Mechanics Today - 1st Edition - ISBN: 9780080247496, 9781483189291

Mechanics Today

1st Edition

Pergamon Mechanics Today Series

Editors: S. Nemat-Nasser
eBook ISBN: 9781483189291
Imprint: Pergamon
Published Date: 1st January 1981
Page Count: 226
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Mechanics Today, Volume 6 is part of a series of book that compiles various materials about mechanical engineering. The coverage of the title includes theoretical and applied mechanics and applied mathematics. The text first details the general framework within which macroscopic overall response parameters of continuous bodies. Next, the selection covers the integration of theory of singularities and the calculus of variations. The third chapter deals with the elastic-plastic response of a structure to cyclic loading. The title also talks about the mixed boundary-value problems in mechanics. The book will be of great use to both student and professional mechanical engineers.

Table of Contents



Contents of Volume 1

Contents of Volume 2

Contents of Volume 3

Contents of Volume 4

Contents of Volume 5


I Macroscopic Response of Continua with Random Microstructures

1. Introduction

2. Formal Solution

2.1 The Governing Equations

2.2 The Method of Smoothing

2.3 Renormalization

2.4 The Case of a Homogeneous £(0) Field

2.5 A Few References

3. The Local Approximation (Effective Modulus Theory)

3.1 The Weakly Inhomogeneous Limit and Corrections

3.2 The Dilute Suspension and Corrections

3.3 Bounds on the Effective Elastic Moduli Tensor

3.4 Self-Consistent Calculations

3.5 Miscellaneous Calculations

4. Nonlocal Theory

4.1 Form of the Theory and a Uniqueness Theorem

4.2 The Kernel Function Cijkl(x-x')

4.3 Solutions of the Nonlocal Theory

5. Wave Propagation Experiments

5.1 Extension of General Formalism

5.2 Other Statistical Treatments

5.3 Nonstatistical and Phenomenological Treatments

6. References

II Degenerate Duality, Catastrophes and Saddle Functional

1. Morse Functions

1.1 Introduction

1.2 Morse Functions

1.3 Two-Variable Morse Functions

1.4 Legendre Transformations

1.5 Saddle Functions

1.6 Example: Plastic Constitutive Equations at a Yield Vertex

1.7 Sets of Equivalent Problems

1.8 Examples

2. Non-Morse Functions

2.1 Co-rank

2.2 Structural Instability of Non-Morse Functions

2.3 Legendre Transformations

2.4 One-Parameter Family of Legendre Transformations

2.5 Two-Parameter Family of Legendre Transformations

2.6 Pause

2.7 Two-Parameter Functions in a Minimum Norm Problem

2.8 A Pure Catastrophe Machine

2.9 Swallowtail Free Enthalpy

3. Saddle Functionals

3.1 Two Inner Product Spaces

3.2 Generating Functional

3.3 Saddle Functional

3.4 Uniqueness Criteria

3.5 Bifurcation Set

3.6 Dual Extremum Principles

3.7 Problems with Non-Linear Programming Structure

3.8 Estimates for Linear Functionals

4. Examples of Generating Functionals

4.1 Non-Morse Functionals

4.2 Solid Mechanics

4.3 Classical Elasticity

4.4 Rigid/Plastic Yield Point Problem

4.5 Small-Deflection Cantilever Beam or Strut

4.6 Potential Energy of Strut

4.7 Finite Elasticity

4.8 Incipient Plastic Distortion from a Stressed State

4.9 Theoretical Physics

4.10 Legendre Transformation for Compressible Fluids

4.11 Magnetohydrodynamic Pipe Flow

4.12 Minimum Norm Extremum Principles

5. References

III Elastic-Plastic Response of a Structure to Cyclic Loading: Practical Rules

1. Introduction

2. The Symmetric Three-bar System

2.1 Hypothesis

2.2 Elastic-Perfectly Plastic Material

2.3 Kinematically Hardening Material

3. Bree's Tube

3.1 Hypothesis

3.2 Perfectly Plastic Material

3.3 Kinematically Hardening Material

4. Plane Rectangular Plate

4.1 Hypothesis

4.2 Perfectly Plastic Material

4.3 Kinematically Hardening Material

5. A Non-symmetric Three-bar System

5.1 Hypothesis

5.2 Perfectly Plastic Material

5.3 Kinematically Hardening Material

6. General Analysis of Periodic Limiting Responses of Structures. Practical Rules

6.1 Initial-boundary-value Problem for an Elastic-plastic Structure of Kinematically Hardening Material

6.2 Fundamental Properties for Kinematically Hardening Material

6.3 Elastic Shakedown for the Kinematically Hardening Material

6.4 Plastic Shakedown for the Kinematically Hardening Material

6.5 Application Examples

6.6 Extension to Other Materials

7. References

IV Mixed Boundary-value Problems in Mechanics: Addendum

Author Index


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© Pergamon 1981
eBook ISBN:

About the Editor

S. Nemat-Nasser

Affiliations and Expertise

La Jolla, CA, USA

Ratings and Reviews