Shape optimal design of periodic microstructural materials

  • We are concerned with the optimal design of composite materials with periodic microstructures. A homogenization approach is applied to obtain a computationally feasible macromodel. The microstructural geometrical details of the microcells are considered as design variables. The goal is to find the best material-and-shape combination in order to achieve optimal performance of the material with respect to a mechanical merit function. The resulting PDE constrained optimization problem is based on the equations of elasticity as state equations and additional technically motivated equality and inequality constraints. The numerical solution uses an all-at-once approach featuring an adaptive path-following prima-dual interior point method. Numerical results illustrate the performance of the algorithm.

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Author:Ronald H. W. HoppeGND, Svetozara I. Petrova
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2008-16)
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston, Bulgarian Academy of Sciences
Release Date:2008/04/07
Tag:shape optimization; perodic microstructural materials
GND-Keyword:Deterministische Optimierung; Verbundwerkstoff; Mikrostruktur; Gestaltoptimierung
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik