Load History Overview

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:

Figure 1.

σ_{i j} (t) = \sum_{k = 1}^{n} (\frac{σ_{i j, k}}{P_{F E A, k}} P_{k} (t))

$σ_{i j} (t) = \sum_{k = 1}^{n} (\frac{σ_{i j, k}}{P_{F E A, k}} P_{k} (t))$

Where $n$ $n$ is the total number of load cases, $P_{k} (t)$ $P_{k} (t)$ and $σ_{i j} (t)$ $σ_{i j} (t)$ are, respectively, the time variation of the k^th load time history and the total stress tensor, and $P_{F E A, k}$ $P_{F E A, k}$ and $σ_{i j} (t)$ $σ_{i j} (t)$ are, respectively, the k^th 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.

Figure 2.

σ_{i j} (t) = \frac{σ_{i j . F E A}}{L D M} (P (t) S c a l e + O f f s e t)

$σ_{i j} (t) = \frac{σ_{i j . F E A}}{L D M} (P (t) S c a l e + O f f s e t)$

Where:

$σ_{i j} (t)$ $σ_{i j} (t)$: Results stress tensor at time t
$σ_{i j . F E A}$ $σ_{i j . F E A}$: Stress tensor from static analysis
$P (t)$ $P (t)$: The y point value of load-time history at time t