4 Full-Field Strain Shape Estimation from 3D SLDV 39 Fig. 4.11 Direct methods for strain shape estimation Fig. 4.12 Area patches where surface strains were calculated Figures 4.13 and 4.14 also illustrate the differences between ODS and modal strain shapes, even for a structure whose modes are well spaced and the ODS are very similar to the mode shapes, as illustrated by the MAC between the two in Fig. 4.15. 4.5 LDV Transformation Methods The second category of methods utilize transformations to derive full-field modal strain shapes, as shown in Fig. 4.16. The workflow on the right side of the figure will be referred to as the “Transformation Modal Method”. In this method, the displacement mode shapes extracted froma measurement points (Ea) are expanded to the full FEMn-space using SEREP, as shown in Eq. (4.8). These En shapes are then post-processed to obtain full n-space modal strain shapes τn. Alternatively, if the FEM includes analytical strain shapes (εn), the expansion in Eq. (4.9) can be used to directly arrive at the same τn without the need to use a standalone strain post-processor. Provided that strains are calculated the same in the FEM as the standalone strain post-processor, these two variations will be identical and only circumstance would dictate which should be used. In this work, εn were available from the FEM, so Eq. (4.9) is used for the Transformation Modal Method results herein, but the alternative path was also computed to verify they produce equivalent results. On the left side of Fig. 4.16 is the so-called “Transformation ODS Method”, although it is noted that both ODS " Oa and mode shapes Ea are required. It should be noted that while this method required both shape sets, it does not need a FEM of the test object. The first variation would be to use the ODS to smooth the measured mode shapes per Eq. (4.10) and then
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