Shakedown analysis for complex loading using superposition

Martin Muscat, R. Hamilton, J.T. Boyle

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Bounding techniques for calculating shakedown loads are of great importance as design criteria since these eliminate the need for performing full cyclic loading programs either numerically or experimentally. The classical Melan theorem provides a way to recognize whether or not elastic shakedown occurs under a specified loading. Polizzotto extended Melan's theorem to the case where a combination of steady and cyclic loads are acting on the structure. The purpose of this paper is to present a finite element method, based on Polizzotto's theorem, to estimate elastic shakedown for a structure subjected to loads resulting from a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a biaxially loaded square plate with a central hole. Results obtained for the plate with a hole problem are compared with those available in the literature and are verified by means of cyclic elastoplastic finite element analysis.
LanguageEnglish
Pages399-412
Number of pages13
JournalJournal of Strain Analysis for Engineering Design
Volume37
Issue number5
DOIs
Publication statusPublished - 2002

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Superposition
Finite element method
Cyclic loads
Theorem
Cyclic Loading
Elasto-plastic
Eliminate
Finite Element Method
Finite Element
Estimate

Keywords

  • plasticity
  • cyclic loading
  • non-proportional
  • ratcheting
  • mechanical engineering

Cite this

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Shakedown analysis for complex loading using superposition. / Muscat, Martin; Hamilton, R.; Boyle, J.T.

In: Journal of Strain Analysis for Engineering Design, Vol. 37, No. 5, 2002, p. 399-412.

Research output: Contribution to journalArticle

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AU - Muscat, Martin

AU - Hamilton, R.

AU - Boyle, J.T.

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AB - Bounding techniques for calculating shakedown loads are of great importance as design criteria since these eliminate the need for performing full cyclic loading programs either numerically or experimentally. The classical Melan theorem provides a way to recognize whether or not elastic shakedown occurs under a specified loading. Polizzotto extended Melan's theorem to the case where a combination of steady and cyclic loads are acting on the structure. The purpose of this paper is to present a finite element method, based on Polizzotto's theorem, to estimate elastic shakedown for a structure subjected to loads resulting from a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a biaxially loaded square plate with a central hole. Results obtained for the plate with a hole problem are compared with those available in the literature and are verified by means of cyclic elastoplastic finite element analysis.

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