Fixed point theory and structural optimization

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

This paper discusses the existence of solutions to problems of structural optimization which are of an iterative nature and possess explicit recurrence relationships for redesign. Five optimization problems are presented. These are the stress constrained truss, the stress constrained prestressed truss under two loading conditions, the natural frequency constrained truss, the overall stability constrained truss and the rigid frame. Common to the five problems is an ‘‘allowable stress” algorithm. Schauder’s fixed point theorems are discussed and utilized to prove existence, fundamental to which is the scaling property of the individual mappings. A discussion on fixed points, fully stressed designs and optimal solutions follows.

Original languageEnglish
Pages (from-to)251-261
Number of pages11
JournalEngineering Optimization
Volume17
Issue number4
DOIs
StatePublished - 1 Jun 1991
Externally publishedYes

Keywords

  • Schauder’s
  • Structural optimization
  • fixed points
  • frequency
  • prestress
  • rigid frames
  • stability
  • theorems
  • trusses

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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