Master Thesis - OUFTI-1
Master Thesis - OUFTI-1 Master Thesis - OUFTI-1
• Young's modulus: E = 205 GP a • Poisson ratio: ν = 0.3 • Density: ρ = 7850 kg/m 3 Consider also that the plate has a constant thickness of 1.6 mm (which is the given thickness of OUFTI-1 PCBs). This plate was meshed once with volume elements and once with shell elements. Then, the two sets of results are correlated. The most popular correlation techniques make use of natural frequencies ω and mode shapes φ. And, the most popular indicators of the correlation between two sets of data are: • The frequency deviation, that can be calculated using Equation 4.2.3. This indicator is generally expressed in %. ∆f (ω 1 , ω 2 ) = |ω 1 − ω 2 | ω 1 (4.2.3) • The Modal Assurance Criterion (MAC), that can be calculated using Equation 4.2.4. MAC (φ 1 , φ 2 ) = ( φ T 1 φ 2 ) 2 (φ T 1 φ 1 ) (φ T 2 φ 2 ) (4.2.4) MAC values oscillate between 0 and 1, a unitary value meaning perfect correlation. The results obtained by using these two indicators in our particular case, are presented in Table 4.1 and in Figure 4.5. Natural frequencies obtained Natural frequencies obtained Frequency using volume elements (Hz) using shell elements (Hz) deviations (%) 1 528.2 527.8 0.08 2 771 770.2 0.1 3 954.8 953.8 0.1 4 1364.1 1361.9 0.16 5 1364.1 1361.9 0.16 Table 4.1: Frequency deviations between the two models 77
Figure 4.5: MAC between the two models According to these results, it can be armed that the shell elements allow to obtain results as accurate as the ones obtained using volume elements. The slight dierence in the MAC matrix is only due to the fact that the fourth and fth modes of the plate are symmetrical ones, as it is shown in Figure 4.6. Figure 4.6: Symmetrical modes of the steel plate So, from this point, the shell elements will be used to mesh the electronic cards during FE analysis until the end of this thesis. 78
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Figure 4.5: MAC between the two models<br />
According to these results, it can be armed that the shell elements allow to obtain<br />
results as accurate as the ones obtained using volume elements. The slight dierence in<br />
the MAC matrix is only due to the fact that the fourth and fth modes of the plate are<br />
symmetrical ones, as it is shown in Figure 4.6.<br />
Figure 4.6: Symmetrical modes of the steel plate<br />
So, from this point, the shell elements will be used to mesh the electronic cards during<br />
FE analysis until the end of this thesis.<br />
78
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