Appendix A

TYPICAL PHYSICAL PROPERTIES OF SOME MATERIALS

	Density	Ultimate Strength		Yield	Modulus of	Poisson's	Coef. of	Thermal
Material	kg/m^3	Tension MPa	Comp. MPa	Strength MPa	Elasticity E GPa	ratio	Thermal Exp. 10^-6/°C	Conductivity W/m °C
Aluminum 2014-T6	2800	470		410	72	0.33	23	210
(alloy) 6061-T6	2800	228		131	70	0.33	23	210
Brass cold rolled	8470	540		420	105	0.35	19	105
annealed	8470	330		100	105	0.35	19	105
Bronze Manganese	8800	450		170	100	0.34	20	58
Cast Iron
Gray	7200	170	650		95	0.25	12	45
Malleable	7200	370		250	170	0.25	12	45
Concrete
Low strength	2400	2	20		22	0.15	11	1
High strength	2400	3	41		32	0.15	11	1
Medium strength	2400	4	62		40	0.15	11	1
Copper hard-drawn	8900	380		330	120	0.33	17	380
Glass Silicon	2400	80	400		70	0.17	8	0.8
Magnesium 8.5% Al	1800	350		250	45	0.35	26	160
Steel
0.2%C HR	7850	410		250	200	0.30	12	42
0.2%C HR	7850	550		350	200	0.30	12	42
0.2%C HR	7850	690		370	200	0.30	12	42
0.8%C HR quenched	7850	830		700	200	0.30	12	42
Stainless 302 CR	7920	860		600	194	0.30	17	18
Titanium 6% Al 4%V	4460	900		830	110	0.34	9	14

Properties vary widely depending on changes in composition, temperature and treatment conditions.

CR = Cold rolled HR = Hot rolled

IMPORTANT CONSTANTS

Constant	U.S. Unit	SI Unit
Absolute zero	-459.67 °F	-273.15 °F
Acceleration of gravity	32.174 ft/s^2	9.8066 m/s^2
Atmospheric pressure	14.694 psi	0.10132x10^6 Pa
Stefan-Boltzmann constant	0.1714x10^-8 Btu/hr ft^2 °R^4 where °R = °F + 459.67	5.669x10^-8 W/m^2 °K^4 where °K = °C + 273.15

APPROXIMATE PROPERTIES OF MILD STEEL AT ROOM TEMPERATURE

Quantity	U.S. Unit	SI Unit
Conductivity	28.9 Btu/ft hr °F 2.4 Btu/in hr °F	50 W/m °C
Density	15.13 slug/ft^3(lbf s^2/ft^4) 0.730x10^-3 lbf s^2/ft^4 0.282 lbm/in^3	7800 kg/m^3
Elastic modulus	30x10^6 psi	207x10^9 Pa
Specific heat	0.11 Btu/lbm °F	460 J/kg °C
Yield stress	30x10^3 psi	207x10^6 Pa

SI System – Units

Temperature			Kelvin		K
Length			meter		m
Time			second		s
Mass			kilogram		kg
Force			newton		N		kg·m/s^2
Pressure			pascal		Pa		N/m^2
Work and energy			joule		J		N·m
Power			watt		W		J/s
Electric current			ampere		A
Electric charge			coulomb		C		s·A
Electric potential			volt		V		W/A
Electric resistance			ohm				V/A
Electric conductance			seimens		S		A/V
Capacitance			farad		F		C/V
Permittivity							F/m
Magnetic flux			weber		Wb		V·s
Magnetic flux density			tesla		T		Wb/m^2
Inductance			henry		H		Wb/A
Magnetic field							A/m
Permeability							H/m
Concentration							mol/m^3
Frequency			hertz		Hz		cycle/s
Common SI Prefixes
Tera	T	10^12		milli		m		10^-3
Giga	G	10^9		micro				10^-6
Mega	M	10^6		nano		n		10^-9
Kilo	k	10^3		pico		p		10^-12

Constants

Quantity	Symbol	Value
Electron charge	e0	1.602 x 10^-19 C
Electron mass	me	9.1091 x 10^-31 kg
Bohr magneton		9.273 x 10^-24 J/K
Boltzmann constant	k	1.381 x 10^-23 J/K
Avogadro’s number	Nav	6.022 x 10^-23 mol^-1
Gas constant	R	8.314 J/(mol K)
Faraday’s constant	F	9.6485 x 104 C/mol
Permeability of free space		4 x 10^-7 H/m
Permittivity of free space		8.854 x 10^-12 F/m
Characteristic impedance of free space	z0	377
Speed of light in vacuum	c0	2.998 x 10^-8 m/s
Atmospheric pressure	patm	101.325 kPa
Zero degrees Celsius	0°C	273.15 K
Gravitational constant	G	6.673 x 10^-11 N·m^2/kg^2

Notes:

· 1Å = 1 ångström = 10^-10 m

· Avogadro’s number is the number of elementary entities in one mole. The elementary entity must be specified; it may be atoms, molecules, ions, electrons or other particles. Values found for Avogadro’s number range within 1% of the listed value.

· Relationships between constants: .

Appendix B

USEFUL RELATIONSHIPS AMONG ISOTROPIC
ELASTIC CONSTANTS

Also Useful Are

Constant Names

Lame's constants

Shear modulus

Bulk modulus

Young's modulus

Poisson's ratio

Appendix C

UNITS, CONVERSIONS AND ABBREVIATIONS

General Prefixes

10 deka (da) 10^-1 deci (d)

10² hecto (h) 10^-2 centi (c)

10³ kilo (k) 10^-3 milli (m)

10⁶ mega (M) 10^-6 micro (m)

10⁹ giga (G) 10^-9 nano (n)

10¹² tera (T) 10^-12 pico (p)

10¹⁵ peta (P) 10^-15 femto (f)

10¹⁸ exa (E) 10^-18 atto (a)

Length

1 meter (m) = 100 centimeters (cm) = 3.281 feet (ft) = 39.37 inches (in)

1 mile = 5280 ft = 1.609 kilometers (km)

1 micron (m) = 10^-6 m

1 angstrom (Å) = 10^-10 m

Area

1 hectare (ha) = 10⁴ square meters (m²) = 2.47 acres

1 acre = 43,560 square feet (ft²)

1 barn (b) = 10^-24 cm²

Volume

1 cubic meter (m³) = 1000 liters = 264.2 U.S. gallons = 35.31 cubic feet (ft³)

1 liter (1) = 10³ cubic centimeters(cm³ or ml) = 1.057 U.S. quarts

1 acre foot = 1.234 x 10³ m³

1 cord = 128 ft³

1 board foot = 2.36 x 10^-3 m³

1 cubic mile = 4.17 cubic kilometers (km³)

1 barrel of petroleum (bbl) = 42 U.S. gallons = 0.159 m³

Angles

360 degrees (°) = 2p radians

1 degree = 60 minutes (') of arc

1 minute of arc = 60 seconds (") of arc

Time

1 year (y or yr) = 3.1536 x 10⁷seconds (s or sec)

= 8.76 x 10³ hours (h or hr)

1 day (d) = 8.64 x 10⁴ sec = 1440 minutes (min)

Mass

1 kilogram (kg) = 2.205 pounds (lb)

1 metric ton (tonne or MT) = 10³ kilograms (kg)

= 1.102 short tons

= 0.9842 long tons

1 pound (lb) = 16 ounces avoirdupois (oz) = 453.6 grams (g)

Energy

1 joule (J) = 1 kg m²/sec²

= 10⁷ ergs = 0.2390 calories (cal)

= 9.484 x 10^-4 British thermal units (Btu)

= 1 watt-second (Ws)

= 6.242 x 10¹⁸ electron volts (eV)

= 1 newton-meter (Nm)

1 kilowat-hour (kWh) = 3.6 x 10⁶ J

= 3414 Btu

1 quad = 10¹⁵ Btu = 1.05 x 10¹⁸ J

1 Calorie = 1 kilocalorie (Kcal) = 10³ cal

1 therm = 10⁵ Btu

1 foot pound = 1.356 J

1 kiloton of TNT (KT) = 4.2 x 10¹² J

Power

1 watt (W) = 1 joule/second

1 horsepower (hp) = 0.746 kilowatts (kW)

Force

1 newton (N) = 1 kg m/sec² = 10⁵ dynes (dyn)

Pressure

1 pascal = 1 N/m² = 1 J/m³

1 bar = 10⁵ pascal = 0.9869 atmospheres (atm)

1 atmosphere (atm) = 76 cm of mercury

= 14.7 lb/in²

= 760 torr

Viscosity

1 poise (p) = 1 dyn-sec/cm² = 0.1 kg/m sec

Permeability

1 Darcy = 10^-12 m²

Quantity	Units / Conversion
General
Acceleration	1 in/s^2 = 0.0254 m/s^2
Area	1 in^2 = 645.16 mm^2
Density (i)	1 lbm/in^3 = 27679.905 kg/m^3
(ii)	1 slug/ft^3 = 515.379 kg/m^3
Force	1 lb = 4.448 N (N = Newton)
Frequency	Hz (hertz = cycle/s)
Length	1 in = 0.0254 m; 1 ft = 0.3048 m
Mass (i)	1 lbm = 0.45359 kg
(ii)	1 slug = 14.594 kg
Moment	1 in-lb = 0.1130 N • m
Moment of inertia (area)	1 in^4 = 416231.4 mm^4
Moment of inertia (mass) (i)	1 lbm-in^2 = 2.9264 10^-4 kg • m^2
(ii)	1 slug-in^2 = 0.009415 kg • m^2
Power (i)	1 in-lb/s = 0.1130 W (watt = J/s)
(ii)	1 hp = 0.746 kW (1 hp = 550 ft-lb)
Pressure	1 psi = 6894.8 Pa (psi = pounds/in^2; Pa = N/m^2)
Stiffness	1 lb/in = 175.1 N/m
Stress (i)	1 psi = 6894.8 Pa
(ii)	1 ksi = 6.8948 MPa; 1 MPa = 145.04 psi (ksi = 1000 psi; MPa = 10^6Pa)
Time	s (second)
Velocity	1 in/s = 0.0254 m/s
Volume	1 in^3 = 16.3871 10^-6m^3
Work, energy	1 in-lb = 0.1130 J (joule = N • m)
Heat Transfer
Convection coefficient	1 Btu/h.ft^2 °F = 5.6783 W/m^2 °C
Heat	1 Btu = 1055.06 J (1 Btu = 778.17 ft-lb)
Heat flux	1 Btu/h.ft^2 = 3.1546 W/m^2
Specific heat	1 Btu/°F = 1899.108 J/°C
Temperature (i)	T °F = [(9/5)T + 32] °C
(ii)	T °K = T °C + 273.15 (K = kelvin)
Thermal conductivity	1 Btu/h.ft °F = 1.7307 W/m. °C
Fluid Flow
Absolute viscosity	1 lb.s/ft^2 = 478.803 P (poise = g/cm • s)
Kinematic viscosity	1 ft^2/s = 929.03 St (stroke = cm^2/s)
Electric and Magnetic Fields
Capacitance	F (farad)
Charge	C (coulomb)
Electric charge density	C/m^3
Electric potential	V (volt)
Inductance	H (henry)
Permeability	H/m
Permittivity	F/m
Scalar magnetic potential	A (ampere)

Appendix D

ELEMENT TYPES / SHAPES

Appendix E

FORMAT OF DYNAFLOW OUTPUT FILES

This Appendix defines the format of files generated by DYNAFLOW. The data may then be read and converted into the form required by a post-processing program.

Each data set starts with a header of the form:

title

which contains up to 80 characters and is the same as the title defined by the command "DEFINE_PROBLEM" (see Sections 2.1 and 2.2).

Each output file is closed by the following data lines:

title

-1

E.1 TAPE90.name: Nodal Coordinates/Connectivity Data

title

numnp, nsd, ndof, numeg

for node = 1, numnp

node, (x (i, node), i=1, nsd)

end

-1

for neg = 1, numeg

neg, idum, nen, numel, iopt, el_shape, el_name, reg_name

for ne = 1, numel

ne, mat(ne), (ien(i,ne), i=1, nen)

end

end

where:

numnp = number of nodal points

nsd = number of spatial dimensions

ndof = number of degrees of freedom per node

numeg = number of element groups

neg = element group number

nen = number of nodes per element

numel = number of elements

iopt = 0 2d plane analysis

1 1d analysis

2 axisymmetric analysis

3 3d analysis

el_shape = element shape (character string)

el_name = element name (character string)

reg_name = region name (character string)

ne = element number

mat = material number

ien = connectivity list

E.2 TAPE87.name: Nodal Results

title

ns, io, label, ‘step’, ns

for node = 1, numnp

node, (d(i, node), i=1, ndof)

end

-1

where:

ns = step number

label = ‘displacement’ (io=1)

‘velocity’ (io=2)

‘acceleration’ (io=3)

‘reaction’ (io=4)

‘eigenshape’ (io=5)

E.3 TAPE96.name: Strain Energy

title

ns, io, ‘field_w’, ‘step’, ns

for ne = 1, numel_tot

ne, neg, energy

end

-1

E.4 TAPE89.name: Field Results

title

ns, io, ‘field comp’, ‘step’, ns, ‘ncomp’, ncomp

for neg = 1, numeg

for ne = i, numel (neg)

ne, (field (i,ne), i=1, ncomp)

end

end

-1

E.5 TAPE88.name: Time Histories

title

nts, ‘time’

(time(i), i=0, nts) (8 values per line)

title

nts, i1, i2, io, neg, label1, label2, label3, i1, label4, neg

(comp(i), i=0, nts)

where:

nts = number of time steps

i1 = node/element number

i2 = component number

label1 = ‘displ.’ for diplacement (io=4)

‘veloc.’ for velocity (io=5)

‘acc.’ for acceleration (io=6)

‘react’ for reaction (io=15)

‘stress’ for solid element (io=1,2,3)

label2 = component name (character string)

label3 = ‘node’ for nodal time history

‘elmnt’ for field time history

label4 = ‘group’ for field time history

neg = group number (for field time history)

Notes . .