PSI - Issue 52

Haolin Li et al. / Procedia Structural Integrity 52 (2024) 752–761 HaolinLi / Structural Integrity Procedia 00 (2023) 000–000

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4. Results

Two case studies are carried out by the proposed approach, one for a perforated plate structure and other for a single-layer woven composites. The obtained results are compared to the FEM results for verification. Both the two structures are applied with the six plate periodic boundary conditions (PBCs), stated as: • PBC. 1: ¯ ε = 0 . 01 0 0 0 , ϕ = 0 • PBC. 2: ¯ ε = 0 0 0 0 . 01 , ϕ = 0 • PBC. 3: ε = 0 0 . 01 0 . 01 0 , ϕ = 0 • PBC. 4: ε = 0 , ϕ = 0 . 01 0 0 0 • PBC. 5: ε = 0 , ϕ = 0 0 0 0 . 01 • PBC. 6: ε = 0 , ϕ = 0 0 . 01 0 . 01 0 The first three PBCs contribute to the membrane properties of a structure and the latter three are the bending contri butions.

4.1. A Perforated Plate

A perforated plate with ‘ + ’ shaped holes is analysed using the developed FFT-based approach. The modelling process is depicted in Fig.1 which illustrates the macro structure of the perforated plate and its micro unit cell. The unit cell under consideration is a square, each side measuring 4 . 0 mm . Centrally located within this square is a ’ + ’ shaped pore, characterized by a width of 0 . 5 mm and a length of 2 . 0 mm . The plate’s thickness is set at 0 . 2 mm . The homogenised properties of the structure are presented in Table.1, obtained by both the FEM and the FFT-based approach. Note here that only the FFT-based approach within CPT is employed for the analysis in this case since the thickness to length ratio of the studied plate is smaller than 10%. From Table.1, it is seen that the FFT-based and FEM results show perfect agreement to each other.

Unit Cell

Plate Element Model

Periodic Perforated Plate

Fig. 1. Plate modelling of the perforated plate.

The maximum principal strain distributions of structure with the six PBCs are shown in Fig.2. The distributions are visualised on the 3D deformed profiles for clearer demonstration.