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

Chapter
Part of the Advanced Structured Materials book series (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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Notes

Acknowledgements

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

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Structural MechanicsBudapest University of Technology and Economics and Engineering Center BudapestBudapestHungary
  2. 2.EA 4250, Institut de Recherche Dupuy de Lôme (IRDL), Centre de RechercheUniversité de Bretagne SudLorientFrance

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