Homogenization of heterogeneous thin and thick plates / Karam Sab, Arthur Lebée.

Format:

Book

Author/Creator:

Sab, Karam, author.

Lebée, Arthur, author.

Series:

Iste

Language:

English

Subjects (All):

Plates (Engineering)--Mathematical models.

Plates (Engineering).

Physical Description:

1 online resource (245 p.)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, 2015.

Language Note:

English

Summary:

This book gives new insight on plate models in the linear elasticity framework tacking into account heterogeneities and thickness effects. It is targeted to graduate students how want to discover plate models but deals also with latest developments on higher order models. Plates models are both an ancient matter and a still active field of research. First attempts date back to the beginning of the 19th century with Sophie Germain. Very efficient models have been suggested for homogeneous and isotropic plates by Love (1888) for thin plates and Reissner (1945) for thick plates. However, the extension of such models to more general situations --such as laminated plates with highly anisotropic layers-- and periodic plates --such as honeycomb sandwich panels-- raised a number of difficulties. An extremely wide literature is accessible on these questions, from very simplistic approaches, which are very limited, to extremely elaborated mathematical theories, which might refrain the beginner. Starting from continuum mechanics concepts, this book introduces plate models of progressive complexity and tackles rigorously the influence of the thickness of the plate and of the heterogeneity. It provides also latest research results. The major part of the book deals with a new theory which is the extension to general situations of the well established Reissner-Mindlin theory. These results are completely new and give a new insight to some aspects of plate theories which were controversial till recently.

Contents:

Intro

Table of Contents

Dedication

Title

Copyright

Introduction

I.1. Motivation

I.2. A brief history of plate models

1: Linear Elasticity

1.1. Notations

1.2. Stress

1.3. Linearized strains

1.4. Small perturbations

1.5. Linear elasticity

1.6. Boundary value problem in linear elasticity

1.7. Variational formulations

1.8. Anisotropy

PART 1: Thin Laminated Plates

2: A Static Approach for Deriving the Kirchhoff-Love Model for Thin Homogeneous Plates

2.1. The 3D problem

2.2. Thin plate subjected to in-plane loading

2.3. Thin plate subjected to out-of-plane loading

3: The Kirchhoff-Love Model for Thin Laminated Plates

3.1. The 3D problem

3.2. Deriving the Kirchhoff-Love plate model

3.3. Application of the two-energy principle

PART 2: Thick Laminated Plates

4: Thick Homogeneous Plate Subjected to Out-of-Plane Loading

4.1. The 3D problem

4.2. The Reissner-Mindlin plate model

5: Thick Symmetric Laminated Plate Subjected to Out-of-Plane Loading

5.1. Notations

5.2. The 3D problem

5.3. The generalized Reissner plate model

5.4. Derivation of the Bending-Gradient plate model

5.5. The case of isotropic homogeneous plates

5.6. Bending-Gradient or Reissner-Mindlin plate model?

6: The Bending-Gradient Theory

6.1. The 3D problem

6.2. The Bending-Gradient problem

6.3. Variational formulations

6.4. Boundary conditions

6.5. Voigt notations

6.6. Symmetries

7: Application to Laminates

7.1. Laminated plate configuration

7.2. Localization fields

7.3. Distance between the Reissner-Mindlin and the Bending-Gradient model

7.4. Cylindrical bending

7.5. Conclusion

PART 3: Periodic Plates

8: Thin Periodic Plates

8.1. The 3D problem

8.2. The homogenized plate problem.

8.3. Determination of the homogenized plate elastic stiffness tensors

8.4. A first justification: the asymptotic effective elastic properties of periodic plates

8.5. Effect of symmetries

8.6. Second justification: the asymptotic expansion method

9: Thick Periodic Plates

9.1. The 3D problem

9.2. The asymptotic solution

9.3. The Bending-Gradient homogenization scheme

10: Application to Cellular Sandwich Panels

10.1. Introduction

10.2. Questions raised by sandwich panel shear force stiffness

10.3. The membrane and bending behavior of sandwich panels

10.4. The transverse shear behavior of sandwich panels

10.5. Application to a sandwich panel including Miura-ori

10.6. Conclusion

11: Application to Space Frames

11.1. Introduction

11.2. Homogenization of a periodic space frame as a thick plate

11.3. Homogenization of a square lattice as a Bending-Gradient plate

11.4. Cylindrical bending of a square beam lattice

11.5. Discussion

11.6. Conclusion

Bibliography

Index

End User License Agreement.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed November 9, 2015).

ISBN:

9781119008163

1119008166

9781119008156

1119008158

9781119005247

1119005248

OCLC:

935355276