8 Mechanical Shape Correlation: A Novel Integrated Digital Image Correlation Approach 53 0 10 20 30 40 50 −20 −15 −10 −5 0 5 10 15 20 y [μm] x [μm] y [μm] x [μm] 0 10 20 30 40 50 −20 −15 −10 −5 0 5 10 15 20 y [μm] x [μm] 0 10 20 30 40 50 −20 −15 −10 −5 0 5 10 15 20 signed shortest distance to sample edge [μm] 0 5 10 15 20 x y z Rotation around x-axis Fig. 8.6 Signed distance maps for a selection of increments of the virtual experiment concerning a torsion beam. Note that the y-coordinate in the signed distance maps coincides with the z-coordinate in the FE simulation Iteration # -4 -2 0 2 4 6 8 10 12 14 Absolute relative error in E: E = | EMSC−E| E 10-10 10-8 10-6 10-4 10-2 100 init. guess = 6.91e-2 init. guess = 7.00e-2 init. guess = 7.50e-2 init. guess = 9.00e-2 P =1e −5 P =1e −3 P =1e −1 Fig. 8.7 Convergence plot of the MSC algorithm for the torsion beam experiment, for different values of the perturbation factor Pand different initial guess values The algorithm is run again for different initial guesses and various values of the perturbation factor P. The convergence behavior based on the error is plot in Fig. 8.7. It can be seen that convergence with a good accuracy is reached in a reasonable amount of iterations for all tried variations in initial guess andP. This gives a good perspective to use the method with other test cases.
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