Static Fatigue Analysis: Linear Superposition of Multiple FEA/Load Time History
Load Cases
When there are several load cases at the same time, all of which vary independently
of one another, the principle of linear superposition will be used to combine all
load cases together to determine the stress variation at each calculation point due
to the combination of all loads. The formula is:(1)
Where is the total number of load cases, and are, respectively, the time variation of the
kth load time history and the total stress tensor, and and are, respectively, the kth load magnitude
and stress tensor from FE analysis.
The following equation depicts how LDM, Scale, and Offset values work together to
scale the FEA stress tensor at time t.(2)
Where:
Results stress tensor at time t
Stress tensor from static analysis
The y point value of load-time history at time t
Transient Fatigue Analysis
During Transient Fatigue Analysis, the load-time history input is not required, as it
is calculated internally during Transient Analysis.
Load Time History Compression
This option is used to save calculation time. It will remove small cycles (defined by
a gate value) and intermediate points.
When removing small cycles, adjacent turning points, where the difference is less
than the maximum range multiplied by relative gate value, will be removed from each
channel. However, phase relationship will be maintained, when peaks and valleys
occur on different channels at different times. This is shown by the sample above.
In the first channel (top), the points at time 4 and 5 will be removed when the
absolute gate equals one, while in the second channel (bottom), the points at time 1
and 2 will not be removed in order to keep the phase relationship between
channels.
Removing intermediate points is another important mechanism to save computation time.
If any point on the load-time history is neither a peak nor valley point, it will
not contribute in determining any stress cycle. Such points could be screened out in
the fatigue computation without losing the accuracy, but the computation time could
be saved significantly. For example, the left column in Figure 2
shows three load-time histories of three super-positioned loadcases, respectively.
After removing the intermediate points, the three load-time histories are obtained
as in the right column, which can produce the same fatigue results as the left
column, but use much less time. This mechanism is built in HyperLife and is effective automatically.