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Nonlocal Euler–Bernoulli Beam Theories

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Abstract

The Euler–Bernoulli beam equation was originally derived based on the local continuum mechanics with the following two assumptions: first, the beam deformation is small such that the linear elastic theory holds; second, the cross sections of the beam remain plane and perpendicular to the neutral axis after the deformation. The nonlocal Euler-Bernoulli beam follows these two assumptions while the loading-deformation relation is defined nonlocally. This chapter provides a brief introduction on the beam theories derived from the nonlocal theories, including the classical Eringen’s nonlocal theory and the recent-developed peridynamics.

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Authors and Affiliations

  1. College of Mechanical and Electronic Engineering, China University of Petroleum, Qingdao, China

    Dr. Jingkai Chen

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  1. Dr. Jingkai Chen
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Correspondence to Jingkai Chen .

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Chen, J. (2021). Introduction. In: Nonlocal Euler–Bernoulli Beam Theories. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-030-69788-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-69788-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-69787-7

  • Online ISBN: 978-3-030-69788-4

  • eBook Packages: EngineeringEngineering (R0)

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