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Nonlocal Euler-Bernoulli Beam Theories

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This book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, includi... Weiterlesen
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Beschreibung

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.



Autorentext

Dr. Jingkai Chen is currently the instructor (tenure track) at China University of Petroleum (East China). He got his Ph.D degree from Rice University supervised by Prof. Pol D. Spanos. His research interests are drilling engineering, stochastic mechanics and peridynamics.



Inhalt

Chapter 1 Introduction

Chapter 2 Eringen's nonlocal beam theories
2.1 Eringen's nonlocal theory
2.2 Nonlocal beam equation derivation
Chapter 3 Peridynamic beam theory
3.1 Bond-based peridynamics
3.2 State-based peridynamics
3.3 Peridynamic beam equation derivation
3.4 Differential equation representation
Chapter 4 Analytical solution to benchmark examples
4.1 Clamped-clamped beam
4.2 Simply-supported beam
Chapter 5 Numerical solution to integral-form peridynamic beam equation
5.1 Boundary condition discussion
5.2 Benchmark examples
5.2.1 Clamped-clamped beam
5.2.2 Simply-supported beam
Chapter 6 Conclusion
References & Appendix

Produktinformationen

Titel: Nonlocal Euler-Bernoulli Beam Theories
Untertitel: A Comparative Study
Autor:
EAN: 9783030697884
Digitaler Kopierschutz: Wasserzeichen
Format: E-Book (pdf)
Hersteller: Springer International Publishing
Genre: Technik
Anzahl Seiten: 59
Veröffentlichung: 27.02.2021
Dateigrösse: 3.4 MB