Free Material Optimization for Shells and Plates [Elektronische Ressource] = Freie Materialoptimierung für Schalen und Platten / Stefanie Gaile. Betreuer: Günter Leugering

FREE MATERIAL OPTIMIZATIONFOR SHELLS AND PLATES¨FREIE MATERIALOPTIMIERUNG FUR SCHALEN UND PLATTENDer Naturwissenschaftlichen Fakulta¨tder Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnbergzurErlangung des Doktorgrades Dr. rer. nat.vorgelegt vonStefanie Gaileaus Mu¨nchenAls Dissertation genehmigtvon der Naturwissenschaftlichen Fakulta¨tder Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnbergTag der mu¨ndlichen Pru¨fung: 27. Mai 2011Vorsitzender der Promotionskommission: Prof. Dr. Rainer FinkErstberichterstatter: Prof. Dr. Gu¨nter LeugeringZweitberichterstatter: Prof. Dr. Michael StinglAbstractWithin this thesis we develop mathematical models and numerical methods for the Free Ma-terial Optimization problem for shells and plates. In Chapter 1 we provide a motivation arisingfrom structural engineering to address this problem and classify the Free Material Optimizationapproach within other common methods in structural design optimization.In Chapter 2 we introduce the foundations of differential geometry and continuum mechanicsnecessary for a reliable prediction of the shell’s elastic behavior. The chosen description is basedon the theory of Cosserat continua, a direct approach to the shell as a two-dimensional midsur-face in physical space endowed with director vectors to provide additional degrees of freedom inorder to model bending and shear deformations.