Non-local Structural Mechanics

Serving as a review on non-local mechanics, this book provides an introduction to non-local elasticity theory for static, dynamic and stability analysis in a wide range of nanostructures.  The authors draw on their own research experience to present fundamental and complex theories that are relevant across a wide range of nanomechanical systems, from the fundamentals of non-local mechanics to the latest research applications.

Danilo Karlicic is a Lecturer at the Mechanical Engineering Faculty at the University of Niš, Serbia.

Tony Murmu is a Lecturer of Mechanical Engineering at the University of the West of Scotland, United Kingdom.

Sondipon Adhikari is the Chair of Aerospace Engineering at the College of Engineering at Swansea University, United Kingdom.

Michael McCarthy is Professor of Aeronautical Engineering at the University of Limerick, Ireland.

Chapter 1 

1. Introduction to nonlocal elasticity

1.1 Classical Elasticity

1.2 Size-dependent Continuum Theories

1.3 Nonlocal Elasticity vs. Molecular Dynamics

1.4 Nonlocal effects at small-scale

1.5 Nonlocal Modulus

1.6 What is nonlocal parameter?

1.7 Nonlocal constitutive relations

Chapter 2

2. Nonlocal Rod Theory

Chapter 3

3. Nonlocal Beam Theory

3.1 Euler Bernoulli Beam Theory

3.1.1 Bending of small-scale beam

3.1.2 Vibration of small-scale beam

3.1.3 Buckling of small-scale beam

3.2 Timoshenko Beam Theory

3.2.1 Bending of small-scale beam

3.2.2 Vibration of small-scale beam

3.2.3 Buckling of small-scale beam

3.3 Higher Order Beam Theory

3.3.1 Bending of small-scale beam

3.3.2 Vibration of small-scale beam

3.3.3 Buckling of small-scale beam

3.4 Torsional vibration of small-scale beam

Chapter 4

4. Nonlocal Plate Theory

4.1 Kirchhoff plate

4.1.1 Bending

4.1.2 Vibration

4.1.3 Buckling

4.2 Mindlin Plate

4.2.1 Bending

4.2.2 Vibration

4.2.3 Buckling

4.3 Higher Order Plate Theory

4.3.1 Bending

4.3.2 Vibration

4.3.3 Buckling

4.4 In-plane vibration of plates

4.5 Orthotropic plates vs. Isotropic plates

Chapter 5

5. Nonlocal Shell Theory

5.1 Donnell Shell theory

5.2 Love Shell theory

5.3 Flugge Shell theory

Chapter 6

6. Influence of Elastic Medium

6.1 Winkler Foundation Model

6.2 Pasternak Foundation Model

Chapter 7

7. Thermal effect on the mechanical properties of nonlocal structures

Chapter 8

8. Double Nanostructure Systems

8.1 Vibration of nonlocal double nanorod-system

8.2 Vibration of nonlocal double-nanobeam-system

8.3 Buckling of nonlocal double-nanobeam-system

8.4 Vibration of nonlocal double-nanoplate-system

8.5 Buckling of nonlocal double-nanoplate-system

Chapter 9 

9. Application of Nonlocal Elastic Theory

9.1 Bending of single-walled carbon nanotubes

9.2 Bending of multi-walled carbon nanotubes

9.3 Free vibration of single-walled carbon nanotubes

9.4 Free vibration of multi-walled carbon nanotubes

9.5 Buckling of single-walled carbon nanotubes

9.6 Buckling of multi-walled carbon nanotubes

9.7 Bending of single-walled Graphene-sheets

9.8 Bending of multi-walled Graphene-sheets

9.9 Free vibration of single-walled Graphene-sheets

9.10 Free vibration of multi-walled Graphene-sheets

9.11 Buckling of single-walled Graphene-sheets

9.12 Buckling of multi-walled Graphene-sheets

9.13 Nonlocal parameter Values

9.14 Rotational Vibration

9.15 Mechanisms of Nonlocal Effect on the Vibration of Nanoplates

Chapter 10

10. Nanosensors Design Based on Nonlocal Elasticity

10.1 Vibration of CNT-Buckyball Coupled Systems

10.2 Torsion of CNT-Buckyball Coupled Systems

10.3 Nonlocal model of CNT with attached bio molecule

10.4 Nonlocal model with attached distributed bio molecules

10.5 Nonlocal sensor equations

10.6 Frequency of SWCNT with deoxythymidine as a point biomolecule

10.7 Frequency of SWCNT with strands of deoxythymidine as distributed bio molecules

10.8 Nonlocal sensors: point mass vs. distributed mass

Chapter 11

11. Nonlocal Finite Element Method

11.1 Variational Principle

11.2 Finite Element Method

11.2.1 Vibration of nanobeam

11.2.2 Vibration of nanoplates

11.3 Dynamic Finite Element Method

11.3.1 Vibration of nanorod

11.3.2 Vibration of nanobeam

Chapter 12

12. Introduction of Molecular dynamics of small scale structures

12.1 Overview of molecular dynamics

12.2 Molecular dynamic simulation

12.2.1 Deflection of carbon Nanotubes

12.2.2 Vibration of carbon Nanotubes

12.2.3 Buckling of carbon Nanotubes

12.2.4 Vibration of graphene sheets

12.2.5 Buckling of graphene sheets

12.3 Molecular dynamics experiments for nonlocal elasticity

Bibliography

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