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Generalized Models and Non-classical Approaches in Complex Materials 1 pp 451–486Cite as

On the Foundation of a Generalized Nonlocal Extensible Shear Beam Model from Discrete Interactions

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 89))

Abstract

In this paper a generalized discrete elastica model including bending, normal and shear interactions is developed. Nonlinear static analysis of the discrete model is accomplished, its buckling and post-buckling behavior are thoroughly studied. It is revealed that based on what finite strain theory is used, the discrete model yields a generalized (extensible) Engesser elastica, or a generalized (extensible) Haringx elastica. The local continuum counterparts of these models are also obtained. Then nonlocal models are developed from the introduced flexural, extensible, shearable discrete systems using a continualization technique. Analytical and numerical solutions are given for the discrete and nonlocal models, and it is shown that the scale effects of the discrete models are well captured by the continualized nonlocal models.

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Acknowledgements

The work of A. Kocsis was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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Authors and Affiliations

  1. Department of Structural Mechanics, Budapest University of Technology and Economics and Engineering Center Budapest, Robert Bosch Kft., Budapest, 1111, Hungary

    Attila Kocsis

  2. EA 4250, Institut de Recherche Dupuy de Lôme (IRDL), Centre de Recherche, Université de Bretagne Sud, Rue de Saint Maudé-BP 92116, F-56100, Lorient, France

    Noël Challamel

Authors
  1. Attila Kocsis
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  2. Noël Challamel
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Correspondence to Attila Kocsis .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität, Magdeburg, Germany

    Holm Altenbach

  2. Université Pierre et Marie Curie, Institut Jean Le Rond d’Alembert, Paris, France

    Joël Pouget

  3. Université Pierre et Marie Curie, Institut Jean Le Rond d’Alembert, Paris, France

    Martine Rousseau

  4. Université Pierre et Marie Curie, Institut Jean Le Rond d'Alembert, Paris Cedex 05, France

    Bernard Collet

  5. Institut Jean le Rond d'Alembert, Université Pierre et Marie Curie, Paris, France

    Thomas Michelitsch

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Kocsis, A., Challamel, N. (2018). On the Foundation of a Generalized Nonlocal Extensible Shear Beam Model from Discrete Interactions. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_24

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  • DOI: https://doi.org/10.1007/978-3-319-72440-9_24

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  • Print ISBN: 978-3-319-72439-3

  • Online ISBN: 978-3-319-72440-9

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