Bending and Stretching of Plates (eBook)

International Series of Monographs on Aeronautics and Astronautics: Solid and Structural Mechanics, Vol. 6

E. H. Mansfield (Autor)

R. L. Bisplinghoff, W. S. Hemp (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
160 Seiten
Elsevier Science (Verlag)
978-1-4832-2266-0 (ISBN)

Infos

The Bending and Stretching of Plates deals with elastic plate theory, particularly on small- and large-deflexion theory. Small-deflexion theory concerns derivation of basic equations, rectangular plates, plates of various shapes, plates whose boundaries are amenable to conformal transformation, plates with variable rigidity, and approximate methods. Large-deflexion theory includes general equations and some exact solutions, approximate methods in large-deflexion theory, asymptotic large-deflexion theories for very thin plates. Asymptotic theories covers membrane theory, tension field theory, and inextensional theory. The book explains stress-strain relations, effect of forces in the plane of the plate, and rectangular plates that have all edges simply supported, or where plates that have all edges clamped. The text also considers plates of constant thickness whose boundaries are circular, sector-shaped, elliptical, or triangular. Muskhelishvili (1933) addresses boundary value problems of plane stress using analytical methods of the biharmonic equation. The book also investigates some approximate methods of analysis of large-deflexion behavior of plates of constant thickness where there is either a uniformly distributed load, or a compressive load in the plane of the plate in excess of that necessary to cause initial buckling. The book explains that the engineer can use the principle of minimum potential energy to investigate large deflexion of plates. The text is suitable for structural engineers in civil, mechanical or marine engineering, as well as to structural research workers and students.

Inhalt

Front Cover 1
The Bending and Stretching of Plates 6
Copyright Page 7
Table of Contents 8
Preface 10
Principal Notation 12
PART I: SMALL-DEFLEXION THEORY 14
Chapter 
16 
1.1 Stress-strain relations 17
1.2 Rotation of axes of reference 20
1.3 Equilibrium 23
1.4 Differential equation for the deflexion 24
1.5 Effect of forces in the plane of the plate 24
1.6 General boundary conditions 29
References 33
Chapter 
34 
2.1 Plates with all edges simply supported 34
2.2 Plates with two opposite edges simply supported 38
2.3 Plates with all edges clamped 44
References 47
Chapter 
48 
3.1 Circular plates 48
3.2 Uniformly loaded sector plate 56
3.3 Sector and wedge-shaped plates with general boundary conditions 57
3.4 Elliptical plate 58
3.5 Equilateral triangular plate 58
3.6 Isosceles right-angled triangular plate 58
References 59
Additional References 59
Chapter IV. Plates whose boundaries are amenable to 
60 
4.1 Governing differential equation in complex coordinates 61
4.2 General solution for a clamped plate 68
4.3 General solution for a simply supported plate 71
4.4 Square plate with rounded corners 72
References 76
Additional References 76
Chapter 
77 
5.1 Flexure and torsion of a strip of variable rigidity 77
5.2 Rectangular plate with exponential variation of rigidity 81
5.3 Rectangular plate with linear variation of rigidity 84
5.4 Circular plates 86
5.5 Circular plates with rotational symmetry 89
References 91
Additional References 91
Chapter 
92 
6.1 The strain energy of a deformed plate 92
6.2 Principle of minimum total potential energy—Ritz method 95
6.3 The Galerkin method 99
6.4 A variational method 100
6.5 Method of boundary error minimization 106
References 108
Additional References 109
PART II: LARGE-DEFLEXION THEORY 110
Chapter 
112 
7.1 Governing differential equations 112
7.2 Cylindrical deflexion of long strip 113
7.3 Uniformly loaded circular plate 117
7.4 Flexure and torsion of a thin strip with lateral thickness variation 119
References 126
Additional References 126
Chapter 
127 
8.1 Perturbation method for normally loaded plates 127
8.2 Perturbation method in post-buckling problems 130
8.3 An energy method 135
References 139
Additional References 140
Chapter 
141 
9.1 Membrane theory 141
9.2 Inextensional theory 146
References 155
Additional References 156
Author Index 158
Subject Index 160

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-2266-7 / 1483222667
• ISBN-13: 978-1-4832-2266-0 / 9781483222660