PSI - Issue 75

Alberto Visentin et al. / Procedia Structural Integrity 75 (2025) 593–601 Alberto Visentin, Alberto Campagnolo,Vittorio Babini, Giovanni Meneghetti/ Structural Integrity Procedia (2025)

599

7

Two different global shell models were generated, referred as Model 2 and Model 3 (see Table 2), which implement the empirical rules to increase the thickness of shell elements locally at the brace-to-chord junction line according to (Meneghetti and Tovo 2002; Meneghetti 2008) and (Eriksson and Lignell 2003), respectively. For each joint configuration, the solid submodels were constructed as described in STEP 2 (Paragraph 2). As prescribed in STEP 3 (Paragraph 2), the displacements at the cut boundaries resulting from the global shell model were mapped to the solid submodel by taking advantage of the procedure available in Ansys® Workbench/Mechanical (see Fig. 3). After solving each solid submodel, the PSM has been applied to the brace-side and chord-side weld toes. Table 2 provides a comparison between the equivalent peak stress values calculated at point “P” (Fig.2) coming from the three adopted models. A fair agreement was observed between the equivalent peak stress results coming from Model 1 and Model 2, with percent deviations ranging between ~10% and ~15% (see Table 2). A better adherence was observed between the equivalent peak stress results coming from Model 1 and Model 3, the percent deviations being below 10% in all considered cases. Regardless of the considered analysis strategy, a good agreement can be appreciated between experimental fatigue data in Table 2, re-evaluated in terms of the equivalent peak stress, and the PSM-based fatigue design scatter band for pure mode I local stress (see Fig. 4). Table 2. Experimental fatigue results by (Gandhi and Berge 1998) re-evaluated according to the PSM; comparison between the equivalent peak stress results obtained by adopting the procedure for solid models (Fig. 2) and the equivalent peak stress results obtained by adopting the procedure for shell models (Fig. 3). Specimen Number ∆σ nom [mm] * Retest (see (Gandhi and Berge 1998)) ^ Percentual deviation between the maximum equivalent peak stress values calculated at critical node “P” with Model 1 and Model 2, respectively. ° Percentual deviation between the maximum equivalent peak stress values calculated at critical node “P” with Model 1 and Model 3, respectively. + 10-node tetrahedral elements = 3 dof/node; 8-node shell elements = 5 dof/node. It is worth noting that all FE analyses were performed on a machine having a Intel® Core® i7-1255U CPU and 32 GB RAM. Table 2 also reports the time required to solve all FE models. The solution time of the linear elastic FE analysis is reported in the case of Model 1; concerning Model 2 and Model 3, on the other hand, the solution time of both the global shell model (see (a)) and the solid submodel (see (b)) have been reported. The ratio between the total time required to complete the analysis procedure for Model 2 and Model 3 and the time required for linear elastic FE solution of Model 1 ranges between 0.10 and 0.50, effectively proving that a noticeable advantage can be achieved by adopting the proposed shell-to-solid analysis procedure, especially when large FE models are involved (see, for instance, the case of specimen “TA7” in Table 2). Moreover, a reduction factor in the range between 16 and 30 was observed between the total number of DOFs associated to Model 1 and the total number of DOFs associated to the solid submodels relevant to Model 2 and Model 3 (also in Fig. 2 and Fig. 3). As a final remark, it should be noted that the stiffness contribution due to the weld bead has been accounted here by locally increasing the thickness of shell elements according to the empirical rules proposed by (Meneghetti and Tovo 2002; Meneghetti 2008), i.e. a local thickness increase equal to 0.5∙z , and by (Eriksson and Lignell 2003), i.e. a local thickness increase equal to 0 .7∙z . Such rules should be furtherly validated in the case of welded structures subjected to a general multiaxial loading condition, i.e. generating a mixed mode I+II+III stress state at the weld toe and weld root. Moreover, a dedicated calibration could be performed in order to find the optimal value of the coefficient linking the shell thickness increase to the weld leg length z, which has been assumed here equal to either 0.5 (Meneghetti and Tovo 2002; Meneghetti 2008) or 0.7 (Eriksson and Lignell 2003). N init (∙10 5 ) [cycles] Global solid model Model 1 (Fig. 2) Global shell model (a) Solid submodel (b) Model 2 (see Fig. 3) Global shell model (a) Solid submodel (b) Model 3 (see Fig. 3) ∆σ eq,peak [MPa] Solution time [s] DOFs (∙10 5 ) + 5.55 5.76 15.20 2.80 5.52 15.05 5.55 ∆σ eq,peak [MPa] ∆ % ^ [%] 10.7 15.7 11.9 12.9 15.4 12.5 10.7 Solution time [s] DOFs (∙10 5 ) + ∆σ eq,peak [MPa] ∆ % ° [%] Solution time [s] 10(a)+4(b) 12(a)+4(b) 24(a)+5(b) 7(a)+4(b) 12(a)+4(b) 42(a)+5(b) 10(a)+4(b) DOFs (∙10 5 ) + TA1 TA2 TA4 TA5 TA6 TA7 TA1 * 33.20 32.18 49.58 18.91 29.58 15.37 33.20 0.25 586.8 697.2 775.3 577.6 891.3 547.3 586.8 61 71 83 21 53 649.6 806.4 867.5 651.9 1028.9 615.7 649.6 10(a)+4(b) 12(a)+4(b) 24(a)+5(b) 7(a)+4(b) 12(a)+4(b) 42(a)+5(b) 10(a)+4(b) 1.95(a)+0.19(b) 2.14(a)+0.28(b) 3.94(a)+0.62(b) 1.29(a)+0.14(b) 2.26(a)+0.33(b) 6.14(a)+0.49(b) 1.95(a)+0.19(b) 603.9 750.1 812.9 592.8 956.3 577.4 603.9 2.9 7.6 4.8 2.6 7.3 5.5 2.9 1.95(a)+0.19(b) 2.14(a)+0.28(b) 3.94(a)+0.62(b) 1.29(a)+0.14(b) 2.26(a)+0.33(b) 6.14(a)+0.49(b) 1.95(a)+0.19(b) - 0.32 0.75 0.3 - 355 0.40 61