PSI - Issue 75

Thomas Constant et al. / Procedia Structural Integrity 75 (2025) 660–676 Author name / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 1. Initial Design of Experiments with n c cut points and associated Hyperplanes in two-dimensional space.

• if σ 2 , x ∗ B ) related to the critical configuration, and with the projected points (¯ x A 2 , x ∗ B ) , . . . , (¯ x A nc , x ∗ B ) related to non-critical configurations. Moreover, D A is enriched with the point ( x ∗ A 1 , ¯ x B ). The computational cost is c A + ( n c + 1) c B . • otherwise, if σ 2 ˜ d A 1 ( x ∗ A 1 ) < σ 2 ˜ d B ( x ∗ B ), the imputation is performed. Then the enrichment consists of the projected point (¯ x A 1 , x ∗ B ), and also of the points (¯ x A 2 , x ∗ B ) , . . . , (¯ x A nc , x ∗ B ), related to non-critical configuration. D B is also enriched with the point (¯ x A 1 , x ∗ B ). In this case, the computational cost become n c c B . ˜ d A 1 ( x ∗ A 1 ) ≥ σ 2 ˜ d B ( x ∗ B ), the imputation is not possible. Then D is enriched with the point ( x ∗ A 1

4. Validation and Discussion

The fatigue reliability of a bracket, see Figure 3, is considered for highlighting the potential of the proposed approach. The simulation chain starts with a finite element (FE) modal superposition analysis on Abaqus (model m A , see equation 7), followed by a multiaxial critical plane fatigue analysis using fe-safe in the folded area of the bracket (model m B , see algorithm 1). The respective CPU times for m A and m B are approximately 59.451 seconds and 0.181 seconds, measured on an Intel ® Core TM i7-9850H CPU at 2.6 GHz with 32 GB of RAM. This results in a computational cost ratio of c A c B ≈ 329. The excitation applied at the base of the bracket consists of a time-dependent rotational acceleration a R z ( t ) about the z -axis, applied over a duration of 0.4 seconds. This time serie is assumed to exhibit random amplitude variability, characterized by a random coe ffi cient C R z . A set of n c = 4 load configurations is here considered, resulting in four levels of amplification of the rotational acceleration, see table 1 . Each configuration c is characterized by a random