Page 82 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

ChaPter 3

Probabilistic Design

analysis

3.1 ProBaBiListiC design

Probabilistic design is an analysis technique for assessing the effect of
uncertain input parameters and assumptions on your model. A probabilis-
tic analysis allows you to determine the extent to which uncertainties in
the model affect the results of a finite element analysis. An uncertainty (or
random quantity) is a parameter whose value is impossible to determine
at a given point in time (if it is time-dependent) or at a given location (if
it is location-dependent). An example is ambient temperature; you can-
not know precisely what the temperature will be one week from now in
a given city. In a probabilistic analysis, statistical distribution functions
(such as the Gaussian or normal distribution, the uniform distribution,
etc.) describe uncertain parameters.
Computer models are expressed and described with specific numer-
ical and deterministic values; material properties are entered using cer-
tain values, the geometry of the component is assigned a certain length or
width, and so on. An analysis based on a given set of specific numbers and
values is called a deterministic analysis. Naturally, the results of a deter-
ministic analysis are only as good as the assumptions and input values
used for the analysis. The validity of those results depends on how correct
the values were for the component under real-life conditions.
In reality, every aspect of an analysis model is subjected to scatter
(in other words, is uncertain in some way). Material property values are
different if one specimen is compared to the next. This kind of scatter
is inherent for materials and varies among different material types and
material properties. For example, the scatter of the Young’s modulus for
many materials can often be described as a Gaussian distribution with