TY - JOUR
T1 - Traversing Singularities in Nonlinear Analyses on Cable Network Structures
AU - Mitsugi, Jin
PY - 1994
Y1 - 1994
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.
KW - Computational Mechanics
KW - Finite Element Method
KW - Nonlinear Problem
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U2 - 10.1299/kikaia.60.867
DO - 10.1299/kikaia.60.867
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 -