PSI - Issue 39

O.N. Belova et al. / Procedia Structural Integrity 39 (2022) 761–769 Author name / Structural Integrity Procedia 00 (2021) 000–000

766

6

Fig. 4. Fringe skeletons - fringe thinned images for 80 kg (left) and 90 kg (right).

Fig. 5. Fringe skeletons - fringe thinned images for 95 kg (left) and 100 kg (right).

3. The classical over-deterministic method and the Broyden – Fletcher – Goldfarb – Shanno algorithm Eqs. (1) and (2) give us an over-deterministic system of linear equations in terms of the unknown parameters l k a . The common approach is based on the over-deterministic method (Ramesh et al. (1997), Malikova and Vesely (2014), Vivekanandan and Ramesh (2019), Jobin et al. (2020), Hou et al. (2021), Patil et al. (2017), Li and Zheng (2021)). Thus, the classical over-deterministic method for the determination of the Williams series expansion is applied. It is worth noting that here the over-deterministic method in the form based on the stress field is used. According to numerous computational experiments performed one can conclude that this form relying on the stress field has indisputable advantages compared to the classical over-deterministic method based on the displacement field (Stepanova (2020), Stepanova (2021)). This advantage is elucidated by the simplicity of the approach because it is not necessary to exclude the displacements of the rigid body from the analysis. Along with the conventional over deterministic method the Broyden – Fletcher – Goldfarb – Shanno (BFGS) algorithm which is an iterative method for solving nonlinear optimization problems has been used. The BFGS method is regarded as the most popular and efficient quasi-Newton algorithm. The algorithm was realized by the use of package scipy.optimize of Python. SciPy