Asymptotic Analysis and Design Optimization for Periodic Perforated Shells.

The core of this thesis lies in the task of structural optimization of periodic perforated cylindrical shells under a given point load. The problem is divided into three subcategories: Asymptotic analysis, macroscopic model and optimization. In this work we show a qualitative derivation, together with an algorithm for calculating the effective properties. We start with a decomposition of the applied displacements. Using the Unfolding-Rescaling operator we can decouple the two small parameters. The homogenization on beam-like structures is executed numerically and symbolically. The effective properties depend solely on the periodicity cell. We calculate the analytical solution of the limit equation. The solution is determined via a Fourier transformation and series. Moreover, this function depends on the effective properties. It is possible to represent the displacements w.r.t. certain design variables. This allows performing optimization with simple methods. We use a steepest descent method to minimize the resulting displacement. This yields the optimal configuration w.r.t. our admissible design space. Applied industrial problems can thus be effectively solved.