Upper bound limit analysis of plates using a rotation-free isogeometric approach

Hung Nguyen-Xuan; Chien Hoang Thai; Jeremy Bleyer; Vinh Phu Nguyen

doi:10.1186/s40540-014-0012-5

Upper bound limit analysis of plates using a rotation-free isogeometric approach

Hung Nguyen-Xuan, Chien Hoang Thai, Jeremy Bleyer, Vinh Phu Nguyen

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Background
This paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending.

Methods
The formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers.

Results and conclusions
Several numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.

Original language	English
Article number	12
Number of pages	29
Journal	Asia Pacific Journal on Computational Engineering
Volume	1
DOIs	https://doi.org/10.1186/s40540-014-0012-5
Publication status	Published - 27 Aug 2014
Externally published	Yes

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10.1186/s40540-014-0012-5

2581032-oaFinal published version, 3.52 MB

Cite this

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title = "Upper bound limit analysis of plates using a rotation-free isogeometric approach",

abstract = "BackgroundThis paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending.MethodsThe formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers.Results and conclusionsSeveral numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.",

author = "Hung Nguyen-Xuan and Thai, {Chien Hoang} and Jeremy Bleyer and Nguyen, {Vinh Phu}",

year = "2014",

month = aug,

day = "27",

doi = "10.1186/s40540-014-0012-5",

language = "English",

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journal = "Asia Pacific Journal on Computational Engineering",

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T1 - Upper bound limit analysis of plates using a rotation-free isogeometric approach

AU - Nguyen-Xuan, Hung

AU - Thai, Chien Hoang

AU - Bleyer, Jeremy

AU - Nguyen, Vinh Phu

PY - 2014/8/27

Y1 - 2014/8/27

N2 - BackgroundThis paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending.MethodsThe formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers.Results and conclusionsSeveral numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.

AB - BackgroundThis paper presents a simple and effective formulation based on a rotation-free isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending.MethodsThe formulation relies on the kinematic (or upper bound) theorem and namely B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers.Results and conclusionsSeveral numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.

U2 - 10.1186/s40540-014-0012-5

DO - 10.1186/s40540-014-0012-5

M3 - Article

VL - 1

JO - Asia Pacific Journal on Computational Engineering

JF - Asia Pacific Journal on Computational Engineering

SN - 2196-1166

M1 - 12

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