52 S.M. Kleinendorst et al. 0 5 10 15 20 10−8 10−6 10−4 10−2 100 Iteration # 6.89e-2 6.80e-2 6.00e-2 init. guess = Masked Not masked Absolute relative error in E: E = |EMSC−E| E ϵ (a) P =1e−5 0 1 2 3 4 5 6 7 8 10−8 10−6 10−4 10−2 100 Iteration # 6.89e-2 6.80e-2 6.00e-2 init. guess = Masked Not masked Absolute relative error in E: E = |EMSC−E| E ϵ (b) P =1e−3 0 1 2 3 4 5 6 7 8 10−8 10−6 10−4 10−2 100 Iteration # 6.89e-2 6.80e-2 6.00e-2 init. guess = Masked Not masked Absolute relative error in E: E = |EMSC−E| E ϵ (c) P =1e 1 Fig. 8.5 Comparison of the convergence behavior of the MSC method for images where the structure itself is masked and images for which the structure is not masked, i.e., where the entire image is used. The comparison is executed for different values of the perturbation factor Pand for different initial guesses. (a) PD1e 5. (b) PD1e 3. (c) PD1e 1 of the initial guess and perturbation factor P. The resulting convergence graphs are shown in Fig. 8.5. It can be seen that for all settings the convergence behavior is improved in case the structure itself is masked. Especially for a small perturbation factor the effect is large. This is because a small perturbation increases the effect of numerical instability due to very small deviations. 8.4.2 Torsion of Beams The second virtual experiment is executed for a beam in torsion, which is beside the bending of beams also a deformation mode in stretchable electronic interconnect. A beam of 50 m 10 m is modeled and a prescribed moment is applied on one end, while the other end is clamped. The model is again elastic with one parameter, the Young’s modulus E, which determines how much the beam rotates upon the prescribed moment. Signed distance projections are made at various increments and these are used as the ‘experimental’ input images, see Fig. 8.6.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==