A primal–dual algorithm for shakedown analysis of structures

Vu, Duc Khôi; Yan, Aimin; Hung, Nguyen Dang

doi:10.1016/j.cma.2004.03.011

Cited by 79 publications

(53 citation statements)

References 6 publications

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“…They showed that the application of the duality combining with Newton method may lead to very accurate results in limit analysis. Vu et al [14] then presented a primal-dual algorithm for shakedown analysis of structures with the use of kinematically admissible finite elements. By using Newton-like iteration, it was found that upper and lower bounds of the load factor converge rapidly to the accurate solution of shakedown limit.…”

Section: Introductionmentioning

confidence: 99%

A dual algorithm for shakedown analysis of plate bending

Tran

2011

Numerical Meth Engineering

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SUMMARYIn this paper, the duality between the lower and the upper bound shakedown analyses of plate bending is presented. Based on the duality theory, the shakedown load multiplier formulated by static theorem is proved actually to be the dual form of the shakedown load multiplier formulated by kinematic theorem. A dual algorithm based upon the von Mises yield criterion and a non-linear optimization procedure is then developed to compute simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The DKQ plate bending element is used to discrete the problem field. Numerical examples are presented to show the excellent convergence and accuracy of solutions obtained by the present method.

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Section: Introductionmentioning

confidence: 99%

A dual algorithm for shakedown analysis of plate bending

Tran

2011

Numerical Meth Engineering

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“…A very efficient primal-dual algorithm, which can derive lower and upper bound simultaneously of shakedown limit load factor for complicated structures, has been introduced by Vu, Yan and Nguyen Dang [20][21][22] and Vu [23]. In these works, dual relationship between upper bound and lower bound for shakedown analysis of perfectly plastic structures has been proven.…”

Section: Introductionmentioning

confidence: 99%

FEM-based shakedown analysis of hardening structures

Phạm

Staat

2014

Asia Pac. J. Comput. Engin.

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This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.

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“…Many direct methods for modelling cyclic plasticity behaviour of the material have been developed in the past decades [5,6,7,8,9,10]. These direct methods use simple material models,…”

Section: Introductionmentioning

confidence: 99%

Effect of circular holes on the ratchet limit and crack tip plastic strain range in a centre cracked plate

Chen¹,

Chen²,

Li³

et al. 2011

Engineering Fracture Mechanics

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This version is available at https://strathprints.strath.ac.uk/31452/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. 1Effect of circular holes on the ratchet limit and crack tip plastic strain range in a centre cracked plate Haofeng Chen * , Weihang Chen, Tianbai Li, James UreDepartment of Mechanical Engineering, University of Strathclyde, Glasgow, G1 1XJ, UK Abstract: In this paper a centre cracked plate subjected to cyclic tensile loading and cyclic bending moment is considered. The effect of circular holes drilled in the region of the crack tip on the ratchet limit and crack tip plastic strain range is studied. Direct evaluation of the ratchet limit and crack tip plastic strain range is solved by employing the new Linear Matching Method (LMM).Parametric studies involving hole diameter and location are investigated. The optimum hole location for reducing the crack tip plastic strain range with the least reduction in ratchet limit is identified, and located at a distance 10% of the semi-crack length from the crack tip on the side opposite the ligament for both cyclic tensile loading and cyclic bending moment cases. It is also observed that the optimum location is independent of the hole size for both cyclic loading cases.

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A primal–dual algorithm for shakedown analysis of structures

Cited by 79 publications

References 6 publications

A dual algorithm for shakedown analysis of plate bending

A dual algorithm for shakedown analysis of plate bending

FEM-based shakedown analysis of hardening structures

Effect of circular holes on the ratchet limit and crack tip plastic strain range in a centre cracked plate

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