### 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 language | English |
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Pages (from-to) | 867-874 |

Number of pages | 8 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 60 |

Issue number | 571 |

Publication status | Published - 1994 Mar |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

**Traversing singularities in nonlinear analyses on cable network structures.** / Mitsugi, Jin.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Traversing singularities in nonlinear analyses on cable network structures

AU - Mitsugi, Jin

PY - 1994/3

Y1 - 1994/3

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0028397406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028397406&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0028397406

VL - 60

SP - 867

EP - 874

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 571

ER -