An algorithm for fast critical plane search in computer-aided engineering durability analysis under multiaxial random loadings: Application to the Carpinteri–Spagnoli–Vantadori spectral method

This paper presents a new algorithm to implement the Carpinteri–Spagnoli–Vantadori (CSV) multiaxial fatigue criterion for random loading and to shorten the computation time. This goal is achieved after calculating the exact expressions of stress spectral moments in every rotated plane, which allow the maximum variance and expected maximum peak of normal/shear stress to be computed directly. This permits the new algorithm to determine the five rotations of the critical plane without using ‘for/end’ loops (which represent a slow numerical operation), although some information on stress signals examined is lost. Two examples are presented to demonstrate the advantages of the new algorithm in comparison with its standard version, which are particularly remarkable when considering the stress output of all finite element model nodes. The approach behind the new algorithm can be extended to other multiaxial spectral criteria that use angular rotations or direction cosines to locate the critical plane or the direction of maximum stress variance.