ENGS 171 Wegst L06 27 Apr 2012 f - dartmouth.educushman/courses/engs171/Wegst-Lecture6.pdf · M. F....

© MFA 2011 © UGKW 2012

Ulrike G.K. WegstThayer School of Engineering

Dartmouth College, Hanover, NH [email protected]

Cummings 106

Lecture 6

Chapter 8

www.grantadesign.com/education/resourcesM. F. Ashby, 2011 © UGKW 2012

Selection Strategies


Selecting a Car

Minimize or maximize objective


Car Energy Consumption (Gas, LPG, Hybrid, MJ/km)

LPG = Liquefied Petroleum Gas


Car Energy Consumption (Diesel, MJ/km)


CO2 Rating versus Energy Consumption


Tradeoff

The tradeoff between carbon footprint and car ownership


Selecting a Material for a Portable Bike Shed

Minimize or maximize objective

Need to translate component function and design requirements into material properties.


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.


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).


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


Screening Using a Bar Chart

The materials in the “search region” below the selection line meet the constraint.


Screening Using a Bubble Chart

The materials in the “search region” at the upper left meet both constraints.


Property Charts and Material Indices I

Material indices for stiff, lightweight structures: /E1/3, /E1/2, /E.

Deriving Material Indices


Generic Components and Functions


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


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.


Minimizing Beam’s Mass, Cost, Embodied Energy

Minimizing mass, m:


• For stiff beam of minimum mass minimize:

Minimizing material cost, C:


• For stiff beam of minimum mass minimize:

Minimizing embodied energy, H:


• For stiff beam of minimum mass minimize: 21 /EHM

ALHmHH

mH

mm

21 /ECM

ALCmCC

mC

mm

21 /EM

ALm

m


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.


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


Example 3: A Plate in Bending

Derivation of Material Index for light, stiff plate:Ashby Chapter 8, pages 189-190


Property Charts and Material Indices II

Grid lines for the index /E1/3.


Multiple Objectives

Mass and cost for a component made from alternative material choices. The tradeoff surface links non-dominated solutions.

Five Useful Property Charts


Stiffness at Minimum Weight


Strength at Minimum Weight


Stiffness at Minimum Embodied Energy


Strength at Minimum Embodied Energy


Minimum Thermal Loss


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?

ENGS 171 Wegst L06 27 Apr 2012 f - dartmouth.educushman/courses/engs171/Wegst-Lecture6.pdf · M. F....

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