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Nonlocal Euler–Bernoulli Beam Theories [electronic resource] : A Comparative Study / by Jingkai Chen.

By: Chen, Jingkai [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: SpringerBriefs in Continuum Mechanics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2021Edition: 1st ed. 2021.Description: XII, 59 p. 41 illus., 27 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030697884.Subject(s): Mechanics, Applied | Continuum mechanics | Engineering Mechanics | Continuum MechanicsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 620.1 Online resources: Click here to access online
Contents:
Introduction -- Eringen’s nonlocal beam theories -- Peridynamic beam theory -- Analytical solution to benchmark examples -- Numerical solution to integral-form peridynamic beam equation -- Conclusion.
In: Springer Nature eBookSummary: This book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, including the Eringen’s stress-gradient beam theory, the Mindlin’s strain-gradient beam theory, the higher-order beam theory and the peridynamic beam theory. Benchmark examples are solved analytically and numerically using these nonlocal beam equations, including the simply-supported beam, the clamped-clamped beam and the cantilever beam. Results show that beam deformations governed by different nonlocal theories at different boundary conditions show complex behaviors. Specifically, the Eringen’s stress-gradient beam equation and the peridynamic beam equation yield a much softer beam deformation for simply-supported beam and clamped-clamped beam, while the beam governed by the Mindlin’s strain-gradient beam equation is much stiffer. The cantilever beam exhibits a completely different behavior. The higher-order beam equation can be stiffer or softer depending on the values of the two nonlocal parameters. Moreover, the deformation fluctuation of the truncated order peridynamic beam equation is observed and explained from the singularity aspect of the solution expression. This research casts light on the fundamental explanation of nonlocal beam theories in nano-electromechanical systems.
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Introduction -- Eringen’s nonlocal beam theories -- Peridynamic beam theory -- Analytical solution to benchmark examples -- Numerical solution to integral-form peridynamic beam equation -- Conclusion.

This book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, including the Eringen’s stress-gradient beam theory, the Mindlin’s strain-gradient beam theory, the higher-order beam theory and the peridynamic beam theory. Benchmark examples are solved analytically and numerically using these nonlocal beam equations, including the simply-supported beam, the clamped-clamped beam and the cantilever beam. Results show that beam deformations governed by different nonlocal theories at different boundary conditions show complex behaviors. Specifically, the Eringen’s stress-gradient beam equation and the peridynamic beam equation yield a much softer beam deformation for simply-supported beam and clamped-clamped beam, while the beam governed by the Mindlin’s strain-gradient beam equation is much stiffer. The cantilever beam exhibits a completely different behavior. The higher-order beam equation can be stiffer or softer depending on the values of the two nonlocal parameters. Moreover, the deformation fluctuation of the truncated order peridynamic beam equation is observed and explained from the singularity aspect of the solution expression. This research casts light on the fundamental explanation of nonlocal beam theories in nano-electromechanical systems.

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