3.3 Iso-Geometric Model Updating (IGMU) Framework An isogeometric model updating method is similar to FEMU in its principle, but uses Iso-Geometric Analyses (IGA) instead of finite element simulations (Fig. 3.2). The measured (Dirichlet) boundary conditions (computed via Stereo-DIC) are prescribed to the IGA model. As in FEMU, the simulations provide sensitivity fields (i.e., displacement field and load variations with respect to the chosen parameters) using finite differences, to be considered in a functional to be minimized via, for example, a Newton–Raphson algorithm. Using this procedure on the virtual experiment, leads to identified values of Young’s modulus and Poisson’s ratio. Figure 3.3a illustrates the change of Young’s modulus during the iterations of the identification procedure. The residual error at convergence is 3.5 % of the reference value. The change of Poisson’s ratio is shown in Fig. 3.3b. The error between the prescribed value and the identified parameter is 3.3 %. In both cases, acceptable error levels are reached. The root mean square error between the simulated and measured displacement fields is shown in Fig. 3.4. At convergence, the level (44 μm) is very small, thereby validating the proposed framework. 3.4 Integrated CAD-based Stereo-DIC An integrated approach can be derived from the IGMU framework. In such formalism, the kinematic basis used during the correlation process is replaced by the sensitivity fields with respect to the chosen parameters [8]. Thus the generalized degrees of freedom become the material parameters themselves. The principle of integrated CAD-based Stereo-DIC is illustrated in Fig. 3.5. In this approach, the kinematic basis is supplied as the sensitivity fields computed from the IGA code. The virtual experiment is analyzed again using this integrated approach and Fig. 3.6 shows the change of the Poisson’s ratio during iterations of the integrated code. The residual error in this case is 0.1 % of the reference value, which is significantly lower than that observed with the IGMU approach. Deformed configuration a b 300 250 200 150 100 50 0 50 0 -50 0 20 Fig. 3.1 Deformed model used in the simulation (a). Example of gray level image created from the deformed surface (b) 18 J.-E. Dufour et al.
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