Page 84 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

probabilistic Design analysis • 71
3.1.1 TRADiTionAL (DeTeRMiniSTiC) VeRSUS
PRobAbiLiSTiC DeSign AnALySiS MeThoDS

In traditional deterministic analyses, uncertainties are either ignored or
accounted for by applying conservative assumptions. Uncertainties are
typically ignored if the analyst knows for certain that the input parameter
has no effect on the behavior of the component under investigation. In
this case, only the mean values or some nominal values are used in the
analysis. However, in some situations the influence of uncertainties exists
but is still neglected; for example, the Young’s modulus mentioned ear-
lier or the thermal expansion coefficient, for which the scatter is usually
ignored. Let’s assume that you are performing a thermal analysis and
you want to evaluate the thermal stresses (thermal stresses are directly
proportional to the Young’s modulus as well as to the thermal expansion
coefficient of the material). The equation is:

σ = E α ΔT
therm

If the Young’s modulus alone has a Gaussian distribution with a 5
percent standard deviation, then there is almost a 16 percent chance that
the stresses are more than 5 percent higher than what you would think
they are in a deterministic case. This figure increases if you also take into
account that, typically, the thermal expansion coefficient also follows a
Gaussian distribution.

Probability that the Probability that
thermal stresses the thermal
are more than stresses are more
Random input variables 5% higher than than 10% higher
taken into account expected than expected
Young’s modulus (Gauss-
ian distribution with 5% ~16% ~2.3%
standard deviation)
Young’s modulus and
thermal expansion coef-
ficient (each with Gauss- ~22% ~8%
ian distribution with 5%
standard deviation)

When a conservative assumption is used, this actually tells you that
uncertainty or randomness is involved. Conservative assumptions are usu-
ally expressed in terms of safety factors. Sometimes regulatory bodies