calculation - part 2

calculation methods
Sfere2 can use different calculation methods. Currently there are only two available:
  • The Automated Basic Iterator-method, this is the most advanced of the Basic Iterators. It calculates the deformations as a result of gravity. It regards all joints as non-rigid/hinging, regardless of the settings. The setup of this method is partly automated for ease of use.
  • The Basic Iterator-method, functions just like it's automated cousin (see above). It's setup is done manually.
  • The Test Calculator-method is basically a remnant of the first trials in background calculation. Although it only makes use of the geometry of the frame structure and has a truly strange way of implementing gravity, the resulting deformations can give a reasonable insight into stability of structures. The reason why it is still supplied with Sfere2 is it's simplicity: it has no setup options. It does not store the member stresses.
  • The Velocity Iterator-method, is still under development. It actually incomporates time and speed within the calculation. Although it does function, it's setup and feedback is quite tricky.

To select the calculation method use   Calculate > Method > ...  .
By default the calculation method is set to 'Automated Basic Iterator'.

automated basic iterator setup
The basic iterator method has a number of settings that can be changed. This can be done by opening the 'Calculation Setup Window' using   Calculate > Setup...  .

automated basic iterator settings:
E factor  the factor with which the modulus of elasticity is multiplied before it's used in calculation.
default: 0.1
g  the acceleration of gravity in negative Z-direction
default: 9.81 m/s2
Convergence Factor  see below.


convergence factor
This calculation method uses an iteration to approach a static equilibrium. The iteration uses a factor that causes the iteration to be convergent or divergent. A converging iteration approaches the requested results. A divergent iteration does the opposite: each iteration step, the results are futher away from the expected answer.
The Convergence Factor is used to make sure the iteration converges.
If the factor is too low, the iteration will be very slow and there is even the possibility that the steps the iteration makes are so small, that the computer looses them during round off.
If the factor is too high, the iteration won't converge: the iteration will ajust the used values in the right direction, but it will overshoot it's 'target'. After a number of steps the computer won't be able to handle the ever growing values, and will define them as 'infinite', rendering 'normal' maths incompetent. Resulting in disappearing displaced members.

Apart from convergent and divergent, there is a third state in which the iteration can be: non-convergent alternating. The iteration will jump back and forth around it's target, without converging, resulting in a 'jumping structure'.

By default the convergence factor is set to 'Automatic'. This uses the FactorBase value (default: 2.5) combined with the properties of the stiffest member to set the convergence factor.
  • Increasing the FactorBase will slow down the convergence of the iteration.
  • Decreasing the FactorBase will speedup the iteration but can lead to a non-convergent alternating iteration or even a divergent iteration.

Basic set of rules to setup the iteration:
  • If the iteration is too slow decrease either the EFactor or the FactorBase, together the constitute the biggest infuence on the iteration speed.
  • If the iteration results in jumping displaced members: increase the FactorBase.
  • If the displaced members have disappeared: increase the FactorBase and Reset the calculation; the reset is necessary to reset the infinite displacements to zero.


expected displacements


jumping displacements


disappeared displacements


numerical results
The resulting displacements can be viewed using the Property List. Simply select the joints who's displacements your interested in and select "Add to Property List" (  Tools > Property List > Add Selected  ). This will show the Property List window.

property list
The Property List shows a number of properties of objects. Using the tabs at the top of the window, one can select which type of object should be shown. To see calculation results, select either the 'Member'- or 'Joint'-tab. In the Member list the resulting stresses can be viewed. In the Joint list the displacements can be viewed.

the Property List

By default all columns in the list are sized equally. The size of the columns can be altered dragging the dividers between the property names in the top-line of the list. By dragging the the property names themselves, the order of the columns can be changed.

More properties will be added in future releases.

property list update
The Property List updates itself every three seconds. The programming behind it still needs a lot of optimizing, so on slow systems the List could have a negative impact on program performance. If this is the case, close the list when it's not needed (it can be opened afterwards using   Tools > Property List > Show  )