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Title:Stability of finite element models for distributed-parameter optimization and topology design
Author(s):Jog, Chandrashekhar S.; Haber, Robert B.
Subject(s):Topology Design
Finite Element Models
Distributed-parameter Optimization
Abstract:We address a problem of numerical instability that is often encountered in finite element solutions of distributed-parameter optimization and variable-topology shape design problems. We show that the cause of this problem is numerical rather than physical in nature. We consider a two-field, distributed-parameter optimization problem involving a design field and a response field, and show that the optimization problem corresponds to a mixed variational problem. An improper selection of the discrete function spaces for these two fields leads to grid-scale anomalies in the numerical solutions to optimization problems, similar to those that are sometimes encountered in mixed formulations of the Stokes problem. We present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models. The general theoretical framework is specialized to analyze the stability of specific optimization problems, and stability results for various mixed finite element models are presented. We propose patch tests that are useful in identifying unstable elements.
Issue Date:1994-07
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 758
Genre:Technical Report
Sponsor:National Science Foundation 94/07; Danish Reseach Academy 94/07; Cray Research 94/07
Rights Information:Copyright 1994 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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