Imse 302 spring 2002

Design, Cost & Material Relationships

Integration of Material Properties(), Mechanical Properties(, E) and Cost(Cw($/wt))

Cu= Cw x M

= Cw x  x V

= Cw x  x A x L

where

Cu = Unit CostCw= Cost/WeightM = Mass(Weight)

V= VolumeA = AreaL = Length

= density

A = is typically a function of design parameters and mechanical material properties 1/2, 2/3, or 1 or E1/3, 1/2, or 1

Models

  1. Single Constraint Models(performance ratios)
  2. Multiple Constraint Models

Examples

  1. Simple Tension
  2. Simple Extension(Deflection)
  3. Simple Bending

Basic Strength of Material Relationships

 = S = P/A(simple tension)

= mc/I(bending)

= PL/AE(simple tension)

= PL3/48EI(bending of center load)

Imse 302 spring 2002

Functions to be Optimized

  1. Cost = Minimize Cu

Cu= Cw x M

= Cw x  x V

= Cw x  x A x L

  1. Weight = Minimize M

M =  x V

=  x A x L

  1. Volume = Minimize V

V = A x L

where

A = Function of [1/(mechanical property)X ]

Mechanical property = yield strength, modulus, etc

X = exponent, typically has the value of 1/3, 1/2, 2/3, or 1

Key Factors in Design

  1. Specification of Performance Criteria
  2. Load (implies material strength –P & )
  3. Deflection (implies material stiffness -  & E)
  4. Fatigue Life
  5. Energy Absorption
  6. ……
  1. Type of Loading
  2. Simple Tension
  3. Compression
  4. Bending
  5. Torsion
  6. ……
  1. Shape of Structure
  2. Circular-solid, hollow
  3. Square-solid, hollow
  4. Rectangular-solid, hollow
  5. Ellipse-solid, hollow
  6. …….

Ashby Plots

Dr. Michael Ashby of Cambridge University in England developed computer programs to aid in the selection of materials for various applications. This software has been referred to as:

  1. Cambridge Materials Selector
  2. Cambridge Process Selector
  3. Cambridge Engineering Selector

This program has a large data base which permits selection of materials, but it cannot easily optimize which is the best material when there is more than one constraint.

I. Single Constraints(Performance Ratios)

Simple Tension & Elongation

A. Simple Tension

Cu= Cw x  x A x L

Simple Tension

 = P/A and thus A = P/

thus Cu= Cw x  x A x L = Cw x  x (P/) x L = [Cw x  /  ] x P x L = [performance ratio] x constants

Lowest performance ratio[Cw/] = lowest cost

Lowest [ / ] = lowest weight

Lowest [1/ ] or highest  = lowest volume

B. Simple Elongation

Cu= Cw x  x A x L

Simple Elongation

 = PL/AE and A = PL/E

thus Cu= Cw x  x A x L = Cw x  x (PL/E) x L = [Cw x  / E ] x PL2/ = [performance ratio] x constants

Lowest performance ratio[Cw/E] = lowest cost

Lowest [ / E] = lowest weight

Lowest [1/E ] or highest E = lowest volume

C. Simple Bending(Rectangle)

Cu= Cw x  x A x L

Simple Bending-Strength

 = Mc/I, where c = h/2 and I = 1/12(wh3)

Let the depth(h) be variable and w=constant

 =Mc/I = (PL/4)(h/2)/(1/12 wh3) =(3/2)(PL/wd2)

A=wd, so  = (3/2)(PL)(w/A2) or A=[(3/2)(PLw/]1/2

thus Cu= Cw x  x A x L = Cw x  x [(3/2)(PLw/)]1/2 x L = [Cw x  / 1/2 ] x [(3/2)(PL3 w)]1/2 = [performance ratio] x constants

II. Multiple Constraints

  1. Find Area for Each Constraint
  2. Use the Maximum Area obtained from All of the constraints. This is the controlling constraint.

DO NOT SUBSTITUTE AREA FOR ONE CONSTRAINT INTO ANOTHER CONSTRAINT. SOLVE EACH INDEPENDENTLY.

Illustrate procedure with simple tension-elongation example

Illustrate procedure & numerical solution with simple cantilever bending example

Assign Project & Project Teams

Teams

1. Record meeting times, attendance, and assignments to members – meet at least once per week out of class