Engineering components and structures are often subjected to in-service multiaxial random stresses. The available multiaxial fatigue criteria are typically formulated in time-domain, as step-by-step algorithms applied to simulated or measured stress time-histories. However, time-domain criteria may become computationally demanding and thus impractical with the extremely long analysis times required for processing multiaxial histories with many sample points. This issue can be even more critical for random stress histories simulated in finely discretized or three-dimensional finite element models having hundreds of thousands of nodes, or when processing very long stress histories samples.
Frequency-based multiaxial criteria (often known as spectral methods) have progressively been developed as valid alternative tools, as they are able to drastically reduce the overall computational time, while still providing high levels of accuracy. In frequency-based approaches the statistical properties of multiaxial random stresses are characterized by a Power Spectral Density (PSD) matrix in the frequency-domain and analytical expressions are used to estimate fatigue damage and life directly from the frequency spectrum.
This paper aims to present an application of a frequency-based multiaxial criterion, called “Projection-by-Projection” (PbP) approach, suitable for vibration multiaxial fatigue analysis. The proposed criterion is particularly useful for the durability assessment of complex structures under random input loadings, as those studied by finite element spectrum analysis. Advantages of the PbP method has already been discussed for time-domain [1,2], as well as for frequency-domain applications .
An L-shaped steel beam excited by a random input acceleration has been analyzed as an illustrative example. The L-beam has a hole and two lateral notches, and it is clamped at both ends. Shell elements are used to discretize the structure. A spectrum analysis is first used to compute the stress PSD matrix at every node in the structure. Then, the local multiaxial fatigue damage is estimated by the proposed PbP criterion. MatLab routines have been used to post-process nodal PSD matrix obtained by Ansys. Calculations have been performed on a standard workstation.