Plates and shells theory and analysis

619 Pages·2018·11.55 MB·English

by  Ansel C

1
PLATES AND SHELLS
Theory and Analysis
CRC Series in
APPLIED and COMPUTATIONAL MECHANICS
Series Editor: J.N. Reddy, Texas A&M University
PUBLISHED TITLES
ADVANCED MECHANICS OF CONTINUA
Karan S. Surana
ADVANCED THERMODYNAMICS ENGINEERING, SECOND EDITION
Kalyan Annamalai, Ishwar K. Puri, and Miland Jog
APPLIED FUNCTIONAL ANALYSIS
J. Tinsley Oden and Leszek F. Demkowicz
COMBUSTION SCIENCE AND ENGINEERING
Kalyan Annamalai and Ishwar K. Puri
COMPUTATIONAL MODELING OF POLYMER COMPOSITES:
A STUDY OF CREEP AND ENVIRONMENTAL EFFECTS
Samit Roy and J. N. Reddy
CONTINUUM MECHANICS FOR ENGINEERS, THIRD EDITION
Thomas Mase, Ronald Smelser and George F. Mase
DYNAMICS IN ENGINEERING PRACTICE, ELEVENTH EDITION
Dara W. Childs and Andrew Conkey
EXACT SOLUTIONS FOR BUCKLING OF STRUCTURAL MEMBERS
C. M. Wang, C. Y. Wang, and J. N. Reddy
THE FINITE ELEMENT METHOD FOR BOUNDARY VALUE PROBLEMS:
MATHEMATICS AND COMPUTATIONS
Karan S. Surana and J. N. Reddy
THE FINITE ELEMENT METHOD FOR INITIAL VALUE PROBLEMS:
MATHEMATICS AND COMPUTATIONS
Karan S. Surana and J. N. Reddy
THE FINITE ELEMENT METHOD IN HEAT TRANSFER AND FLUID DYNAMICS,
THIRD EDITION
J. N. Reddy and D. K. Gartling
MECHANICS OF MATERIALS
Clarence W. de Silva
MECHANICS OF SOLIDS AND STRUCTURES
Roger T. Fenner and J. N. Reddy
MECHANICS OF LAMINATED COMPOSITE PLATES AND SHELLS,
SECOND EDITION
J. N. REDDY
MICROMECHANICAL ANALYSIS AND MULTISCALE MODELING USING THE
VORONOI CELL FINITE ELEMENT METHOD
Somnath Ghosh
NUMERICAL AND ANALYTICAL METHODS WITH MATLAB®
William Bober, Chi-Tay Tsai, and Oren Masory
NUMERICAL AND ANALYTICAL METHODS WITH MATLAB®
FOR ELECTRICAL ENGINEERS
William Bober and Andrew Stevens
PLATES AND SHELLS: THEORY AND ANALYSIS, FOURTH EDITION
Ansel C. Ugural
PHYSICAL COMPONENTS OF TENSORS
Wolf Altman and Antonio Miravete
PRACTICAL ANALYSIS OF COMPOSITE LAMINATES
J. N. Reddy and Antonio Miravete
SOLVING ORDINARY AND PARTIAL BOUNDARY VALUE PROBLEMS IN
SCIENCE AND ENGINEERING
Karel Rektorys

PLATES AND SHELLS
Theory and Analysis
Fourth Edition
ANSEL C. UGURAL
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Library of Congress Cataloging-in-Publication Data
Names: Ugural, A. C., author.
Title: Plates and shells : theory and analysis / by Ansel C. Ugural.
Other titles: Stresses in plates and shells
Description: Fourth edition. | Boca Raton : CRC Press, [2018] | Series:
Applied and computational mechanics | Original edition published
under the title: Stresses in plates and shells / Ansel C. Ugural. |
Includes bibliographical references and index.
Identifiers: LCCN 2017014434| ISBN 9781138032453 (hardback : alk. paper) |
ISBN 9781315104621 (ebook)
Subjects: LCSH: Plates (Engineering) | Shells (Engineering) | Girders. |
Strains and stresses.
Classification: LCC TA660.P6 U39 2018 | DDC 624.1/776--dc23
LC record available at https://lccn.loc.gov/2017014434
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Contents
Preface .............................................................................................................................................xv
Acknowledgments ......................................................................................................................xix
Author ...........................................................................................................................................xxi
Symbols ......................................................................................................................................xxiii
Section I Fundamentals
1. Basic Concepts .........................................................................................................................3
1.1 Introduction ...................................................................................................................3
1.2 Methods of Analysis .....................................................................................................3
1.2.1 Case Studies in Analysis .................................................................................5
1.3 Loading Classes and Equilibrium ..............................................................................5
1.3.1 Conditions of Equilibrium ..............................................................................5
1.3.2 Free-Body Diagrams ........................................................................................6
1.4 Units and Conversion ...................................................................................................7
1.5 Stress Defined ................................................................................................................8
1.5.1 Components of Stress ......................................................................................9
1.5.2 Sign Convention .............................................................................................10
1.6 Internal-Force Resultants ...........................................................................................10
1.7 Differential Equations of Equilibrium .....................................................................13
1.8 Transformation of Stress ............................................................................................15
1.8.1 Mohr’s Circle for Stress .................................................................................16
1.9 Strain Defined ..............................................................................................................19
1.10 Components of Strain .................................................................................................20
1.10.1 Conditions of Compatibility .........................................................................21
1.10.2 Large Strains ...................................................................................................22
1.11 Transformation of Strain ............................................................................................23
1.12 Engineering Materials ................................................................................................24
1.12.1 Stress–Strain Diagrams .................................................................................25
1.13 Hooke’s Law, Poisson’s Ratio .....................................................................................26
1.14 General Properties of Materials ................................................................................29
1.14.1 Metals ..............................................................................................................30
1.14.2 Plastics .............................................................................................................30
1.14.3 Ceramics ..........................................................................................................30
1.14.4 Composites ......................................................................................................31
1.15 Engineering Design ....................................................................................................32
1.15.1 Design Procedure ...........................................................................................32
1.16 Factor of Safety ............................................................................................................33
1.16.1 Selection of a Factor of Safety ......................................................................34
1.17 Problem Formulation and Solutions ........................................................................35
vii
viii Contents
1.17.1 Numerical Accuracy and Significant Digits ..............................................35
1.17.2 Computational Tools .....................................................................................35
Problems ..................................................................................................................................36
References ...............................................................................................................................42
2. Simple Structural Members ...............................................................................................43
2.1 Introduction .................................................................................................................43
2.2 Types of Structures .....................................................................................................44
2.3 Axially Loaded Members ..........................................................................................45
2.3.1 Columns ..........................................................................................................48
2.4 Stress Concentration Factors .....................................................................................50
2.5 Torsion of Circular Bars .............................................................................................50
2.5.1 Shear Stress .....................................................................................................51
2.5.2 Angle of Twist ................................................................................................52
2.6 Rectangular Torsion Bars ...........................................................................................53
2.7 Theory of Beams .........................................................................................................54
2.8 Stresses in Beams ........................................................................................................55
2.8.1 Normal Stress .................................................................................................55
2.8.2 Shear Stress .....................................................................................................56
2.8.3 Shear Flow .......................................................................................................57
2.9 Deflection of Beams ....................................................................................................62
2.9.1 Method of Integration ...................................................................................62
2.9.2 Method of Superposition ..............................................................................66
2.10 Thin-Walled Pressure Vessels ...................................................................................68
2.11 Yield and Fracture Criteria ........................................................................................69
2.11.1 Maximum Principal Stress Theory .............................................................70
2.11.2 Coulomb–Mohr Theory ................................................................................70
2.11.3 Maximum Shear Stress Theory ...................................................................71
2.11.4 Maximum Distortion Energy Theory .........................................................72
2.11.5 A Typical Case of Combined Loadings ......................................................72
2.12 Strain Energy ...............................................................................................................75
2.13 Castigliano’s Theorem ................................................................................................77
2.13.1 Statically Indeterminate Structures ............................................................79
Problems ..................................................................................................................................80
References ...............................................................................................................................87
Section II Plates
3. Plate-Bending Theory ..........................................................................................................91
3.1 Introduction .................................................................................................................91
3.2 Historical Development of Plate and Shell Theory ................................................92
3.3 General Behavior and Theory of Plates ...................................................................93
3.4 Strain–Curvature Relations .......................................................................................94
3.4.1 Mohr’s Circle of Curvature ...........................................................................96
3.5 Stresses and Stress Resultants ...................................................................................97
3.6 Equations for Transformation of Moment ...............................................................99
3.7 Variation of Stress within a Plate ............................................................................101
Contents ix
3.8 Governing Equation for Deflection of Plates ........................................................103
3.8.1 Reduction of Plate-Bending Problem to That of Deflection
of a Membrane ..............................................................................................103
3.9 Boundary Conditions ...............................................................................................105
3.10 Exact Theory of Plates ..............................................................................................107
3.11 Methods for Solution of Plate Deflections .............................................................109
3.11.1 Cylindrical Bending of Plate Strips ...........................................................110
3.11.2 Variously Loaded Plates ..............................................................................113
3.12 Strain Energy of Plates .............................................................................................116
3.13 Energy Methods in Theory of Plates: Variational Principles ..............................117
3.13.1 The Principle of Virtual Work ....................................................................117
3.13.2 The Principle of Minimum Potential Energy ..........................................118
3.13.3 The Ritz Method ..........................................................................................119
3.14 *Natural Frequencies of Plates by the Energy Method .......................................120
Problems ................................................................................................................................121
References .............................................................................................................................124
4. Circular Plates .....................................................................................................................127
4.1 Introduction ...............................................................................................................127
4.2 Basic Relations in Polar Coordinates ......................................................................127
4.3 The Axisymmetrical Bending .................................................................................131
4.4 Equations of Equilibrium for Axisymmetrically Loaded Circular Plates ........133
4.5 Uniformly Loaded Circular Plates .........................................................................134
4.5.1 Plate with Clamped Edge ...........................................................................134
4.5.2 Plate with Simply Supported Edge ...........................................................136
4.5.3 Comparison of Deflections and Stresses in Built-in and Simply
Supported Plates ..........................................................................................137
4.6 *Effect of Shear on the Plate Deflection .................................................................139
4.7 Local Stresses at the Point of Application of a Concentrated Load ...................140
4.8 Circular Plates under a Concentrated Load at the Center ..................................141
4.8.1 Plate with Clamped Edge ...........................................................................141
4.8.2 Plate with Simply Supported Edge ...........................................................142
4.8.3 A Short Catalog of Solutions ......................................................................143
4.9 Annular Plates with Simply Supported Outer Edges ..........................................143
4.9.1 Plate Loaded by Edge Moments ................................................................143
4.9.2 Plate Loaded by Shear Force at Inner Edge ..............................................146
4.10 Deflection and Stress by Superposition .................................................................149
4.10.1 Design Tables for Annular Plates ..............................................................149
4.11 The Ritz Method Applied to Bending of Circular Plates ....................................153
4.12 Asymmetrical Bending of Circular Plates.............................................................157
4.13 *Deflection by the Reciprocity Theorem ................................................................159
Problems ................................................................................................................................160
References .............................................................................................................................166
5. Rectangular Plates ..............................................................................................................167
5.1 Introduction ...............................................................................................................167
5.2 Navier’s Solution for Simply Supported Rectangular Plates ..............................167
5.3 Simply Supported Rectangular Plates under Various Loadings .......................170
5.4 Lévy’s Solution for Rectangular Plates ..................................................................176