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Non-local Structural Mechanics,9781848215221
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Non-local Structural Mechanics



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This is the edition with a publication date of 11/11/2013.

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This book gives science and engineering graduates and researchers a detailed understanding of the methods of
non-local analysis necessary for nanoscale structures.
The conventional local elasticity theory has underpinned the majority of applications of continuum mechanics in applied science and engineering since its inception in the early 19th Century. The application of the local elasticity theory in the context of nanoscale objects has been repeatedly questioned in various research articles over the past decade. Non-local elasticity theory, pioneered from the 1970s, is a scale-dependent theory and is considered to be more suitable for analyzing nanoscale objects such as carbon nanotubes and graphene sheets.
This book is the first comprehensive text to cover non-local elasticity theory for static, dynamic and stability analysis of wide-ranging nanostructures. The authors draw on their considerable research experience in this field. The text will be written from a mechanics standpoint, with numerous worked examples relevant across a wide range of nanomechanical systems.

Table of Contents

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


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