Page 107 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

94 • using ansys for finite eLement anaLysis
±5 percent around the measured mean value; then let’s assume that
for the material type you are using, you only know its mean value.
In this case, you could consider using a Gaussian distribution with
a standard deviation of ±5 percent around the given mean value.
• For temperature-dependent materials it is prudent to describe the
randomness by separating the temperature dependency from the
scatter effect. In this case, you need the mean values of your mate-
rial property as a function of temperature in the same way that you
need this information to perform a deterministic analysis. If M(T)
denotes an arbitrary temperature-dependent material property then
the following approaches are commonly used:
Multiplication equation:

MT () = C M
rand rand T ()
Additive equation:

MT () = M + ∆ M
rand T () rand
Linear equation:

MT () = C M + ∆ M
rand rand T () rand
• Here, M(T ) denotes the mean value of the material property as a
function of temperature. In the “multiplication equation” the mean
value function is scaled with a coefficient C and this coefficient is
rand
a random variable describing the scatter of the material property. In
the “additive equation” a random variable ∆M is added on top of
rand
the mean value function M(T ). The “linear equation” combines both
approaches and here both C rand and ∆M are random variables. How-
rand
ever, you should take into account that in general for the “linear equa-
tion” approach C rand and ∆M rand are, correlated.
• Deciding which of these approaches is most suitable to describe
the scatter of the temperature-dependent material property requires
that you have some raw data about this material property. Only by
reviewing the raw data and plotting it versus temperature you can
tell which approach is the better one.

3.3.3.3 Load Data

• For loads, you usually only have a nominal or average value. You
could ask the person who provided the nominal value the following