# 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
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 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
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 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
SPCFORCES(PLOT,REAL) = ALL
SUBCASE 1
LABEL = Subcase - Statics 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

SummaryDetails

### Associated Components

Other SOL101 SOL103 SOL105 SOL106 SOL107 SOL108 SOL109 SOL110 SOL111-SOL112 SOL144 SOL145 SOL146 SOL153 SOL159 SOL200 SOL401 SOL402 SOL414 SOL601-SOL701 Superelement