PSI - Issue 68

Gül Demirer et al. / Procedia Structural Integrity 68 (2025) 190–196 G. Demirer and A. Kayran / Procedia Structural Integrity 00 (2024) 000–000

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2.3. Pixelated finite element method

The pixelated finite element (FE) method is designed to capture the as-manufactured behavior of composite panels by determining whether the centroid of each element resides within a defective region or a regular composite area. The defect distribution identified in Section 2.2 is mapped onto the FE mesh, as illustrated in Fig. 3. For each layer, the centroid of each element is evaluated to check for the presence of gaps or overlaps. Elements whose centroids fall within a gap region are assigned properties corresponding to the resin. Conversely, if the centroid is located within an overlap region, the thickness of that element is e ff ectively doubled to account for the additional material.

Fig. 3. (a) Gap and (b) overlap distribution for a [ + < 27 | 46 | 27 > ] lamina mapped on the FE mesh

2.4. Defect layer method

The defect layer method characterizes the change in properties of each layer by accounting for the defect area percentage. For gap-modified defect layers, the elastic properties are reduced while the thickness remains consistent with that of a regular composite layer. The procedure described in Fayazbakhsh (2013) is followed to establish a relation between the elastic properties and the gap area percentage. The gap area percentage is calculated for each finite element in every layer, and the corresponding modified elastic property values are assigned to those elements. In the case of overlap-modified defect layers, the elastic properties remain unchanged; however, the thickness of each element in the layer is increased in proportion to the overlap area percentage calculated for that finite element.

3. Results and discussion

First, a linear buckling analysis is performed in Abaqus, followed by a non-linear buckling analysis to obtain the load-displacement relationship using the Riks method, with an imposed imperfection of 10%. Fig. 4 shows the buckling mode shapes of the baseline [45 | 0 | − 45 | 90] 2 s laminate and optimized [ ± < 27 | 46 | 27 > ] 4 s VS laminate without accounting for the existence of defects. The colorbar labels apply to both laminates, highlighting the enhancement in buckling performance achieved through the implementation of curvilinear fiber paths. Fig. 5 presents the load-displacement response of the defective models for di ff erent mesh densities. It is evident that mesh dependency is more significant in the analysis of panels with gaps than those with overlaps. The pixelation method encounters convergence issues when capturing the e ff ects of gaps, whereas the defect layer method demon strates good convergence for both gaps and overlaps without requiring a high element count. Consequently, the model employing the defect layer method with 640 elements is chosen to present the results shown in Fig. 6 and Table 1.