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A simple approach to bifurcation and limit point calculations
Author(s) -
Fujikake Masahisa
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210115
Subject(s) - tangent stiffness matrix , tangent , stiffness matrix , mathematics , positive definite matrix , bifurcation , simple (philosophy) , finite element method , stiffness , nonlinear system , matrix (chemical analysis) , mathematical analysis , limit load , critical load , limit (mathematics) , limit point , adina , direct stiffness method , geometry , buckling , structural engineering , eigenvalues and eigenvectors , engineering , philosophy , physics , materials science , epistemology , quantum mechanics , composite material
A simple approach is proposed to calculate the bifurcation and limit points of structures, talcing into account the pre‐unstable behaviour, by the finite element method. The approach is as follows: at each load step, the triangular factorization of the tangent stiffness matrix is checked to determine if the matrix is positive definite or not. When the tangent stiffness matrix is positive definite at a certain load step and non‐positive definite at the next load step, the structure is considered to become unstable between the two load steps and an eigenproblem is constructed based on the difference of the tangent stiffness matrices at the two load steps. The critical load and corresponding mode of the structure are then derived from solving the eigenproblem. The proposed procedure is simple and economical, and it can be easily incorporated into a conventional geometric nonlinear analysis computer program. It is implemented in the ADINA program and some sample calculations are shown.