A probabilistic model for the fatigue reliability of structures under random loadings with phase shift effects

A probabilistic model is proposed for the high-cycle fatigue reliability of structures subject to multiaxial Gaussian random loadings with non-zero means. It is based on the Sines’criterion combined with an oriented prismatic hull approach for its equivalent shear stress amplitude J2,a in order to account for possible phase shifts between stresses involves in these loadings. The extreme value distributions along the founded directions are efficiently assessed in the frequency domain, from which we formulate the distribution of J2,a. This allows assessing the fatigue reliability of 3D structures. The complete methodology is illustrated by a didactic example and on a realistic problem having a wide-band power spectral density field of stresses.