1. Selection Strategies

2. Making selections Let’s attempt to remove the emotional and intangibles from this discussion: It’s cool Johnny has one I love the color

3. Logical Approach Assemble data for the characteristics of the thing you want to select; make a database, mental or physical Formulate the characteristics that the thing must have to satisfy your requirements; list the constraints. Decide on the ranking criterion you will use to decide which is best; choose and apply the objective Research top ranked candidates more fully to satisfy yourself nothing has been overlooked; seek documentation.

4. Example: New Car Need a new car, mid-sized, 4 doors, gasoline engine, at least 150 HP. Want to minimize the cost to own and operate

5. Constraints Simple Constraints - MUST have these to be a candidate: 4 doors & gasoline powered Limit Constraints - fits in a range At LEAST 150 HP (more than this is OK)

6. Objective Objective: a criterion of acceptance Minimize cost to own/operate Oh, and we should probably look at carbon footprint too!

7. Desired features expressed as Constraints Objective Desired features expressed as Constraints Objective Car Data Performance Economy What car? rating Car Data Performance Economy What car? rating Selection Engine Screening Ranking Documentation Selection Engine Screening Ranking Documentation Final Selection Mid-sized family sedan 4 door Gasoline fuel 150+ HP Lowest cost of ownership Lowest CO 2 footprint Make Model Price Dimensions Fuel Type Fuel Consumption CO 2 rating Cost of ownership etc.

8. Objectives When we have more than one objective things get complicated. We have lowest cost and lowest CO 2 profile. Plus there might still be some “other” aspects - so don’t just list one result - keep a couple for comparison The lowest cost car might not be the most carbon efficient car.

9. Trade-Offs We need to handle trade-offs. Suppose we have two objectives and we look at different cars and plot out their performance for each objective.

10. High Low Low cost, high carbonUnacceptable Low carbon, high cost Low carbon, low cost

11. Storage Shed for Bikes Need properties like weather resistance, UV resistance, sufficient stiffness and strength, low weight, low cost The material properties associated with these are things like density, price, stiffness, strength, etc.

12. Design Requirements expressed as Constraints Objective Design Requirements expressed as Constraints Objective Materials Data Material attributes Process Attributes Documentation Materials Data Material attributes Process Attributes Documentation Selection Engine Screening Ranking Documentation Selection Engine Screening Ranking Documentation Final Selection Able to be molded Water and UV resistant Modulus > 40 GPa Strength > 80 MPa As light as possible As cheap as possible Density Price Modulus Strength Thermal Properties Electrical Properties Durability Process Compatibility Etc.

13. A bit more complicated The properties we are seeking are not as obviously presented as in the case of a car. We have to translate the design requirements into materials related constraints and objectives. The screening process works similarly.

14. Translate Design Requirements express as function, constraints, objectives and free variables Screen using constraints eliminate materials that cannot do the job Rank using objectives find the screened materials that do the best job Seek Documentation research the family history of top ranked candidates FINAL MATERIAL CHOICEALL MATERIALS

15. Translation Engineered components have functions This is achieved through constraints: certain dimensions are fixed, component must carry design load w/o failure transfer or insulate heat, electricity must function in given temperature range

16. Translation Designer has one or more objectives Certain parameters can be adjusted to optimize the objective. These are called free variables.

17. Functions, Constraints, Objectives & Free Variables FunctionWhat does the component do? ConstraintsWhat non-negotiable conditions must be met? ObjectiveWhat is to be maximized/minimized? Free variables What parameters is the designer free to change?

18. Common ConstraintsCommon Objective Must be:Minimize: Electically conductiveCost Optically transparentMass Corrosion ResistantVolume NontoxicThermal losses Non-restricted substanceResource depletion RecyclableEnergy consumption Carbon Emissions Must meet target:Waste StiffnessEnvironmental Impact Strength Fracture toughness Thermal Conductivity Service temperature

19. Screening Constraints are gates - keeps out concepts that will fail. Screening is the process of using the constraints to identify candidate solutions.

20. Ranking To rank the materials that pass screening, we need a criteria: objectives Performance is sometimes limited by a single property, sometimes by a combination of them. If we want to minimize heat losses, we look for materials with the smallest thermal conductivity (at least those that have passed the screening evaluation and meet other criteria). Sometimes we are combining things - for a light weight high stiffness tie-rod, we actually want to maximize stiffness divided by weight. This combines both properties into a single ranking element.

21. Rankings: Material Indices Sometimes the actual parameter to be ranked can be complex. For example, in our light stiff tie rod application, we can minimize But for a strong beam with low embodied energy, we would minimize

22. Material Indices These complex terms are identified during engineering analysis. There are some standard terms that we can accept from other peoples’ work. Ultimately it depends on what we are trying to do.

23. Stiffness and Strength indices Configuratio n and objective Configuratio n Minimize volume Minimize mass Minimize embod. energy Minimize material cost Stiffness Limited Tie Beam Panel Strength limited Tie Beam Panel Above values should be minimized to meet goals

24. Thermal property indices Minimum steady state heat loss: λ Minimum thermal inertia: C p ρ Minimum heat loss in thermal cycle: √(λ C p ρ)

25. Stiffness design Tie Rod Materia l EρHmHm CmCm Aluminu m 802.72002 Steel2007.9351 CFRP1701.628040 GFRP281.811220 VolumeMass Energ y Cost 0.0125 0.033 8 6.750.068 0.0050 0.039 5 1.380.040 0.0059 0.009 4 2.640.376 0.0357 0.064 3 7.201.286

26. MInimum volume design

27. Minimum mass design

28. MInimum energy design

29. Minimum cost design

30. Resolving Conflicts In most real design applications, a compromise is needed because different design parameters have different optimal material choices. Some methods are Weighting and Tradeoff Strategies

31. Weight Factors This is an attempt to quantify judgement. Key properties are identified and there values are listed Then they are combined, but not in equal amounts. the “weights” are the importance factors associated with each characteristic

32. Weighting functions First we identify all parameters and their values. M i represents the value of the ith parameter of interest, and M i,max is the largest value of all being considered. The weights are a set of numbers w i between 0 and 1 that indicate the importance of parameter i.

33. Weighting Functions

34. Weighting FUnctions Some parameters don’t have experimental numerical values. These are usually rated something like 5=good, to 1= bad. Sometimes a property has a good low value, then we use the reciprocal of the property so that in all cases a large number is a good thing for the calculation.

35. Weighting Function Then we can calculated the weighted value of the material by simply summing everything up

36. Example with our Plate Suppose we want to have low mass, energy and cost. MaterialMassEnergyCost Aluminum0.627125.321.25 Steel1.35147.281.35 CFRP0.28980.8711.55 GFRP0.59366.3911.86

37. Best Plate Because we want to minimize all three values, we can either take reciprocals of each value and do the normal weighting process, or we can do the normal weighting and look for the smallest value. Let’s take the reciprocals to get the feel for the process.

38. Best Plate Material1/Mass1/Energy1/Cost Aluminum1.5960.0080.798 Steel0.7400.0210.740 CFRP3.4620.0120.087 GFRP1.6870.0150.084 MAXIMUM3.4620.0210.798

39. Best Plate Now we come up with the weighted values. We could make them equally weighted (case 1): w 1 =1/3; w 2 =1/3; w 3 = 1/3 Or we could use some other combination, say where mass is most important, followed by cost then energy (case 2): w 1 = 0.5; w 2 =0.2; w 3 =0.3 First we renormalize all the data by taking each materials value and dividing it my the maximum value for the characteristic.

40. Best Plate MaterialM 1 /M 1,max M 2 /M 2,max M 3 /M 3,max Aluminum0.460.381.00 Steel0.211.000.93 CFRP1.000.580.11 GFRP0.490.710.11

41. Weighted Values MaterialCase 1Case 2 Aluminum0.6130.606 Steel0.7140.585 CFRP0.5640.649 GFRP0.4350.418

42. Weighting So, although weighting reduces the problem to a simple numerical calculation, the choice of the weights can affect the results.

43. Systematic tradeoff strategies We define a solution as a viable choice of material that meets all the constraints but is not necessarily optimal for the objectives. Consider some data where we are to minimize cost and mass (while meeting some other constraints). Let’s say P 1 is the cost and P 2 is the mass. The next slide shows some material choices.

44. P 1 : Cost P 2 : Mass CheapExpensive Light Heavy

45. Dominated Solutions A solution is said to be dominated if there are better solutions on either parametric axis. We can draw a box towards the axis and see if there are any solutions contained in that region. If there are, then the solution is dominated.

46. P 1 : Cost P 2 : Mass CheapExpensive Light Heavy Dominated Solution

47. Tradeoff Surface If we can make a curve out of all of the non-dominated solutions (by connecting the dots) we call this the trade-off surface. Points on the trade-off surface offer the best compromises. This can create our shortlist from which we choose a solution.

48. P 1 : Cost P 2 : Mass CheapExpensive Light Heavy

49. Penalty Function Suppose we want to minimze the cost (C) and the mass (m). We create a simple equation: Z = C + α m The term α is the change in Z associated with a increase in m (mass) so has units of cost/mass ($/kg, for example). It is called the exchange constant.

50. Penalty Function If we think of our data as a plot of mass vs. cost, we can re-write our penalty function to look like y = mx + b. m = -(1/α) C + (Z/α) Our choice of alpha describes the shape of the penalty function. We can plot these lines for different values of Z and find the solution corresponding to the smallest Z value.

51. P 1 : Cost P 2 : Mass CheapExpensive Light Heavy Decreasing values of Z

52. P 1 : Cost P 2 : Mass CheapExpensive Light Heavy Decreasing values of Z Different values of α can result in different choices

53. Exchange constants The exchange constant must be chosen appropriate to the problem. In our case, comparing mass and cost, our exchange constant is the cost of a kilogram of mass. So for a family car, this might be a relatively small value. But for a spaceship this would be some very high value. For many engineering applications this exchange constant can actually be calculated based on the life cost of the system being designed.

54. Exchange Constants SystemBasis of estimate Exchange constant ($/kg) Family carFuel savings1-2 TruckPayload5-20 Civil aircraftPayload100-500 Military aircraft Payload/performan ce 500-1,000 Space vehiclePayload3,000-10,000

55. Exercise You are designing a disposable fork for a fast-food restaurant. identify the objective and constraints you think are important for this application.

56. Exercise A maker of polypropylene patio furniture hires you to evaluate his product. The competition makes cast-iron patio furniture and claims their product is much “greener” than the PP. The PP chair weighs about 1 kg and the cast iron about 11 kg. Considering energy and carbon as the metrics, which chair is greener? Does the projected life of the chairs matter? If so, how long before the answer changes?