Details
| Original language | English |
|---|---|
| Pages (from-to) | 2419-2440 |
| Number of pages | 22 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 60 |
| Issue number | 15 |
| Publication status | Published - 21 Aug 2004 |
Abstract
The construction of energy-momentum methods depends heavily on three kinds of non-linearities:(1) the geometric (non-linearity of the strain-displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric nonlinearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law.
Keywords
- Chaotic motion, Energy-momentum methods, Non-linear dynamics, Shell theory, Structural dynamics
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 60, No. 15, 21.08.2004, p. 2419-2440.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the design of energy-momentum integration schemes for arbitrary continuum formulations. Applications to classical and chaotic motion of shells
AU - Sansour, Carlo
AU - Wriggers, Peter
AU - Sansour, Jamal
PY - 2004/8/21
Y1 - 2004/8/21
N2 - The construction of energy-momentum methods depends heavily on three kinds of non-linearities:(1) the geometric (non-linearity of the strain-displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric nonlinearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law.
AB - The construction of energy-momentum methods depends heavily on three kinds of non-linearities:(1) the geometric (non-linearity of the strain-displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric nonlinearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law.
KW - Chaotic motion
KW - Energy-momentum methods
KW - Non-linear dynamics
KW - Shell theory
KW - Structural dynamics
UR - http://www.scopus.com/inward/record.url?scp=4143072586&partnerID=8YFLogxK
U2 - 10.1002/nme.931
DO - 10.1002/nme.931
M3 - Article
AN - SCOPUS:4143072586
VL - 60
SP - 2419
EP - 2440
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 15
ER -