Metal Foams: A Design Guide

244 Appendix: Catalogue of material indices
(d) Strength-limited design at minimum mass (cost, energy a )
Function and constraints a,c Maximize b
1/2
f /
PLATE (flat plate, compressed in-plane, buckling failure)
Collapse load, and width specified, thickness free
CYLINDER WITH INTERNAL PRESSURE
Elastic distortion, pressure and radius specified; wall f/
thickness free
SPHERICAL SHELL WITH INTERNAL PRESSURE
Elastic distortion, pressure and radius specified, wall f/
thickness free
FLYWHEELS, ROTATING DISKS
Maximum energy storage per unit volume; given velocity
Maximum energy storage per unit mass; no failure f/
aTo minimize cost, use the above criteria for minimum weight, replacing density by Cm ,whereCmis the material cost per
kg. To minimize energy content, use the above criteria for minimum weight replacing density by q where q is the energy
content per kg.
b
f D failure strength (the yield strength for metals and ductile polymers, the tensile strength for ceramics, glasses and brittle
polymers); D density.
cFor design for infinite fatigue life, replace f by the endurance limit e.
(e) Strength-limited design: springs, hinges etc for maximum performance a
Function and constraints a,c Maximize b
ELASTIC HINGES
Radius of bend to be minimized (max. flexibility without failure) f/E
COMPRESSION SEALS AND GASKETS
Maximum conformability; limit on contact pressure
3/2
f /E
and 1/E
ROTATING DRUMS AND CENTRIFUGES
Maximum angular velocity; radius fixed; wall thickness free f/
aTo minimize cost, use the above criteria for minimum weight, replacing density by Cm ,whereCmis the material cost per
kg. To minimize energy content, use the above criteria for minimum weight replacing density by q where q is the energy
content per kg.
b
f D failure (the yield strength for metals and ductile polymers, the tensile strength for ceramics, glasses and brittle polymers);
H D hardness; D density.
cFor design for infinite fatigue life, replace f by the endurance limit e.