Nonlocal Euler-Bernoulli beam theories : a comparative study / Jingkai Chen.
Chen, Jingkai, author.
2021
QA808.2
Available Online

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Title Nonlocal Euler-Bernoulli beam theories : a comparative study / Jingkai Chen.
Author Chen, Jingkai, author.
ISBN 9783030697884 (electronic bk.)
3030697886 (electronic bk.)
3030697878
9783030697877
DOI https://doi.org/10.1007/978-3-030-69788-4
Published Cham : Springer, [2021]
Language English
Description 1 online resource (xii, 59 pages) : illustrations (some color).
Other Standard Identifiers 10.1007/978-3-030-69788-4 doi
Call Number QA808.2
Dewey Decimal Classification 531
Summary This book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, including the Eringens stress-gradient beam theory, the Mindlins 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 Eringens 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 Mindlins 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.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 30, 2021).
Series SpringerBriefs in applied sciences and technology. Continuum mechanics.
Available in Other Form Nonlocal Euler-Bernoulli beam theories.
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Introduction
Nonlocal beam equations
Peridynamics beam equation
Analytical solution to benchmark examples
Numerical solutions to peridynamic beam
Conclusion.

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