276 G. Chevallier et al. 26.3 Examples The talk will be illustrated with two examples. The first one aims to show that it is possible to reduce FE models of any realistic geometry on a small PJSB. The second one aims to show the lack of accuracy of the modal-based reductions. 26.3.1 Size of the PJSB Methods The following example aims to show that it is possible to find a small basis that span the subspace of the joint-deformations. Let us consider a 3D-Finite Element model, see Fig. 26.2. Its five first modes are shown to be bending modes in xy-plane and in xz-plane and a torsion mode. Their restriction to the region of the joint have been computed. Then thanks to the SVD computation, the PJSB has been extracted. Figure 26.3 show both basis and the Modal Assurance Criterium (MAC) between both. This result is important because it shows that the PJSB is not necessarily collinear to the modal-basis. Moreover the PJSB span the same subspace than the modal basis with less vectors. This leads to less variables in the reduced order model. 26.3.2 Accuracy of the PJSB Methods The PJSB method is investigated on a simple example. The considered whole structure, depicted in Fig. 26.4, is a clampedfree steel beam assembled with a bolted-joint at its middle, see Festjens et al. [14] for more information. The flexural behavior of this structure is investigated. The linear part of its FEM is composed of 10 hermitian 2D beam elements governed by Fig. 26.2 3D Finite Element Model of a jointed structure, see [18] >80% >80% >80% >80% <10% <10% <10% <10% <10% <10% <10% >30% >60% <10% <10% Fig. 26.3 Decomposition of the 5 first modes on the PJSB. Modal Assurance criterium between modal vector and PJSB vectors
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