Least-weight plates with constrained taper

Kong Min Yep Kong Min, Roman Sandler, G. Rozvany

Research output: Contribution to journalArticle

Abstract

W. Prager pointed out that rib-like formations in numerically obtained least-weight plate solutions by Cheng and Olhoff have a similar layout to optimized grillage layouts, derived earlier by Rozvany and Prager. It was then shown analytically by Rozvany, Olhoff, Cheng and Taylor that minimum-weight plastically designed solid plates with a maximum thickness constraint contain ribs of theoretically infinitesimal spacing. The current paper is based on an idea by Niordson, who suggested that ribs in plate solutions can be avoided by prescribing the maximum slope of the thickness variation (taper). After deriving general optimality criteria for axisymmetric plates from variational principles, a built-in circular sandwich plate with a uniformly distributed load is considered. It is shown that, depending on the prescribed maximum value of the taper (S), four types of optimal solutions are possible. For S = 0 and S ≥ 0.38271605, the optimal solutions reduce to classical results derived by Hopkins and Prager and Onat, Schumann and Shield. All solutions are confirmed by four independent methods: 1. (a) static-kinematic optimality criteria based on variational principles; 2. (b) assumed topography and differential calculus; 3. (c) direct minimization; and 4. (d) dual formulation.

Original languageEnglish
Pages (from-to)203-210
Number of pages8
JournalComputers and Structures
Volume25
Issue number2
DOIs
Publication statusPublished - 1987

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Optimality Criteria
Variational Principle
Differentiation (calculus)
Layout
Optimal Solution
Sandwich Plate
Topography
Circular Plate
Differential Calculus
Kinematics
Spacing
Slope
Formulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

Least-weight plates with constrained taper. / Yep Kong Min, Kong Min; Sandler, Roman; Rozvany, G.

In: Computers and Structures, Vol. 25, No. 2, 1987, p. 203-210.

Research output: Contribution to journalArticle

Yep Kong Min, Kong Min ; Sandler, Roman ; Rozvany, G. / Least-weight plates with constrained taper. In: Computers and Structures. 1987 ; Vol. 25, No. 2. pp. 203-210.
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