Simcenter 3D Solutions Consistency of FEA Units
2023-02-01T12:25:06.000-0500
Simcenter Nastran
Simcenter 3D
Summary
Equations and examples for unit consistency in FEA.
Details
Most Finite Element Analysis (FEA) programs do NOT ensure consistency of units. It is the responsibility of the user to use properties of consistent units.
1 g = 9.80665 m / sec^2 (definition)
1 in = 25.4 mm (definition)
1 N = 1 kg m / sec^2 (definition)
1 Pa = 1 N / m^2 (definition)
1 kPa = 1 mN / mm^2 (definition)
F = m g = W (definition)
1 lbf = 1 lbm * 1 g (definition)
1 lbf = 1 lbm * ( 9.80665 m / sec^2 ) ( 1000 mm / m ) ( 1 in / 25.4 mm )
1 lbf = 386.08858 lbm in / sec^2
1 lbf = 32.17405 lbm ft / sec^2
1 lbm = 1 lbf sec^2 / 386.08858 in
1 lbm = 0.0025900 lbf sec^2 / in
1 g = 386.08858 in / sec^2
1 g = 32.17405 ft / sec^2
1 kg = 2.20462 lbm
1 N = 0.22481 lbf
weight density : 1 lbf / in^3
weight density : 1 N / m^3
mass density = ( 1 lbf / in^3 ) / g
mass density = ( 1 lbf / in^3 ) / ( 386.08858 in / sec^2 ) = 0.002590 lbf sec^2 / in^4
mass density = ( 1 N / m^3 ) / g
mass density = ( 1 kg / m^2 sec^2 ) / ( 9.80665 m / sec^2 ) = 0.101972 kg / m^3
EXAMPLE 1 (mN-mm) - What is the WEIGHT and MASS of 1 cubic meter of steel
4130 Alloy Steel, Tempered, Ultra High Strength
E = 2.068428E+11 N / m^2 = 2.068428E+8 kPa = 2.068428E+8 mN / mm^2
nu = 0.32
rho = 7833.394 kg / m^3 = 7.833394E-6 kg / mm^3
$ cubicmeter_mm_steel.dat
ID,NASTRAN,cubicmeter_mm_steel
SOL 101
CEND
ECHO = NONE
OUTPUT
DISPLACEMENT(PLOT,REAL) = ALL
OLOAD(PLOT,REAL) = ALL
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 1
LOAD = 1
SPC = 2
BEGIN BULK
PARAM K6ROT100.0000
PARAM POSTEXT YES
$------------------------------------------------------------------------
PARAM UNITSYS MN-MM
$------------------------------------------------------------------------
GRID* 1 00.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 2 00.0000000000E+000.0000000000E+00+
* 1.0000000000E+03 0
GRID* 3 00.0000000000E+001.0000000000E+03+
* 0.0000000000E+00 0
GRID* 4 00.0000000000E+001.0000000000E+03+
* 1.0000000000E+03 0
GRID* 5 01.0000000000E+030.0000000000E+00+
* 0.0000000000E+00 0
GRID* 6 01.0000000000E+030.0000000000E+00+
* 1.0000000000E+03 0
GRID* 7 01.0000000000E+031.0000000000E+03+
* 0.0000000000E+00 0
GRID* 8 01.0000000000E+031.0000000000E+03+
* 1.0000000000E+03 0
CHEXA 1 1 2 1 3 4 6 5+
+ 7 8
PSOLID 1 1 0 SMECH
$------------------------------------------------------------------------
$ MAT1 MID E G NU RHO A TREF GE
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
MAT1 12.0684+8 0.3200007.8334-6
$------------------------------------------------------------------------
$ GRAV SID CID A N1 N2 N3 MB
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
GRAV 1 0 9806.65 0.0000 0.0000-1.00000
SPC 2 1 123456 0.0000
SPC 2 3 123456 0.0000
SPC 2 5 123456 0.0000
SPC 2 7 123456 0.0000
ENDDATA
The results in the .f06 file of executing the previous Nastran bulk data file yields a reaction force in the T3 direction of
T3 = 7.681902E+07
F = m g = W
m = ( 7.681902E+07 mN ) / ( 9806.65 mm / sec^2 )
m = ( 7.681902E+07 kg mm / sec^2 ) / ( 9806.65 mm / sec^2 ) = 7833.36 kg
EXAMPLE 2 (N-m) - What is the WEIGHT and MASS of 1 cubic meter of steel
4130 Alloy Steel, Tempered, Ultra High Strength
E = 2.068428E+11 N / m^2
nu = 0.32
rho = 7833.394 kg / m^3
$ cubicmeter_m_steel.dat
ID,NASTRAN,cubicmeter_m_steel
SOL 101
CEND
ECHO = NONE
OUTPUT
DISPLACEMENT(PLOT,REAL) = ALL
OLOAD(PLOT,REAL) = ALL
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 1
LOAD = 1
SPC = 2
BEGIN BULK
PARAM K6ROT100.0000
PARAM POSTEXT YES
$------------------------------------------------------------------------
PARAM UNITSYS N-M
$------------------------------------------------------------------------
GRID* 1 00.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 2 00.0000000000E+000.0000000000E+00+
* 1.0000000000E+00 0
GRID* 3 00.0000000000E+001.0000000000E+00+
* 0.0000000000E+00 0
GRID* 4 00.0000000000E+001.0000000000E+00+
* 1.0000000000E+00 0
GRID* 5 01.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 6 01.0000000000E+000.0000000000E+00+
* 1.0000000000E+00 0
GRID* 7 01.0000000000E+001.0000000000E+00+
* 0.0000000000E+00 0
GRID* 8 01.0000000000E+001.0000000000E+00+
* 1.0000000000E+00 0
CHEXA 1 1 2 1 3 4 6 5+
+ 7 8
PSOLID 1 1 0 SMECH
$------------------------------------------------------------------------
$ MAT1 MID E G NU RHO A TREF GE
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
MAT1 12.068+11 0.3200007833.394
$------------------------------------------------------------------------
$ GRAV SID CID A N1 N2 N3 MB
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
GRAV 1 0 9.80665 0.0000 0.0000-1.00000
SPC 2 1 123456 0.0000
SPC 2 3 123456 0.0000
SPC 2 5 123456 0.0000
SPC 2 7 123456 0.0000
ENDDATA
The results in the .f06 file of executing the previous Nastran bulk data file yields a reaction force in the T3 direction of
T3 = 7.681902E+04
F = m g = W
m = ( 7.681931E+04 N ) / ( 9.80665 m / sec^2 )
m = ( 7.681931E+04 kg m / sec^2 ) / ( 9.80665 m / sec^2 ) = 7833.39 kg
EXAMPLE 3 (lbf-in) - What is the WEIGHT and MASS of 1 cubic meter of steel
4130 Alloy Steel, Tempered, Ultra High Strength
E = 3.00E+7 lbf / in^2
nu = 0.32
rho = 7.324E-4 lbm / in^3
$ cubicmeter_in_steel.dat
ID,NASTRAN,cubicmeter_in_steel
SOL 101
CEND
ECHO = NONE
OUTPUT
DISPLACEMENT(PLOT,REAL) = ALL
OLOAD(PLOT,REAL) = ALL
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 1
LOAD = 1
SPC = 2
BEGIN BULK
PARAM K6ROT100.0000
PARAM POSTEXT YES
$------------------------------------------------------------------------
PARAM UNITSYS LBF-IN
$------------------------------------------------------------------------
GRID* 1 00.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 2 00.0000000000E+000.0000000000E+00+
* 3.9370000000E+01 0
GRID* 3 00.0000000000E+003.9370000000E+01+
* 0.0000000000E+00 0
GRID* 4 00.0000000000E+003.9370000000E+01+
* 3.9370000000E+01 0
GRID* 5 03.9370000000E+010.0000000000E+00+
* 0.0000000000E+00 0
GRID* 6 03.9370000000E+010.0000000000E+00+
* 3.9370000000E+01 0
GRID* 7 03.9370000000E+013.9370000000E+01+
* 0.0000000000E+00 0
GRID* 8 03.9370000000E+013.9370000000E+01+
* 3.9370000000E+01 0
CHEXA 1 1 2 4 8 6 1 3+
+ 7 5
PSOLID 1 1 0 SMECH
$------------------------------------------------------------------------
$ MAT1 MID E G NU RHO A TREF GE
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
MAT1 13.0000+7 0.320000 7.324-4
$------------------------------------------------------------------------
$ GRAV SID CID A N1 N2 N3 MB
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
GRAV 1 0386.0886 0.0000 0.0000-1.00000
SPC 2 1 123456 0.0000
SPC 2 3 123456 0.0000
SPC 2 5 123456 0.0000
SPC 2 7 123456 0.0000
ENDDATA
The results in the .f06 file of executing the previous Nastran bulk data file yields a reaction force in the T3 direction of
T3 = 1.725568E+04
( 1.725568E+04 lbf ) ( 386.08858 lbm in / lbf sec^2 ) / ( 386.08858 in / sec^2 )
= 1.725568E+04 lbm
( 1.725568E+04 lbm ) / ( 2.20462 lbm / kg ) = 7827.1 kg
The difference is round-off.
EXAMPLE 4 (mN-mm) -Femap
File / Import / Analysis Model / Nastran / cubicmeter_mm_steel.dat
T3 = 7.681941E+07
Tools / Mass Properties / Mesh Properties
EXAMPLE 5 (N-m) - Femap
File / Import / Analysis Model / Nastran / cubicmeter_m_steel.dat
T3 = 7.681935E+07
Tools / Mass Properties / Mesh Properties
EXAMPLE 6 (lbf-in) -Femap
File / Import / Analysis Model / Nastran / cubicmeter_in_steel.dat
T3 = 1.725568E+04
Tools / Mass Properties / Mesh Properties
1 g = 9.80665 m / sec^2 (definition)
1 in = 25.4 mm (definition)
1 N = 1 kg m / sec^2 (definition)
1 Pa = 1 N / m^2 (definition)
1 kPa = 1 mN / mm^2 (definition)
F = m g = W (definition)
1 lbf = 1 lbm * 1 g (definition)
1 lbf = 1 lbm * ( 9.80665 m / sec^2 ) ( 1000 mm / m ) ( 1 in / 25.4 mm )
1 lbf = 386.08858 lbm in / sec^2
1 lbf = 32.17405 lbm ft / sec^2
1 lbm = 1 lbf sec^2 / 386.08858 in
1 lbm = 0.0025900 lbf sec^2 / in
1 g = 386.08858 in / sec^2
1 g = 32.17405 ft / sec^2
1 kg = 2.20462 lbm
1 N = 0.22481 lbf
weight density : 1 lbf / in^3
weight density : 1 N / m^3
mass density = ( 1 lbf / in^3 ) / g
mass density = ( 1 lbf / in^3 ) / ( 386.08858 in / sec^2 ) = 0.002590 lbf sec^2 / in^4
mass density = ( 1 N / m^3 ) / g
mass density = ( 1 kg / m^2 sec^2 ) / ( 9.80665 m / sec^2 ) = 0.101972 kg / m^3
EXAMPLE 1 (mN-mm) - What is the WEIGHT and MASS of 1 cubic meter of steel
4130 Alloy Steel, Tempered, Ultra High Strength
E = 2.068428E+11 N / m^2 = 2.068428E+8 kPa = 2.068428E+8 mN / mm^2
nu = 0.32
rho = 7833.394 kg / m^3 = 7.833394E-6 kg / mm^3
$ cubicmeter_mm_steel.dat
ID,NASTRAN,cubicmeter_mm_steel
SOL 101
CEND
ECHO = NONE
OUTPUT
DISPLACEMENT(PLOT,REAL) = ALL
OLOAD(PLOT,REAL) = ALL
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 1
LOAD = 1
SPC = 2
BEGIN BULK
PARAM K6ROT100.0000
PARAM POSTEXT YES
$------------------------------------------------------------------------
PARAM UNITSYS MN-MM
$------------------------------------------------------------------------
GRID* 1 00.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 2 00.0000000000E+000.0000000000E+00+
* 1.0000000000E+03 0
GRID* 3 00.0000000000E+001.0000000000E+03+
* 0.0000000000E+00 0
GRID* 4 00.0000000000E+001.0000000000E+03+
* 1.0000000000E+03 0
GRID* 5 01.0000000000E+030.0000000000E+00+
* 0.0000000000E+00 0
GRID* 6 01.0000000000E+030.0000000000E+00+
* 1.0000000000E+03 0
GRID* 7 01.0000000000E+031.0000000000E+03+
* 0.0000000000E+00 0
GRID* 8 01.0000000000E+031.0000000000E+03+
* 1.0000000000E+03 0
CHEXA 1 1 2 1 3 4 6 5+
+ 7 8
PSOLID 1 1 0 SMECH
$------------------------------------------------------------------------
$ MAT1 MID E G NU RHO A TREF GE
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
MAT1 12.0684+8 0.3200007.8334-6
$------------------------------------------------------------------------
$ GRAV SID CID A N1 N2 N3 MB
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
GRAV 1 0 9806.65 0.0000 0.0000-1.00000
SPC 2 1 123456 0.0000
SPC 2 3 123456 0.0000
SPC 2 5 123456 0.0000
SPC 2 7 123456 0.0000
ENDDATA
The results in the .f06 file of executing the previous Nastran bulk data file yields a reaction force in the T3 direction of
T3 = 7.681902E+07
F = m g = W
m = ( 7.681902E+07 mN ) / ( 9806.65 mm / sec^2 )
m = ( 7.681902E+07 kg mm / sec^2 ) / ( 9806.65 mm / sec^2 ) = 7833.36 kg
EXAMPLE 2 (N-m) - What is the WEIGHT and MASS of 1 cubic meter of steel
4130 Alloy Steel, Tempered, Ultra High Strength
E = 2.068428E+11 N / m^2
nu = 0.32
rho = 7833.394 kg / m^3
$ cubicmeter_m_steel.dat
ID,NASTRAN,cubicmeter_m_steel
SOL 101
CEND
ECHO = NONE
OUTPUT
DISPLACEMENT(PLOT,REAL) = ALL
OLOAD(PLOT,REAL) = ALL
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 1
LOAD = 1
SPC = 2
BEGIN BULK
PARAM K6ROT100.0000
PARAM POSTEXT YES
$------------------------------------------------------------------------
PARAM UNITSYS N-M
$------------------------------------------------------------------------
GRID* 1 00.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 2 00.0000000000E+000.0000000000E+00+
* 1.0000000000E+00 0
GRID* 3 00.0000000000E+001.0000000000E+00+
* 0.0000000000E+00 0
GRID* 4 00.0000000000E+001.0000000000E+00+
* 1.0000000000E+00 0
GRID* 5 01.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 6 01.0000000000E+000.0000000000E+00+
* 1.0000000000E+00 0
GRID* 7 01.0000000000E+001.0000000000E+00+
* 0.0000000000E+00 0
GRID* 8 01.0000000000E+001.0000000000E+00+
* 1.0000000000E+00 0
CHEXA 1 1 2 1 3 4 6 5+
+ 7 8
PSOLID 1 1 0 SMECH
$------------------------------------------------------------------------
$ MAT1 MID E G NU RHO A TREF GE
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
MAT1 12.068+11 0.3200007833.394
$------------------------------------------------------------------------
$ GRAV SID CID A N1 N2 N3 MB
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
GRAV 1 0 9.80665 0.0000 0.0000-1.00000
SPC 2 1 123456 0.0000
SPC 2 3 123456 0.0000
SPC 2 5 123456 0.0000
SPC 2 7 123456 0.0000
ENDDATA
The results in the .f06 file of executing the previous Nastran bulk data file yields a reaction force in the T3 direction of
T3 = 7.681902E+04
F = m g = W
m = ( 7.681931E+04 N ) / ( 9.80665 m / sec^2 )
m = ( 7.681931E+04 kg m / sec^2 ) / ( 9.80665 m / sec^2 ) = 7833.39 kg
EXAMPLE 3 (lbf-in) - What is the WEIGHT and MASS of 1 cubic meter of steel
4130 Alloy Steel, Tempered, Ultra High Strength
E = 3.00E+7 lbf / in^2
nu = 0.32
rho = 7.324E-4 lbm / in^3
$ cubicmeter_in_steel.dat
ID,NASTRAN,cubicmeter_in_steel
SOL 101
CEND
ECHO = NONE
OUTPUT
DISPLACEMENT(PLOT,REAL) = ALL
OLOAD(PLOT,REAL) = ALL
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 1
LOAD = 1
SPC = 2
BEGIN BULK
PARAM K6ROT100.0000
PARAM POSTEXT YES
$------------------------------------------------------------------------
PARAM UNITSYS LBF-IN
$------------------------------------------------------------------------
GRID* 1 00.0000000000E+000.0000000000E+00+
* 0.0000000000E+00 0
GRID* 2 00.0000000000E+000.0000000000E+00+
* 3.9370000000E+01 0
GRID* 3 00.0000000000E+003.9370000000E+01+
* 0.0000000000E+00 0
GRID* 4 00.0000000000E+003.9370000000E+01+
* 3.9370000000E+01 0
GRID* 5 03.9370000000E+010.0000000000E+00+
* 0.0000000000E+00 0
GRID* 6 03.9370000000E+010.0000000000E+00+
* 3.9370000000E+01 0
GRID* 7 03.9370000000E+013.9370000000E+01+
* 0.0000000000E+00 0
GRID* 8 03.9370000000E+013.9370000000E+01+
* 3.9370000000E+01 0
CHEXA 1 1 2 4 8 6 1 3+
+ 7 5
PSOLID 1 1 0 SMECH
$------------------------------------------------------------------------
$ MAT1 MID E G NU RHO A TREF GE
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
MAT1 13.0000+7 0.320000 7.324-4
$------------------------------------------------------------------------
$ GRAV SID CID A N1 N2 N3 MB
$--1---|$--2---|$--3---|$--4---|$--5---|$--6---|$--7---|$--8---|$--9---|$--10--|
GRAV 1 0386.0886 0.0000 0.0000-1.00000
SPC 2 1 123456 0.0000
SPC 2 3 123456 0.0000
SPC 2 5 123456 0.0000
SPC 2 7 123456 0.0000
ENDDATA
The results in the .f06 file of executing the previous Nastran bulk data file yields a reaction force in the T3 direction of
T3 = 1.725568E+04
( 1.725568E+04 lbf ) ( 386.08858 lbm in / lbf sec^2 ) / ( 386.08858 in / sec^2 )
= 1.725568E+04 lbm
( 1.725568E+04 lbm ) / ( 2.20462 lbm / kg ) = 7827.1 kg
The difference is round-off.
EXAMPLE 4 (mN-mm) -Femap
File / Import / Analysis Model / Nastran / cubicmeter_mm_steel.dat
T3 = 7.681941E+07
Tools / Mass Properties / Mesh Properties
EXAMPLE 5 (N-m) - Femap
File / Import / Analysis Model / Nastran / cubicmeter_m_steel.dat
T3 = 7.681935E+07
Tools / Mass Properties / Mesh Properties
EXAMPLE 6 (lbf-in) -Femap
File / Import / Analysis Model / Nastran / cubicmeter_in_steel.dat
T3 = 1.725568E+04
Tools / Mass Properties / Mesh Properties