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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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