PSI - Issue 68

Morteza Khomami Abadi et al. / Procedia Structural Integrity 68 (2025) 1312–1318 Morteza Khomami Abadi et al. / Structural Integrity Procedia 00 (2025) 000–000

1317

6

Fig. 3. Validation of GMDH stress intensity factor results and Kumar results for a cracked beam under bending moment In this paper, in addition to proposing a new method for extracting the stress intensity factors in beams, a neural network method was developed to determine the stress intensity factors in single-edge and central cracked plates, etc., and it is validated with Kumar results according to Tables 3, 4. The tensile stress is considered 50 MPa. Table 3. Validation of stress intensity factors of single-edge cracked plate. / FEM (Abaqus) Analytical [Kumar] GMDH Error (%) ( GMDH & Analytical ) Error (%) ( FEM & Analytical ) 0.25 5.84E+07 5.70E+07 5.89E+07 3.35 2.45 0.4 1.03E+08 1.00E+08 1.05E+08 4.51 3.21 0.5 1.64E+08 1.58E+08 1.67E+08 5.56 3.67 0.7 3.94E+08 3.76E+08 4.03E+08 7.18 4.78 Table 4. Validation of stress intensity factors of center cracked plate. / FEM (Abaqus) Analytical [Kumar] GMDH Error (%) ( GMDH & Analytical ) Error (%) ( FEM & Analytical ) 0.25 2.77E+07 2.73E+07 2.81E+07 2.93 1.47 0.4 3.86E+07 3.72E+07 3.87E+07 4.03 3.76 0.5 4.88E+07 4.65E+07 4.95E+07 6.45 4.95 0.7 7.02E+07 6.63E+07 7.19E+07 8.40 5.88 The results show that the maximum error of GMDH neural network is about 8.40% in center cracked plate a/W=0.7, which is acceptable compared to the errors of the finite element method, which is reported to be about 5.88%. 4.2. Results of new solution for determining stress intensity factors One of the fundamental problems of conventional methods of determining stress intensity factors is the limitation of crack length, type of loading and boundary conditions. In this section, the stress intensity factor for a beam under transverse load with simply supported, which are not similar to that presented in other references, are extracted and the efficiency of the GMDH algorithm for is measured by changing the crack depth in Fig. 4.

Fig. 4. Stress intensity factors of SS-SS beam by GMDH neural network