Fatigue sensitivity analysis using complex variable methods

The sensitivity of the computed cycles-to-failure and other lifing estimates to the various input parameters is a valuable, yet largely unexploited, aspect of a fatigue lifing analysis. Two complex variable sensitivity methods, complex Taylor series expansion (CTSE) and Fourier differentiation (FD), are adapted and applied to fatigue analysis through the development of a complex variable fatigue analysis software (CVGROW). The software computes the cycles-to-failure and the sensitivities of the computed cycles-to-failure with respect to parameters of interest such as the initial crack size, material properties, geometry, and loading. The complex variable methods are shown to have advantages over traditional numerical differentiation in that more accurate and stable first and second order derivatives are obtained using CTSE and more accurate and stable higher order derivatives are obtained using FD.

► Sensitivities of fatigue lifing algorithms are computed using complex variables.
► Fatigue quantities (cycles-to-failure, crack size, crack growth parameters are complex variables.
► The desired derivative is carried in the imaginary component.
► Accuracy is superior to standard finite differencing.