On the Solid Plate Paradox in Structural Optimization

George I.N. Rozvany, Niels Olhoff, Keng Tung Cheng, John E. Taylor

Research output: Contribution to journalArticle

52 Citations (Scopus)


This paper discusses the minimum weight design of solid plastic plates subject to constraints on the highest and lowest allowable values of the plate thickness. It is shown that the maximum thickness constraint alone does not ensure a smooth global minimum weight solution because the least weight is furnished, in the limit, by a grillage-like continuum consisting of a dense system of ribs of infinitesimal spacing and uniform depth. The'optimal layout of such continua has already been determined for most loading and boundary conditions by the first author and Prager and is found to be the same for (a) plastic limit design, (b) elastic stress design, (c) design for given compliance, and (d) design for given fundamental frequency. Two refinements of the above layout theory are also considered in the current paper. One formulation takes into consideration the weight savings due to rib intersections in high density grillages. The other development deals with minimum as well as maximum thickness constraints and establishes criteria for the occurrence of a combination of a solid plate and one-way ribs in some regions of the optimal solution. The above theory is illustrated with an example.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalJournal of structural mechanics
Issue number1
Publication statusPublished - Jan 1982


ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Mathematics(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanics of Materials
  • Engineering(all)
  • Mechanical Engineering

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