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Consistent Units
The units used in a model can be specified using the
following command: File>Model
Properties>Geometry>Units...
This defines the symbol for force, length,
mass, time and temperature that will be printed at the top of
the column headings in the LUSAS results output. Specification
of units in this way has no other effect and does not imply any
internal conversion however - the values input to the program
will be used directly as given.
Although LUSAS is unit independent and any
system may be used, it is essential that all data
quantities are specified in a consistent set of units.
For example, if the model dimensions are specified in
millimetres, the elastic modulus must be specified per mm2
and density per mm3. If units are chosen for mass(m),
length(l) and time(t), the measure used for force must
dimensionally correspond with F = m a = ml/t/t.
Using a consistent set of units is essential in dynamic
analyses to obtain meaningful results, it is also necessary when
using some of the new post-processing wizards in Modeller. The
principle behind the "New Model Startup" template is
to make it easy to specify consistent units - although
"other" remains on the form to allow some flexibility
if required.
The standard SI unit system is normally
recommended, i.e. Newton, Metres, Kilograms. This complies
by definition with the equation F=Ma (N = Kg m/sē). If both
sides are divided by 1000, a further set of consistent units
becomes apparent as (kN = T m/sē).
Similarly, multiplying both sides gives (N = T mm/sē).
Any consistent system can be used however. For example:
N, Millimetres, Tonnes
KN, Metres, Tonnes
MN, Metres, kTonnes
Dyne, Gram, Centimetre
Poundal, Pound, Feet
An example of non-standard sets of units would
be (KN, Millimetres, Tonnes), (N, Millimetres, Kg)
One of two simple tests may be used to
determine the consistency of a chosen set of units;
a) A one metre unit cube defined by one plane
strain element and having a Constant Body Force load of 10 m/s2
and corresponding material properties defined in N, m, Kg would
give displacements in metres, stresses in N/m2 and
reactions in N. This would be the base results for later
comparisons.
b) An eigenvalue analysis of a single joint
element of unit mass and stiffness. Frequency should be in Hertz
and would similarly be the base analysis for later comparison.
By changing either of the tests to the
required units, the results can be easily investigated to check
the consistency of the results. For example, to consider whether
N, mm, Tonnes are consistent, the cube would be made 1000 mm in
each direction, the material properties for steel would be 210e3
(N/mm2) and 7800e-12 (Tonnes/mm3).
Poissons' ratio would remain at 0.3 and the acceleration due to
gravity would be 10,000 mm/s2. The results should be
the same as those for the base analysis, but in the chosen
units. So that displacements should be in mm, stresses in N/mm2
and reactions in N.
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