On the return mapping algorithms in structural optimization of biomorphic ceramics

  • The paper deals with structural optimization of biomorphic microcellular ceramics involving an elastoplasticity with the von Mises yield criterion in the macroscopic model. The return mapping algorithms introduced by Simo and Ortiz in 1985 are applied for the numerical solution of the problem. The latter methods are computationally effective, robust, and stable, and have recently become the most popular means of numerically solving elasto-plastic equations. Based on the operator splitting methodology, the return mapping algorithm can be defined by first solving the elastic equations to obtain an elastic predictor and then taken as an initial condition for the plastic equations by using a projection of the trial elastic stress onto the constraint set of admissible stresses. Finite element discretized von Mises plasticity with isotropic strain hardening is included in the state equation as an equality constraint in the structural optimization problem.

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Author:Ronald H. W. HoppeGND, Svetozara I. Petrova
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/544
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-19)
Publishing Institution:Universität Augsburg
Contributing Corporation:Department of Mathematics, University of Houston
Release Date:2007/07/02
Tag:structural optimization; biomorphic ceramics; return mapping algorithm
GND-Keyword:Deterministische Optimierung; Strukturoptimierung; Elastoplastizität; Keramischer Werkstoff
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