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Optimal Design Problem Formulation

Optimal Design Problem Formulation. Rudy J. Eggert, Professor Emeritus http://coen.boisestate.edu/reggert http://highpeakpress.com/eggert/. Today’s lecture. Homework Review Design, Form from Function Optimal design Opt. Des. Problem Formulation Examples. Review.

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Optimal Design Problem Formulation

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  1. Optimal DesignProblem Formulation Rudy J. Eggert, Professor Emeritus http://coen.boisestate.edu/reggert http://highpeakpress.com/eggert/

  2. Today’s lecture • Homework • Review • Design, Form from Function • Optimal design • Opt. Des. Problem Formulation • Examples

  3. Review • Design-decision making activities • Form from Function • Phases: • Formulation • Concept • Configuration • Parametric • Detail • Opt. Design-systematic parametric design

  4. Design Set of decision making processes and activities to determine: the form of an object, given the customer’s desired function. Customer controls control hold move protect store  Function Design decision making processes shape configuration size materials manufacturing processes Form Designer controls

  5. Systematic Parametric Design Designer or team Computer progam

  6. Opt. Design Problem Formulation Develop a mathematical model Include mathematical relations for : 1. A performance criterion or “cost function” (measures “goodness” of the candidate’s design) 2. Necessary behaviors (must do or have) (obey laws of man, or nature, i.e. safety, physics, chemistry etc)

  7. Standard Design Optimzation Model

  8. Design Problem Formulation (Arora) Step 1. Project/problem description Step 2. Data and information collection Step 3. Definition of design variables Step 4. Optimization criterion Step 5. Formulation of constraints Let’s reword these as actions to perform…

  9. Opt. Des. Problem Formulation(Eggert) Step 1. Describe problem Step 2. Collect info Step 3. Define DVs Step 4. Determine objective function Step 5. Formulate constraints

  10. Design of a can • Step 1. Describe problem (restate w/bullets) • Must hold at least 400 ml • Min mfg cost which is proportional to surface area • Diameter no more than 8 cm • Diameter no less than 3.5 • Height no more than 18 cm • Height no less than 8 cm

  11. Design of a can Step 1. Describe problem Step 2. Collect info Step 3. Define DVs Step 4. Determine objective function Step 5. Formulate constraints

  12. Design of a can • Step 2. Collect info • Draw diagram • Relation for volume • Relation for surface area • Other? Volume = Area x height = (πD2/4)H Surface area = top + bottom + side Area top, bottom = πD2 /4 Area side = πDH Total area = πD2 /4 + πD2/4 + πDH (cm3)

  13. Design of a can • Step 3. Define DVs • Diameter, D, (cm) • Height, H, (cm) • x=[x1, x2] = [D, H] • Note: volume and area are functions of the DVs

  14. Design of a can Step 4. Determine objective function  Min f(x) = πD2 /2 + πDH (cm2)

  15. Design of a can Step 5. Formulate constraints Volume ≥ 400 ml (cm3), or (πD2/4)H ≥ 400 (cm3) • Size limits 3.5 ≤ D 3.5 ≤ D ≤ 8 8 ≤ H ≤ 18 D ≤ 8 8 ≤ H H ≤ 18

  16. Design of a can - Summary  Min f(D,H) = πD2 /2 + πDH (cm2) • Subject to: (πD2/4)H ≥ 400 (cm3) 3.5 ≤ D D ≤ 8 8 ≤ H H ≤ 18

  17. More on design variables (DVs) • Parameters that: • can be arbitrarily selected by the design engineer, AND that • influence the behavior of the product (or process) to be designed • For discrete variables... determine set of permissible values

  18. Likely DV’s – think FORM • Sizes • L, W, H, D, t • Shapes • square, circular, cylindrical, slender, short • Configurations • left-handed, on-top, behind, over • Materials • metals, polymers, ceramics • Manufacturing processes • machined, stamped, molded

  19. More on Constraints • How will the product “fail” to function/perform? • Legally • Mechanically • Electrically • Chemically • Other?

  20. Mechanical failure modes Tensile/compressive failure, plastic, brittle Buckle Corrosion Excess deflection Excessive friction Thermal (melts, combusts…) Wear Vibration Unsatisfactory motion (i.e. 4-bar, x,v,a) Other?

  21. Electrical failure modes Short circuit Open circuit Excessive power, heat Poor filtering EM interference Other?

  22. Legal failure modes Violates codes/standards Causes unforeseen property damage Causes unforeseen injury Infringes existing patent Other?

  23. Aids to math. modeling Diagrams Class notebooks Handbooks Textbooks Test results CAD

  24. Summary • Spend time on formulating • 5 Step process • Resulting in math. model

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