Exact analytical solutions for non-selfadjoint variable-topology shape optimization problems

Perforated cantilever plates in plane stress subject to displacement constraints. Part I

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Abstract

Lurie (1994, 1995a, b) proved recently that variable-topology shape optimization of perforated plates in flexure for non-selfadjoint problems leads to rank-2 microstructures which are in general nonorthogonal. An extension of the same optimal microstructures to perforated plates in plane stress will be presented in Part II of this study. Using the above microstructure, the optimal solution is derived in this part for cantilever plates in plane stress, which are subject to two displacement constraints. For low volume fractions the above solutions are shown to converge to the known truss solutions of Birker et al. (1994). The problem of homogenizing the stiffness of nonorthogonal rank-2 microstructures is also discussed.

Original languageEnglish
Pages (from-to)119-127
Number of pages9
JournalStructural Optimization
Volume13
Issue number2-3
Publication statusPublished - 1997

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Plane Stress
Cantilever
Topology Optimization
Shape Optimization
Shape optimization
Microstructure
Analytical Solution
Optimization Problem
Perforated plates
Flexure
Volume Fraction
Volume fraction
Stiffness
Optimal Solution
Converge

ASJC Scopus subject areas

  • Civil and Structural Engineering

Cite this

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title = "Exact analytical solutions for non-selfadjoint variable-topology shape optimization problems: Perforated cantilever plates in plane stress subject to displacement constraints. Part I",
abstract = "Lurie (1994, 1995a, b) proved recently that variable-topology shape optimization of perforated plates in flexure for non-selfadjoint problems leads to rank-2 microstructures which are in general nonorthogonal. An extension of the same optimal microstructures to perforated plates in plane stress will be presented in Part II of this study. Using the above microstructure, the optimal solution is derived in this part for cantilever plates in plane stress, which are subject to two displacement constraints. For low volume fractions the above solutions are shown to converge to the known truss solutions of Birker et al. (1994). The problem of homogenizing the stiffness of nonorthogonal rank-2 microstructures is also discussed.",
author = "G. K{\'a}rolyi and G. Rozvany",
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AU - Rozvany, G.

PY - 1997

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AB - Lurie (1994, 1995a, b) proved recently that variable-topology shape optimization of perforated plates in flexure for non-selfadjoint problems leads to rank-2 microstructures which are in general nonorthogonal. An extension of the same optimal microstructures to perforated plates in plane stress will be presented in Part II of this study. Using the above microstructure, the optimal solution is derived in this part for cantilever plates in plane stress, which are subject to two displacement constraints. For low volume fractions the above solutions are shown to converge to the known truss solutions of Birker et al. (1994). The problem of homogenizing the stiffness of nonorthogonal rank-2 microstructures is also discussed.

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