On the design of energy-momentum integration schemes for arbitrary continuum formulations. Applications to classical and chaotic motion of shells

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OriginalspracheEnglisch
Seiten (von - bis)2419-2440
Seitenumfang22
FachzeitschriftInternational Journal for Numerical Methods in Engineering
Jahrgang60
Ausgabenummer15
PublikationsstatusVeröffentlicht - 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.

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On the design of energy-momentum integration schemes for arbitrary continuum formulations. Applications to classical and chaotic motion of shells. / Sansour, Carlo; Wriggers, Peter; Sansour, Jamal.
in: International Journal for Numerical Methods in Engineering, Jahrgang 60, Nr. 15, 21.08.2004, S. 2419-2440.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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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.",
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AU - Sansour, Carlo

AU - Wriggers, Peter

AU - Sansour, Jamal

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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

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