كتاب Plates and Shells Theory and Analysis
منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Plates and Shells Theory and Analysis

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تاريخ التسجيل : 01/07/2009
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Plates and Shells Theory and Analysis
Ansel C. Ugural  

كتاب Plates and Shells Theory and Analysis  P_a_s_10
و المحتوى كما يلي :

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 35viii 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 101Contents 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 176x Contents
5.4.1 Simply Supported Rectangular Plate under Uniform Loading 178
5.5 Lévy’s Method Applied to Rectangular Plates under Nonuniform Loading 185
5.6 Rectangular Plates under Distributed Edge Moments 190
5.7 Method of Superposition Applied to Bending of Rectangular Plates . 194
5.7.1 Rectangular Plate with Simple and Fixed Edges under Uniform
Load . 194
5.7.2 Fixed-Edge Rectangular Plate Carries Uniform Load 196
5.8 *The Strip Method . 197
5.9 *Simply Supported Continuous Rectangular Plates 200
5.10 *Rectangular Plates Supported by Intermediate Columns .203
5.11 Rectangular Plates on Elastic Foundation .206
5.11.1 Simply Supported Plates .206
5.11.2 Plates with Arbitrary Boundary Conditions . 207
5.12 The Ritz Method Applied to Bending of Rectangular Plates .208
Problems 217
References .222
6. Plates of Various Geometrical Forms .225
6.1 Introduction .225
6.2 *Method of Images 225
6.3 Equilateral Triangular Plate with Simply Supported Edges 228
6.3.1 Equilateral Triangular Plate under Uniform Moment M0
along Its Boundary 228
6.3.2 Equilateral Triangular Plate under Uniform Load p0 229
6.4 Elliptical Plates 230
6.4.1 Uniformly Loaded Elliptic Plate with Clamped Edge .230
6.4.2 Uniformly Loaded Elliptic Plate with Simply Supported Edge 232
6.5 Sector-Shaped Plates . 232
6.6 *Stress Concentration around Holes in a Plate .235
Problems 238
References . 239
7. Numerical Methods . 241
7.1 Introduction . 241
7.2 Finite Differences 241
7.3 Solution of the Finite Difference Equations 246
7.3.1 Load Representation 247
7.4 *Plates with Curved Boundaries .256
7.5 *The Polar Mesh 259
7.6 *The Triangular Mesh 260
7.7 The FEM .263
7.8 Properties of a 2D Finite Element .265
7.8.1 Displacement Matrix .265
7.8.2 Strain, Stress, and Elasticity Matrices .265
7.9 General Formulation of the FEM 267
7.10 Beam Element 270
7.10.1 Methods of Assemblage of the [k]es . 271
7.11 Triangular Finite Element 277
7.11.1 Displacement Function .277Contents xi
7.11.2 The Stiffness Matrix 279
7.11.3 External Nodal Forces . 279
7.12 Rectangular Finite Element . 281
7.12.1 Displacement Function . 281
7.12.2 The Stiffness Matrix 282
7.12.3 External Nodal Forces . 282
Problems 286
References . 291
8. Anisotropic Plates 293
8.1 Introduction . 293
8.2 Basic Relationships . 293
8.3 Determination of Rigidities . 296
8.4 Rectangular Orthotropic Plates 298
8.4.1 Application of Navier’s Method . 298
8.4.2 Application of Lévy’s Method 300
8.4.3 Application of the Finite Difference Method . 301
8.5 Elliptic and Circular Orthotropic Plates 303
8.6 Deflection by the Energy Method .304
8.7 *Plates of Isotropic Multilayers .307
8.8 The Finite Element Solution 309
8.9 A Typical Layered Orthotropic Plate . 312
8.10 Laminated Composite Plates . 314
8.11 Sandwich and Honeycomb Plates 319
8.11.1 Design of Sandwich-Type Beams and Plates . 320
Problems 321
References . 323
9. Plates under Combined Loads . 325
9.1 Introduction . 325
9.2 Governing Equation for the Deflection Surface . 325
9.3 Buckling of Plates 329
9.4 Application of the Energy Method .333
9.5 *The Finite Difference Solution .340
9.6 Plates with Small Initial Curvature 344
9.7 *Bending to a Cylindrical Surface .346
Problems 350
References . 352
10. Large Deflection of Plates .355
10.1 Introduction .355
10.2 Plate Behavior When Deflections are Large 355
10.3 Comparison of Small- and Large-Deflection Theories 356
10.3.1 An Approximate Method for the Circular Plates 356
10.3.2 Exact Solution for the Circular Plate Problem .359
10.4 General Equations for Large Deflections of Plates .360
10.5 Deflections by the Energy Method . 362
10.6 The Finite Element Solution 366
10.6.1 Rectangular Finite Element 367xii Contents
Problems 369
References . 371
11. Thermal Stresses in Plates 373
11.1 Introduction . 373
11.2 Stress, Strain, and Displacement Relations . 373
11.3 Stress Resultants 374
11.4 The Governing Differential Equations 376
11.5 Simply Supported Rectangular Plate Subject to an Arbitrary Temperature
Distribution 377
11.6 Simply Supported Rectangular Plate with Temperature Distribution
Varying over the Thickness . 378
11.7 Analogy between Thermal and Isothermal Plate Problems 380
11.7.1 Plates with Clamped Edges 380
11.7.2 Plates with Simply Supported or Free Edges . 381
11.8 Axisymmetrically Heated Circular Plates 382
Problems 386
References . 387
Section III Shells
12. Membrane Stresses in Shells . 391
12.1 Introduction . 391
12.2 Theories and General Behavior of Shells . 391
12.3 Load Resistance Action of a Shell . 392
12.4 Geometry of Shells of Revolution . 395
12.5 Symmetrically Loaded Shells of Revolution . 396
12.6 Some Typical Cases of Shells of Revolution 398
12.6.1 Spherical Shell 399
12.6.2 Conical Shell .400
12.6.3 Circular Cylindrical Shell . 401
12.7 Axially Symmetric Deformation . 413
12.8 Asymmetrically Loaded Shells of Revolution 415
12.9 *Shells of Revolution under Wind Loading 417
12.10 Cylindrical Shells of General Shape . 419
12.11 *Folded Structures . 424
12.12 *Shell of General Form . 424
12.13 *Breakdown of Elastic Action in Shells 428
Problems 430
References .436
13. Bending Stresses in Shells 439
13.1 Introduction .439
13.2 Shell Stress Resultants 439
13.3 Force, Moment, and Displacement Relations 441
13.4 Compound Stresses in a Shell .443
13.5 Strain Energy in the Bending and Stretching of Shells .444
13.6 Axisymmetrically Loaded Circular Cylindrical Shells .444Contents xiii
13.7 A Typical Case of the Axisymmetrically Loaded Cylindrical Shell 448
13.8 Shells of Revolution under Axisymmetrical Loads . 451
13.8.1 Conical Shells .453
13.8.2 Spherical Shells 453
13.8.3 Cylindrical Shells .454
13.9 Governing Equations for Axisymmetrical Displacements .454
13.10 Spherical Shells under Axisymmetrical Load 456
13.11 Comparison of Bending and Membrane Stresses 458
13.12 *Simplified Theory of Spherical Shells under Axisymmetrical Load .460
13.13 The Finite Element Representations of Shells of General Shape 463
13.14 The Finite Element Solution of Axisymmetrically Loaded Shells .464
Problems 467
References .468
14. Applications to Pipes, Tanks, and Pressure Vessels . 471
14.1 Introduction . 471
14.2 Pipes Subjected to Edge Forces and Moments 471
14.2.1 Long Pipes .472
14.2.2 Short Pipes 474
14.3 Reinforced Cylinders 476
14.3.1 Cylinders with Collars That Prohibit Deflection .477
14.3.2 Cylinders with Collars That Resist Deflection 478
14.3.3 Cylinders with Closed Ends . 478
14.4 Cylindrical Tanks 478
14.5 Thermal Stresses in Cylinders 481
14.5.1 Uniform Temperature Distribution .482
14.5.2 Radial Temperature Gradient 482
14.6 Thermal Stresses in Compound Cylinders .484
14.7 Discontinuity Stresses in Pressure Vessels .488
14.8 Cylindrical Vessel with Hemispherical Heads .489
14.8.1 Cylinder with Semispherical and Heads of Equal Thickness .490
14.8.2 Junction of a Cylinder and Sphere of Different Thickness 492
14.9 Cylindrical Vessels with Ellipsoidal Heads 493
14.10 Cylindrical Vessel with Flat Heads 493
14.11 *Design Formulas for Conventional Pressure Vessels . 495
Problems 498
References . 501
15. Cylindrical Shells under General Loads .503
15.1 Introduction .503
15.2 Differential Equations of Equilibrium .503
15.3 Kinematic Relationships 505
15.4 The Governing Equations for Deflections .507
15.5 *Approximate Relations 508
15.6 A Typical Case of Asymmetrical Loading 509
15.7 Curved Circular Panels 512
15.8 *A Simple Theory of Bending of Curved Circular Panels . 514
15.9 *Curved Circular Panels with Variously Supported Edges 517
15.10 Inextensional Deformations 521xiv Contents
15.11 A Typical Layered Orthotropic Cylindrical Shell 524
15.12 Laminated Composite Cylindrical Shells 528
15.13 *Symmetrical Buckling under Uniform Axial Pressure .530
15.14 Nonsymmetrical Buckling under Uniform Compression 533
15.15 Buckling of Conical Shells .536
15.16 Buckling of Cylindrical and Spherical Pressure Vessels .536
Problems 537
References .538
Appendix A: Fourier Series Expansions . 539
Appendix B: Tables 545
Appendix C: Introduction to Finite Element Analysis 555
Appendix D: Introduction to MATLAB 569
Answers to Selected Problems 573
Index


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