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Asymptotic Analysis and Design Optimization for Periodic Perforated Shells

: Hauck, Michael
: Klar, A.; Panasenko, G.

Fulltext urn:nbn:de:0011-n-5821284 (2.1 MByte PDF)
MD5 Fingerprint: 90daf949ee50fe04e6e3d11abf6bf257
Created on: 19.3.2020

Stuttgart: Fraunhofer Verlag, 2020, V, 124 pp.
Zugl.: Kaiserslautern, TU, Diss., 2019
ISBN: 978-3-8396-1569-0
Dissertation, Electronic Publication
Fraunhofer ITWM ()
optimization; Mechanical engineering; maths for engineers; calculus & mathematical analysis; homogenization; linear elasticity; asymptotic analysis; shell theory; Mathematiker; Verfahrenstechniker; Verfahrensingenieur; Chemieingenieur; Entwicklungsingenieur

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.