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On the Nonlocal Symmetries, Group Invariant Solutions and Conservation Laws of the Equations of Nonlinear Dynamical Compressible Elasticity

Bluman, G. W. / Cheviakov, A. F. / Ganghoffer, J. F.

Abstract A family of new PDE systems of one-dimensional nonlinear elastodynam-ics, which are nonlocally related to the classical Lagrange and Euler formulations, is derived. These new PDE systems provide alternative equivalent descriptions of the one-dimensional nonlinear elasticity model. In particular, nonlocally related systems are used to find nonlocal symmetries of the Euler system for various forms of constitutive and loading functions. Examples of new dynamical solutions arising as group invariant solutions with respect to such nonlocal symmetries are constructed. Another application of nonlocally related systems considered in this paper is the construction of nonlocal conservation laws. Examples of nonlocal conservation laws are derived for several classes of stress-strain relations and loading functions.

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On the Nonlocal Symmetries, Group Invariant Solutions and Conservation Laws of the Equations of Nonlinear Dynamical Compressible Elasticity

Bluman, G. W. / Cheviakov, A. F. / Ganghoffer, J. F.

Abstract A family of new PDE systems of one-dimensional nonlinear elastodynam-ics, which are nonlocally related to the classical Lagrange and Euler formulations, is derived. These new PDE systems provide alternative equivalent descriptions of the one-dimensional nonlinear elasticity model. In particular, nonlocally related systems are used to find nonlocal symmetries of the Euler system for various forms of constitutive and loading functions. Examples of new dynamical solutions arising as group invariant solutions with respect to such nonlocal symmetries are constructed. Another application of nonlocally related systems considered in this paper is the construction of nonlocal conservation laws. Examples of nonlocal conservation laws are derived for several classes of stress-strain relations and loading functions.

On the Nonlocal Symmetries, Group Invariant Solutions and Conservation Laws of the Equations of Nonlinear Dynamical Compressible Elasticity

Bluman, G. W. / Cheviakov, A. F. / Ganghoffer, J. F.

Abstract A family of new PDE systems of one-dimensional nonlinear elastodynam-ics, which are nonlocally related to the classical Lagrange and Euler formulations, is derived. These new PDE systems provide alternative equivalent descriptions of the one-dimensional nonlinear elasticity model. In particular, nonlocally related systems are used to find nonlocal symmetries of the Euler system for various forms of constitutive and loading functions. Examples of new dynamical solutions arising as group invariant solutions with respect to such nonlocal symmetries are constructed. Another application of nonlocally related systems considered in this paper is the construction of nonlocal conservation laws. Examples of nonlocal conservation laws are derived for several classes of stress-strain relations and loading functions.

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Titel:

On the Nonlocal Symmetries, Group Invariant Solutions and Conservation Laws of the Equations of Nonlinear Dynamical Compressible Elasticity

Beteiligte:

Bluman, G. W. (Autor:in) / Cheviakov, A. F. (Autor:in) / Ganghoffer, J. F. (Autor:in)

Erschienen in:

IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics ; 107-120

IUTAM Bookseries ; 17

Erscheinungsdatum:

01.01.2009

Format / Umfang:

14 pages

ISBN:

978-90-481-3447-2 , 978-90-481-3446-5

ISSN:

DOI:

https://doi.org/10.1007/978-90-481-3447-2_10

Medientyp:

Aufsatz/Kapitel (Buch)

Format:

Elektronische Ressource

Sprache:

Englisch

Schlagwörter:

Nonlinear Elasticity , Invariant Solution , Potential System , Lagrange System , Euler System Physics , Numerical and Computational Physics , Mechanics , Thermodynamics , Computational Intelligence , Theoretical and Applied Mechanics , Continuum Mechanics and Mechanics of Materials

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