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)

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Table 1. Dimensions of the CHS-to-SHS steel welded joints and values of the increased thickness of shell elements at the junction line between the chord and brace mid-surfaces applied in the global shell model. Specimen Number B [mm] T [mm] D [mm] t [mm] z [mm] l br [mm] d br [mm] l ch [mm] d ch [mm] T’ * [mm] t’ ** [mm] T’ ^ [mm] t’ ^^ [mm] TA1 200 10 51 6.3 6.3 11.3 5.5 9.50 5.0 13.2 9.50 14.5 10.8 TA2 200 10 82.5 6.3 6.3 11.3 5.5 9.50 5.0 13.2 9.50 14.5 10.8 TA4 200 10 76 4.5 4.5 9.50 5.0 6.80 3.5 12.3 6.80 13.2 7.70 TA5 200 10 82.5 8.8 8.8 13.8 7.0 13.2 6.5 14.4 13.2 16.2 15.0 TA6 300 12.5 127 8.0 8.0 14.5 7.0 12.0 6.0 16.5 12.0 18.2 13.7 TA7 200 6.3 88.9 4.0 4.0 7.20 3.5 6.00 3.0 8.30 6.00 9.10 6.80 *, ** Increased thickness of shell elements at the chord tube and at the brace tube, respectively (Fig. 3), according to the empirical rule proposed by (Meneghetti and Tovo 2002; Meneghetti 2008). ^, ^^ Increased thickness of shell elements at the chord tube and at the brace tube, respectively (Fig. 3), according to the empirical rule proposed by (Eriksson and Lignell 2003). • STEP 1 – Global Shell Model : A global model was defined based on the mid-surface geometry of the tubular components and discretized using 8-node shell elements (SHELL281 of Ansys® FE library) according to Fig. 3. This modelling approach requires the mid-surfaces of the tubes to be connected at the junction line and is a standard practice in industrial applications. The influence of the weld bead stiffness was incorporated by locally increasing the thickness of shell elements, following two different procedures, i.e. (i) the empirical rule proposed by (Meneghetti and Tovo 2002; Meneghetti 2008), as sketched in Fig. 1c, which is based on a local thickness increase equal to 0.5∙z , and (ii) the empirical rule sketched in Fig 1d, being based on a local thickness increase equal to s = z√2/2 ≈ 0.7∙z. The reader is referred to reference (Eriksson and Lignell 2003) quoted in (Echer and Marczak 2015). In both procedures, the reinforced shell region must originate from the junction line of the shell mid-surfaces and extend up to the projections of the weld toe at the brace side and the weld toe at the chord side, respectively, i.e. l br = T/2+z and l ch = t/2+z (see Fig. 1c-1d). The FE sizes reported in Table 1 for the chord and brace tubes allowed to rapidly generate the reinforced shell regions with good approximation by directly increasing the thickness of two adjacent rows of shell finite elements originating from the junction line (see Fig. 3), therefore avoiding the geometrical modeling of dedicated areas corresponding rigorously to the reinforced shell regions. Such an approach ultimately resulted in non-uniform regions of shell elements with increased thickness (see Fig 3); however, a negligible difference was observed in terms of the resulting displacement field as compared to the displacement field calculated by adopting the dedicated geometrical areas just mentioned. • STEP 2 – Solid Submodel : A solid submodel was extracted from the global solid geometry by cutting a disk-shaped volume from the chord tube in the proximity of the weld bead; on the other hand, the brace tube was cut by means of a plane orthogonal to its axis (see Fig. 3). The size of the cut boundary region was chosen by assuming a distance between the weld toes and the cut boundary surfaces equal to D CB = 4∙ max [t, T] (see Fig. 3). The solid submodel included the actual geometry of the weld toes at the chord and brace side, which were represented as sharp V-notches with an opening angle of 135°. A solid free mesh of 10-node tetrahedral finite elements (SOLID187 of Ansys® element library) was generated by adopting a global FE size d = t (see Fig. 3), in compliance with PSM requirements (see (Meneghetti and Campagnolo 2020)) since only a local mode I stress state is expected at the weld toe due to the external axial loading. The displacements computed in the global shell model at the intersection lines of the mid-surface and the cutting surfaces were transferred to the corresponding nodal locations within the submodel with respect to the mid-thickness (also shown in Fig. 3). These locations define the so-called cut boundaries , which ensure kinematic compatibility between the two models, i.e. the global shell model and the solid submodel. This shell-to-solid displacements mapping is enabled by the submodelling functionality available in Ansys® Workbench/Mechanical, as further described in STEP 3. • STEP 3 – Cut Boundary Interpolation : the procedure available in Ansys® Workbench was exploited for performing cut boundary interpolation. It is essential that both the global shell model and the solid submodel share the same global coordinate system to ensure successful mapping (see Fig. 3). Then, the Solution cell of the global shell model’s Static Structural analysis was connected to the Setup cell of the solid submodel’s Static Structural The workflow to apply the PSM in conjunction with shell FE models was implemented within the Ansys® Workbench/Mechanical software environment and is structured as follows: