Page 109 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

96 • using ansys for finite eLement anaLysis
3.4 ProBaBiListiC design teChniques

The Monte Carlo Simulation method is the most common and traditional
method for a probabilistic analysis. This method lets you simulate how
virtual components behave the way they are built. One simulation loop
represents one manufactured component that is subjected to a particular
set of loads and boundary conditions. For Monte Carlo simulations, you
can employ either the Direct Sampling method or the Latin Hypercube
Sampling method.
When you manufacture a component, you can measure its geometry
and all of its material properties (although typically, the latter is not done
because this can destroy the component). In the same sense, if you started
operating the component then you could measure the loads it is subjected
to. Again, to actually measure the loads is very often impractical. But the
bottom line is that once you have a component in your hand and start
using it, then all the input parameters have very specific values that you
could actually measure. With the next component you manufacture you
can do the same; if you compared the parameters of that part with the pre-
vious part, you would find that they vary slightly. This comparison of one
component to the next illustrates the scatter of the input parameters. The
Monte Carlo Simulation techniques mimic this process. With this method
you “virtually” manufacture and operate components or parts one after
the other.
The advantages of the Monte Carlo Simulation method are:

• The method is always applicable regardless of the physical effect
modeled in a finite element analysis. It not based on assump-
tions related to the RPs that if satisfied would speed things up
and if violated would invalidate the results of the probabilistic
analysis. Assuming the deterministic model is correct and a very
large number of simulation loops are performed, then Monte
Carlo techniques always provide correct probabilistic results.
Of course, it is not feasible to run an infinite number of simu-
lation loops; therefore, the only assumption here is that the lim-
ited number of simulation loops is statistically representative
and sufficient for the probabilistic results that are evaluated. This
assumption can be verified using the confidence limits, which the
PDS also provides.
• Because of the reason mentioned previously, Monte Carlo simula-
tions are the only probabilistic methods suitable for benchmarking
and validation purposes.