Details
| Original language | English |
|---|---|
| Pages (from-to) | 165-175 |
| Number of pages | 11 |
| Journal | Communications in Numerical Methods in Engineering |
| Volume | 9 |
| Issue number | 2 |
| Publication status | Published - Feb 1993 |
| Externally published | Yes |
Abstract
The static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non‐linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive‐definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion.
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- Computational Theory and Mathematics
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- Applied Mathematics
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In: Communications in Numerical Methods in Engineering, Vol. 9, No. 2, 02.1993, p. 165-175.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On perturbation behaviour in non‐linear dynamics
AU - Carstensen, C.
AU - Wriggers, Peter
PY - 1993/2
Y1 - 1993/2
N2 - The static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non‐linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive‐definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion.
AB - The static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non‐linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive‐definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion.
UR - http://www.scopus.com/inward/record.url?scp=0027540666&partnerID=8YFLogxK
U2 - 10.1002/cnm.1640090210
DO - 10.1002/cnm.1640090210
M3 - Article
AN - SCOPUS:0027540666
VL - 9
SP - 165
EP - 175
JO - Communications in Numerical Methods in Engineering
JF - Communications in Numerical Methods in Engineering
SN - 1069-8299
IS - 2
ER -