Developed in 1985, the Dirlik method provides an empirical closed-form expression for the PDF of stress amplitudes that works for both narrow and wide-band signals. It is currently the most widely used method in commercial FEA software (nCode, FE-Safe, ANSYS).
The Dirlik PDF is a combination of an exponential distribution and two Rayleigh distributions: $$ p(S) = \fracD_1Q e^-\fracZQ + \fracD_2 ZR^2 e^-\fracZ^22R^2 + D_3 Z e^-\fracZ^22 $$
Where $Z = S / \sqrt\lambda_0$ (normalized stress amplitude) and $D_1, D_2, D_3, Q, R$ vibration fatigue by spectral methods pdf
For a stationary random stress process ( \sigma(t) ), the one-sided PSD ( W(f) ) (units: ( \textMPa^2/\textHz )) satisfies:
[ E[\sigma^2] = \int_0^\infty W(f) df ]
Once the PDF of stress ranges $p(S)$ is obtained, damage is calculated using the Palmgren-Miner linear damage rule combined with the material S-N curve (Basquin’s equation: $N S^k = C$).
The expected fatigue life $T$ is calculated as: Developed in 1985, the Dirlik method provides an
$$E[D] = T \int_0^\infty \fracp(S) \cdot v_pN(S) ds$$
Where $v_p$ is the rate of peaks and $N(S)$ is the number of cycles to failure at stress range $S$. For a stationary random stress process ( \sigma(t)