Page 106 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

probabilistic Design analysis • 93
3.3.3 No dAtA

In situations where no information is available, there is never just one
right answer. Below are hints about which physical quantities are usually
described in terms of which distribution functions. This might help you
with the particular physical quantity you have in mind. Also below is a list
of which distribution functions are usually used for which kind of phenom-
ena. Keep in mind that you might need to choose from multiple options.

3.3.3.1 geometric Tolerances

• If you are designing a prototype, you could assume that the actual
dimensions of the manufactured parts would be somewhere within
the manufacturing tolerances. In this case it is reasonable to use a
uniform distribution, where the tolerance bounds provide the lower
and upper limits of the distribution function.
• Sometimes the manufacturing process generates a skewed distri-
bution; for example, one half of the tolerance band is more likely
to be hit than the other half. This is often the case if missing half
of the tolerance band means that rework is necessary, while falling
outside the tolerance band on the other side would lead to the part
being scrapped. In this case a Beta distribution is more appropriate.
• Often a Gaussian distribution is used. The fact that the normal distribu-
tion has no bounds (it spans minus infinity to infinity) is theoretically
a severe violation of the fact that geometrical extensions are described
by finite positive numbers only. However, in practice this is irrelevant
if the standard deviation is very small compared to the value of the
geometric extension, as is typically true for geometric tolerances.

3.3.3.2 Material Data

• Very often the scatter of material data is described by a Gaussian
distribution.
• In some cases the material strength of a part is governed by the
“weakest-link-theory.” The “weakest-link-theory” assumes that
the entire part would fail whenever its weakest spot would fail.
For material properties where the “weakest-link” assumptions are
valid, then the Weibull distribution might be applicable.
• For some cases, it is acceptable to use the scatter information from
a similar material type. Let’s assume that you know that a material
type very similar to the one you are using has a certain material
property with a Gaussian distribution and a standard deviation of