: Main Menu > Design Opt >
• establish the looping file (log file)
• declare the parameter variables (DV's, SV's, and OBJ)
  • tell ANSYS which parameters are DV's, which are SV's, etc.
  • specify the allowable range or limits for the variables
• select the optimization tool or method
  • "subproblem approximation" or "first order method"
  • random design generation
  • sweep generation
  • factorial evaluation (statistical Design Of Experiments method)
  • gradient evaluation = local design sensitivity
• set any controls for opt. looping (depends on tool/method used)
• run the optimization analysis

Topology Optimization (p. 369-370):

• calculate a shape of constant stress or strain from your loads and constraints
• remove material that does not appear to contribute to the load path

In ANSYS:

• Use element type ID number 1 for portion of model which can be optimized
• Use element type ID numbers > 1 for portions NOT to be optimized
• Describe ALL possible loadings as Solution Load cases, i.e., "Write LS File ..." for each load case.
• Under  "Solution > -Solve- Topologic Opt ..." give ANSYS the:
  • a target volume reduction
  • the number of load cases
  • convergence accuracy
  • number of loops to try
  • display after each loop (on/off)
• when you hit "OK" on this dialog box, ANSYS runs the optimization loops
• In the General Postprocessor:
  • use Plot Results > -Contour Plot- Nodal Solution > Optimization, TOPO to see the result.
  • use Element Table > Define Table, to Add the OPT result (TOPO).  Then, Select > Elements > By Results, TOPO, in a selected range, to see what part of the model is needed to carry the applied loads.

Probabilistic Design

A statistical approach to assess the effect of uncertain input parameters and assumptions on your analysis model.
Uncertain parameters are described by statistical distribution functions such as the Gaussian or normal distribution, the uniform distribution, etc.

• The scatter of the Young's modulus for many materials can often be described as a Gaussian distribution with standard deviation of ±3 - 5%.
• Likewise, the geometric properties of components can only be reproduced within certain manufacturing tolerances.
• The same variation holds true for the loads that are applied to a finite element model.

The output of an ANSYS PDS study is: statistics and trend information:  histograms, Cumulative Distribution Function, probabilities, design sensitivities, scatter, and correlation.

In ANSYS: Main Menu > Prob Design

The ANSYS PDS is best suited for distributed, parallel processing since thousands of loops may be run to evaluate the scattered data.