PSI - Issue 52

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

760

9

Fig. 5. Distributions of the maximum principal strain for six PBCs of the perforated plate. (a)-(f) represent PBCs.1-6.

Table 3. Computing time of di ff erent models for the twill woven composite.

FEM-Plate (CPT)

FEM-Plate (FQPT)

FFT-Plate (CPT)

FFT-Plate (FoPT)

A 11 ( Mpa · m )

A 11 ( Mpa · m )

Resolution

Error (%)

Time

Error (%)

Time

Time

Time

64 ∗ 64 96 ∗ 96

10.516 10.540 10.599 10.601 10.602 10.600 10.598

-0.770 -0.551 0.008 0.030 0.036 0.021

0 . 018 s 0 . 025 s 0 . 033 s 0 . 059 s 0 . 065 s 0 . 076 s 0 . 092 s

10.380 10.396 10.401 10.411 10.410 10.408 10.405

-0.241 -0.092 -0.041 0.051 0.047 0.026

0 . 024 s 0 . 042 s 0 . 061 s 0 . 089 s 0 . 094 s 0 . 124 s 0 . 184 s

0 . 07 s 0 . 26 s 0 . 84 s 2 . 39 s 5 . 86 s

0 . 06 s 0 . 27 s 0 . 84 s 2 . 15 s 5 . 76 s

128 ∗ 128 160 ∗ 160 192 ∗ 192 224 ∗ 224 256 ∗ 256

15 . 39 s 49 . 85 s

15 . 97 s 49 . 56 s

0.0

0.0

5. Conclusion

In this research, an innovative approach was presented employing the FFT-based solution to address plate cell problems. Introducing the plate element modeling framework allowed the derivation of Green operators for plate cell problems, within both the Classic Plate Theory and First-order Plate Theory. The e ffi ciency of this methodology was showcased through two illustrative cases, emphasizing its capability in microscale homogenization for plate architectures. The results derived from this study establish that the proposed FFT-based approach generates outcomes that are in line with those of conventional solid models for cell problems in thin-walled structures, while significantly reducing the computational time required. This considerable reduction of time also illustrates the potential of the proposed method in multiscale analysis in which the computational time intensity is the main challenge. The FFT based method will help improve the multiscale simulation in a significant manner.