173
table a.1 The Symbols
Class
Property
Symbol and Units
General
Density
ρ
(kg/m
3 or Mg/m
3 )
Price
C m
($/kg)
Mechanical
Elastic moduli (Young’s, shear, bulk)
E, G, K
(GPa)
Poisson’s ratio
v
(—)
Failure strength (yield, fracture)
σ f
(MPa)
Fatigue strength
σ e
(MPa)
Hardness
H
(Vickers)
Fracture toughness
K lc
(MPam
1/2 )
Loss coefficient (damping capacity)
η
(—)
Thermal
Thermal conductivity
λ
(W/mK)
Thermal diffusivity
a
(m
2 /s)
Specific heat
C p
(J/kgK)
Thermal expansion coefficient
α
(°K
−1 )
Difference in thermal conductivity
Δα
(°K
−1 )
Electrical
Electrical resistivity
ρ e
(µΩcm)
Ecoproperties
Energy/kg to produce material per kg
E p
(MJ/kg)
CO 2 /kg burden of material production per kg
CO 2
(kg/kg)
table a.2 Stiffness-Limited Design at Minimum Mass (Cost, Energy, Environmental Impact)
Function and Constraints
Maximize
Tie (tensile strut)
Stiffness, length specified; section area free
E/ρ
Shaft (loaded in torsion)
Stiffness, length, shape specified, section area free
G
1/2
/ρ
Stiffness, length, outer radius specified; wall thickness free
G/ρ
Stiffness, length, wall thickness specified; outer radius free
G
1/3
/ρ
Beam (loaded in bending)
Stiffness, length, shape specified; section area free
E
1/2
/ρ
Stiffness, length, height specified; width free
E/ρ
Stiffness, length, width specified; height free
E
1/3
/ρ
Column (compression strut, failure by elastic buckling)
Buckling load, length, shape specified; section area free
E
1/2
/ρ
Panel (flat plate, loaded in bending)
Stiffness, length, width specified, thickness free
E
1/3
/ρ
Plate (flat plate, compressed in-plane, buckling failure)
Collapse load, length and width specified, thickness free
E
1/3
/ρ
Cylinder with internal pressure
Elastic distortion, pressure and radius specified; wall thickness free
E/ρ
Spherical shell with internal pressure
Elastic distortion, pressure and radius specified, wall thickness free
E/(1 − v)ρ
Appendix: Material Indices