Page 83 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

70 • using ansys for finite eLement anaLysis
standard deviation of ±3–5 percent. Likewise, the geometric properties
of components can only be reproduced within certain manufacturing tol-
erances. The same variation holds true for the loads that are applied to a
finite element model. However, in this case the uncertainty is often due to
a lack of engineering knowledge. For example, at elevated temperatures
the heat transfer coefficients are very important in a thermal analysis, yet it
is almost impossible to measure the heat transfer coefficients. This means
that almost all input parameters used in a finite element analysis are inex-
act, each associated with some degree of uncertainty.
It is neither physically possible nor financially feasible to eliminate
the scatter of input parameters completely. The reduction of scatter is typ-
ically associated with higher costs either through better and more precise
manufacturing methods and processes or increased efforts in quality con-
trol; hence, accepting the existence of scatter and dealing with it rather
than trying to eliminate it makes products more affordable and production
of those products more cost-effective.
To deal with uncertainties and scatter, you can use the ANSYS Proba-
bilistic Design System (PDS) to answer the following questions:

• If the input variables of a finite element model are subjected to scat-
ter, how large is the scatter of the output parameters? How robust
are the output parameters? Here, output parameters can be any
parameter that ANSYS can calculate. Examples are the tempera-
ture, stress, strain, or deflection at a node, the maximum tempera-
ture, stress, strain, or deflection of the model, and so on.
• If the output is subjected to scatter due to the variation of the input
variables, then what is the probability that a design criterion given
for the output parameters is no longer met? How large is the prob-
ability that an unexpected and unwanted event takes place (what is
the failure probability)?
• Which input variables contribute the most to the scatter of an output
parameter and to the failure probability? What are the sensitivities
of the output parameter with respect to the input variables?

Probabilistic design can be used to determine the effect of one or
more variables on the outcome of the analysis. In addition to the prob-
abilistic design techniques available, the ANSYS program offers a set of
strategic tools that can be used to enhance the efficiency of the probabi-
listic design process. For example, you can graph the effects of one input
variable versus an output parameter, and you can easily add more samples
and additional analysis loops to refine your analysis.