© MFA 2011 © UGKW 2012

Ulrike G.K. WegstThayer School of Engineering

Dartmouth College, Hanover, NH ulrike.wegst@dartmouth.edu

Cummings 106

Lecture 6

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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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.

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.

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?