Details
| Original language | English |
|---|---|
| Pages (from-to) | 103-109 |
| Number of pages | 7 |
| Journal | Engineering computations |
| Volume | 5 |
| Issue number | 2 |
| Publication status | Published - 1 Feb 1988 |
Abstract
The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path-following methods such as arc-length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch-switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computational Theory and Mathematics
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In: Engineering computations, Vol. 5, No. 2, 01.02.1988, p. 103-109.
Research output: Contribution to journal › Review article › Research › peer review
}
TY - JOUR
T1 - A simple method for the calculation of postcritical branches
AU - Wagner, W.
AU - Wriggers, Peter
PY - 1988/2/1
Y1 - 1988/2/1
N2 - The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path-following methods such as arc-length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch-switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.
AB - The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path-following methods such as arc-length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch-switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.
UR - http://www.scopus.com/inward/record.url?scp=0024035027&partnerID=8YFLogxK
U2 - 10.1108/eb023727
DO - 10.1108/eb023727
M3 - Review article
AN - SCOPUS:0024035027
VL - 5
SP - 103
EP - 109
JO - Engineering computations
JF - Engineering computations
SN - 0264-4401
IS - 2
ER -