# Load History Overview

## Static Fatigue Analysis: Linear Superposition of Multiple FEA/Load Time History Load Cases

Where
$n$
is the total number of load cases,
${P}_{k}\left(t\right)$
and
${\sigma}_{ij}\left(t\right)$
are, respectively, the time variation of the
k^{th} load time history and the total stress tensor, and
${P}_{FEA,k}$
and
${\sigma}_{ij}\left(t\right)$
are, respectively, the k^{th} load magnitude
and stress tensor from FE analysis.

- ${\sigma}_{ij}(t)$
- Results stress tensor at time t
- ${\sigma}_{ij.FEA}$
- Stress tensor from static analysis
- $P(t)$
- 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

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.