PSI - Issue 60

Amardeepa KCS et al. / Procedia Structural Integrity 60 (2024) 60–74 Amardeepa KCS/ StructuralIntegrity Procedia 00 (2023) 000–000

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The resin or the adhesive layer is modelled using 1D CBAR beam elements with the PBAR property card of NASTRAN. And the 1D CBAR beam element is assigned with isotropic material properties of E=10 GPa, G=5 GPa, and υ=0.35, which is the same as the resin material. The 1D resin or adhesive element is connected with 2D CQUAD4 shell elements through each layer, as shown in Figure 10(a) to (d). The cross-sectional area of these 1D CBAR elements is defined so that the cross-sectional area of 1D CBAR elements and 2D CQUAD4 /CTRIA3 elements connected to these elements is almost the same to obey the mass conservation principle [7]. This is achieved by defining half of the density value to the composite layers and the other half to these CBAR elements. The 2D elements in the curve region are divided into minutes of a standard analogous clock dial (ACD) [6] to represent the number of 1D elements possible in a 1/4 th area of ACD [6], as shown in Figure 10(e).

(a) and (b) 2D CQUD4 elements connected with 1D CBAR element, (c) and (d) 3D view of 2D and 1D elements

(e) Standard analogous clock dial representing the minutes at the curved region of an L angle

Fig. 10. 3D view of the L angle FE model; curved region divided into minutes of a clock

A typical illustration is shown in Figure 11(a) to calculate the cross-sectional area of the 1D CBAR elements that can be defined by choosing either a rectangular or circular cross-section shape conveniently. However, in this study, a rectangular cross-sectional shape is considered. The composite laminate of 12 plies (ply thickness is 0.15mm) is divided into 4 shell layers, each consisting of 3 composite plies with the sequence of [ (+45, -45, 0); (+45, -45, 90); (90, -45, +45); (0, -45, +45)]. A circular patterned 2D elements around the stringer cut-out region is modelled for the ease of capturing radial stress distribution precisely as shown in Figure 11(b). More than 10000 1D CBAR elements are modelled in the standalone FE model of the L angle and numbered in chronological order to quickly identify their precise location across the whole face and thickness direction of the composite laminate.

(a)

(b) Fig. 11. A typical illustration for calculating the 1D CBAR Element cross-section; Force components of the bar elements and zones