An efficient algorithm for critical plane search in random multiaxial fatigue based on maximum variance method, 3D matrices and Hadamard’s element-wise product

The numerical algorithms to search for the critical plane in multiaxial random loading by the Maximum Variance Method are discussed. The classical Direct Method using three nested ‘for/end’ loops, and its improved variant based on the eigenvalues/eigenvectors of the shear stress covariant matrix, are summarised from the literature. A faster variant of the Direct Method, which exploits the search for the maximum of a one-dimensional array, is developed. An innovative method that makes use of three-dimensional matrices and Hadamard’s element-wise product is also presented. The algorithm structures are illustrated, and their computation time compared in a numerical case study.