Shear Deformable Beams and Plates (eBook)

Relationships with Classical Solutions

K.H. Lee, J.N. Reddy, C.M. Wang (Herausgeber)

eBook Download: PDF

2000 | 1. Auflage
312 Seiten
Elsevier Science (Verlag)
978-0-08-054115-0 (ISBN)

Infos

Most books on the theory and analysis of beams and plates deal with the classical (Euler-Bernoulli/Kirchoff) theories but few include shear deformation theories in detail. The classical beam/plate theory is not adequate in providing accurate bending, buckling, and vibration results when the thickness-to-length ratio of the beam/plate is relatively large. This is because the effect of transverse shear strains, neglected in the classical theory, becomes significant in deep beams and thick plates. This book illustrates how shear deformation theories provide accurate solutions compared to the classical theory.
Equations governing shear deformation theories are typically more complicated than those of the classical theory. Hence it is desirable to have exact relationships between solutions of the classical theory and shear deformation theories so that whenever classical theory solutions are available, the corresponding solutions of shear deformation theories can be readily obtained. Such relationships not only furnish benchmark solutions of shear deformation theories but also provide insight into the significance of shear deformation on the response. The relationships for beams and plates have been developed by many authors over the last several years. The goal of this monograph is to bring together these relationships for beams and plates in a single volume.
The book is divided into two parts. Following the introduction, Part 1 consists of Chapters 2 to 5 dealing with beams, and Part 2 consists of Chapters 6 to 13 covering plates. Problems are included at the end of each chapter to use, extend, and develop new relationships.

Inhalt

Front Cover 1
Shear Deformable Beams and Plates: Relationships with Classical Solutions 4
Copyright Page 5
Contents 6
Preface 14
Chapter 1. Introduction 16
1.1 Preliminary Comments 16
1.2 An Overview of Plate Theories 18
1.3 Present Study 20
Problems 21
Part 1: Beams 24
Chapter 2. Bending of Beams 26
2.1 Beam Theories 26
2.2 Relationships Between EBT and TBT 39
2.3 Relationships Between EBT and RBT 43
2.4 Examples 46
2.5 Summary 51
Problems 52
Chapter 3. Shear - Flexural Stiffness Matrix 54
3.1 Introduction 54
3.2 Summary of Relationships 56
3.3 Stiffness Matrix 59
3.4 Frame Structure - An Example 63
3.5 Concluding Remarks 65
Problems 67
Chapter 4. Buckling of Columns 70
4.1 Introduction 70
4.2 Relationship Between Euler–Bernoulli 71
4.3 Relationship Between Euler–Bernoulli and Reddy–Bickford Columns 79
4.4 Concluding Remarks 89
Problems 90
Chapter 5. Tapered Beams 92
5.1 Introduction 92
5.2 Stress Resultant- Displacement Relations 93
5.3 Equilibrium Equations 93
5.4 Deflection and Force Relationships 94
5.5 Symmetrically Laminated Beams 100
5.6 Concluding Remarks 101
Problems 101
Part 2: Plates 102
Chapter 6. Theories of Plate Bending 104
6.1 Overview of Plate Theories 104
6.2 Classical (Kirchhoff) Plate Theory (CPT) 107
6.3 First-Order Shear Deformation Plate Theory (FSDT) 115
6.4 Third-Order Shear Deformation Plate Theory (TSDT) 120
Problems 123
Chapter 7. Bending Relationships for Simply Supported Plates 126
7.1 Introduction 126
7.2 Relationships Between CPT and FSDT 127
7.3 Examples 131
7.4 Relationships Between CPT and TSDT 133
7.5 Closure 143
Problems 144
Chapter 8. Bending Relationships for Lévy Solutions 148
8.1 Introduction 148
8.2 Governing Equations 149
8.3 Bending Relationships 152
8.4 Numerical Results 163
Problems 167
Chapter 9. Bending Relationships for Circular and Annular Plates 168
9.1 Governing Equations 168
9.2 Relationships Between CPT and FSDT 171
9.3 Relationships Between CPT and TSDT 180
9.4 Closure 186
Problems 186
Chapter 10. Bending Relationships for Sectorial Plates 192
10.1 Introduction 192
10.2 Formulation 193
10.3 Exact Bending Relationships 197
10.4 Examples 202
10.5 Conclusions 207
Problems 207
Chapter 11. Buckling Relationships 210
11.1 Polygonal Plates 210
11.2 Circular Plates 220
11.3 Sectorial Mindlin Plates 226
Problems 233
Chapter 12. Free Vibration Relationships 238
12.1 Introduction 238
12.2 Relationships Between CPT and FSDT 241
12.3 Relationships Between CPT and TSDT 250
12.4 Concluding Remarks 256
Problems 256
Chapter 13. Relationships for Inhomogeneous Plates 258
13.1 Deflection Relationships for Sandwich Plates 258
13.2 Deflection Relationships for Functionally Graded Circular Plates 268
13.3 Buckling Load Relationships for Sandwich Mindlin Plates 284
13.4 Free Vibration Relationships for Sandwich Plates 287
13.5 Summary 291
References 294
Subject Index 308

Produkt-Details

• Erscheint lt. Verlag: 19.7.2000
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Optik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-054115-1 / 0080541151
• ISBN-13: 978-0-08-054115-0 / 9780080541150