engs 171 wegst l06 27 apr 2012 f - dartmouth.educushman/courses/engs171/wegst-lecture6.pdf · m. f....
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© MFA 2011 © UGKW 2012
Ulrike G.K. WegstThayer School of Engineering
Dartmouth College, Hanover, NH [email protected]
Cummings 106
Lecture 6
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Chapter 8
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Selection Strategies
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Selecting a Car
Minimize or maximize objective
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Car Energy Consumption (Gas, LPG, Hybrid, MJ/km)
LPG = Liquefied Petroleum Gas
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Car Energy Consumption (Diesel, MJ/km)
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CO2 Rating versus Energy Consumption
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Tradeoff
The tradeoff between carbon footprint and car ownership
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Selecting a Material for a Portable Bike Shed
Minimize or maximize objective
Need to translate component function and design requirements into material properties.
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The Selection Strategy
Constraint: an essential condition that must be met, typically expressed as an upper or lower limit.
Objective: a quantity that must be minimized or maximized.
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www.grantadesign.com/education/resourcesM. F. Ashby, 2011 © UGKW 2012
Function, Objectives, and Constraints
Function "What does the component do?“
Objective "What is to be maximized or minimized?“
Constraints * "What non-negotiable conditions must be met?""What negotiable but desirable conditions ...?"
*It is sometimes useful to distinguish between "hard" and "soft" constraints:
• Stiffness and strength might be absolute requirements (hard constraints)
• Cost might be negotiable (a soft constraint).
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Common Constraints and Objectives
Common constraints
Must be:• Electrically conducting• Optically transparent• Corrosion resistant• Nontoxic• Nonrestricted substance• Able to be recycled
Must meet target value of:• Stiffness• Strength• Fracture toughness• Thermal conductivity• Service temperature
Common objectives
Minimize:• Cost• Mass • Volume• Thermal losses• Electrical losses• Energy consumption• Carbon emissions• Waste• Resource depletion• Environmental impact
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Screening Using a Bar Chart
The materials in the “search region” below the selection line meet the constraint.
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Screening Using a Bubble Chart
The materials in the “search region” at the upper left meet both constraints.
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Property Charts and Material Indices I
Material indices for stiff, lightweight structures: /E1/3, /E1/2, /E.
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Deriving Material Indices
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Generic Components and Functions
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Example 1: A Beam in Bending
Derivation of Material Index for light, stiff beam:Ashby Chapter 8, pages 191-194
Minimizing mass, m:
• Objective function:
• For stiff beam of minimum mass minimize Material Index:
21 /EM
ALm
m
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Plotting Material Indices on Property Charts
To plot the Material Index
M = /E1/2
on the E- Property Chart with logarithmic axes, consider the condition
M = /E1/2 = constant C.
Taking logs
log (E) = 2 log (c) – 2 log (C)
For a fixed value of C, this is the equation of a straight line of slope 2 on a plot of log (E) against log (), as
shown above.
• All materials on the line have the same stiffness per unit weight.
• The difference: materials of lower density have a larger cross-sectional area A.
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Minimizing Beam’s Mass, Cost, Embodied Energy
Minimizing mass, m:
• Objective function:
• For stiff beam of minimum mass minimize:
Minimizing material cost, C:
• Objective function:
• For stiff beam of minimum mass minimize:
Minimizing embodied energy, H:
• Objective function:
• For stiff beam of minimum mass minimize: 21 /EHM
ALHmHH
mH
mm
21 /ECM
ALCmCC
mC
mm
21 /EM
ALm
m
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What about Shape?
2
4A
IeB
Shape Factor for Elastic Bending
For more information on Shape Factors see Ashby Chapter 8, 192-4 and CES Help.
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Example 2: A Shaped Beam in Bending
Material Maximum shape factor, (stiffness relative to that of a solid square beam)
Mass ratio by shaping, (relative to that of a solid square beam)
Steels 64 1/8
Al alloys 49 1/7
Composites (GFRP, CFRP) 36 1/6
Wood 9 1/3
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Example 3: A Plate in Bending
Derivation of Material Index for light, stiff plate:Ashby Chapter 8, pages 189-190
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Property Charts and Material Indices II
Grid lines for the index /E1/3.
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Multiple Objectives
Mass and cost for a component made from alternative material choices. The tradeoff surface links non-dominated solutions.
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Five Useful Property Charts
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Stiffness at Minimum Weight
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Strength at Minimum Weight
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Stiffness at Minimum Embodied Energy
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Strength at Minimum Embodied Energy
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Minimum Thermal Loss
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Preparation for Next Class with Prof. Wegst
Textbook and CES Software
• Read Chapters 8 & 9 in Ashby Textbook
• Additional helpful Background Reading:
Useful Solutions to Standard Problems (also in Help section)
Project/Case Study
• Analyze the function of the different components in your respective product:
• Tie in tension, Beam or Plate in bending, etc.?
• Are stiffness, strength, toughness, thermal conductivity, etc. of concern?
• What are the objectives?
• What are the constraints?