Traversing singularities in nonlinear analyses on cable network structures

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Abstract

Nonlinear analyses of cable network structures using Newton's iteration often encounter difficulties in solving for a singular stiffness matrix stemming from the tension-stabilizing nature and slackening of cables. This paper presents a solution method, called null space projection, to traverse such a singular linear system in Newton's iteration. In the method, the current unbalance of internal and external forces is projected on the null space of the stiffness matrix and the contributions of null space basis for the variable updating are derived such that the total potential energy is reduced. Numerical example shows that the method successfully traverses singular systems in Newton's iteration process and consequently gives the equilibrium state of the structure.

Original languageEnglish
Pages (from-to)867-874
Number of pages8
JournalNippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Volume60
Issue number571
Publication statusPublished - 1994 Mar
Externally publishedYes

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Stiffness matrix
Cables
Potential energy
Linear systems

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

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abstract = "Nonlinear analyses of cable network structures using Newton's iteration often encounter difficulties in solving for a singular stiffness matrix stemming from the tension-stabilizing nature and slackening of cables. This paper presents a solution method, called null space projection, to traverse such a singular linear system in Newton's iteration. In the method, the current unbalance of internal and external forces is projected on the null space of the stiffness matrix and the contributions of null space basis for the variable updating are derived such that the total potential energy is reduced. Numerical example shows that the method successfully traverses singular systems in Newton's iteration process and consequently gives the equilibrium state of the structure.",
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AB - Nonlinear analyses of cable network structures using Newton's iteration often encounter difficulties in solving for a singular stiffness matrix stemming from the tension-stabilizing nature and slackening of cables. This paper presents a solution method, called null space projection, to traverse such a singular linear system in Newton's iteration. In the method, the current unbalance of internal and external forces is projected on the null space of the stiffness matrix and the contributions of null space basis for the variable updating are derived such that the total potential energy is reduced. Numerical example shows that the method successfully traverses singular systems in Newton's iteration process and consequently gives the equilibrium state of the structure.

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