@phdthesis{Ziemann2016,
  author    = {Paul Ziemann},
  title     = {Optimal Thickness of Shells with an Application to Cylindrical Bodies},
  journal    = {Optimale Schalendicke mit einer Anwendung auf Zylinderschalen},
  url       = {https://nbn-resolving.org/urn:nbn:de:gbv:9-002625-9},
  year      = {2016},
  abstract  = {This thesis deals with thickness optimization of shells. The overall task is to find an optimal thickness distribution in order to minimize the deformation of a loaded shell with prescribed volume. In addition, lower and upper bounds for the thickness are given. The shell is made of elastic, isotropic, homogeneous material. The deformation is modeled using equations from Linear Elasticity. Here, a basic shell model based on the Reissner-Mindlin assumption is used. Both the stationary and the dynamic case are considered. The continuity and the G{\^a}teaux-differentiability of the control-to-state operator is investigated. These results are applied to the reduced objective with help of adjoint theory. In addition, techniques from shape optimization are compared to the optimal control approach. In the following, the theoretical results are applied to cylindrical shells and an efficient numerical implementation is presented. Finally, numerical results are shown and analyzed for different examples.},
  language  = {en}
}