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E-raamat: Plates and Shells: Theory and Analysis, Fourth Edition

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(New Jersey Institute of Technology, Newark, USA)
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Noted for its practical, accessible approach to senior and graduate-level engineering mechanics, Plates and Shells: Theory and Analysis is a long-time bestselling text on the subjects of elasticity and stress analysis. Many new examples and applications are included to review and support key foundational concepts. Advanced methods are discussed and analyzed, accompanied by illustrations. Problems are carefully arranged from the basic to the more challenging level. Computer/numerical approaches (Finite Difference, Finite Element, MATLAB) are introduced, and MATLAB code for selected illustrative problems and a case study is included.

Preface xv
Acknowledgments xix
Author xxi
Symbols xxiii
Section I: Fundamentals
1 Basic Concepts
3(40)
1.1 Introduction
3(1)
1.2 Methods of Analysis
3(2)
1.2.1 Case Studies in Analysis
5(1)
1.3 Loading Classes and Equilibrium
5(2)
1.3.1 Conditions of Equilibrium
5(1)
1.3.2 Free-Body Diagrams
6(1)
1.4 Units and Conversion
7(1)
1.5 Stress Defined
8(2)
1.5.1 Components of Stress
9(1)
1.5.2 Sign Convention
10(1)
1.6 Internal-Force Resultants
10(3)
1.7 Differential Equations of Equilibrium
13(2)
1.8 Transformation of Stress
15(4)
1.8.1 Mohr's Circle for Stress
16(3)
1.9 Strain Defined
19(1)
1.10 Components of Strain
20(3)
1.10.1 Conditions of Compatibility
21(1)
1.10.2 Large Strains
22(1)
1.11 Transformation of Strain
23(1)
1.12 Engineering Materials
24(2)
1.12.1 Stress-Strain Diagrams
25(1)
1.13 Hooke's Law, Poisson's Ratio
26(3)
1.14 General Properties of Materials
29(3)
1.14.1 Metals
30(1)
1.14.2 Plastics
30(1)
1.14.3 Ceramics
30(1)
1.14.4 Composites
31(1)
1.15 Engineering Design
32(1)
1.15.1 Design Procedure
32(1)
1.16 Factor of Safety
33(2)
1.16.1 Selection of a Factor of Safety
34(1)
1.17 Problem Formulation and Solutions
35(1)
1.17.1 Numerical Accuracy and Significant Digits
35(1)
1.17.2 Computational Tools
35(1)
Problems
36(6)
References
42(1)
2 Simple Structural Members
43(48)
2.1 Introduction
43(1)
2.2 Types of Structures
44(1)
2.3 Axially Loaded Members
45(5)
2.3.1 Columns
48(2)
2.4 Stress Concentration Factors
50(1)
2.5 Torsion of Circular Bars
50(3)
2.5.1 Shear Stress
51(1)
2.5.2 Angle of Twist
52(1)
2.6 Rectangular Torsion Bars
53(1)
2.7 Theory of Beams
54(1)
2.8 Stresses in Beams
55(7)
2.8.1 Normal Stress
55(1)
2.8.2 Shear Stress
56(1)
2.8.3 Shear Flow
57(5)
2.9 Deflection of Beams
62(6)
2.9.1 Method of Integration
62(4)
2.9.2 Method of Superposition
66(2)
2.10 Thin-Walled Pressure Vessels
68(1)
2.11 Yield and Fracture Criteria
69(6)
2.11.1 Maximum Principal Stress Theory
70(1)
2.11.2 Coulomb-Mohr Theory
70(1)
2.11.3 Maximum Shear Stress Theory
71(1)
2.11.4 Maximum Distortion Energy Theory
72(1)
2.11.5 A Typical Case of Combined Loadings
72(3)
2.12 Strain Energy
75(2)
2.13 Castigliano's Theorem
77(3)
2.13.1 Statically Indeterminate Structures
79(1)
Problems
80(7)
References
87(4)
Section II: Plates
3 Plate-Bending Theory
91(36)
3.1 Introduction
91(1)
3.2 Historical Development of Plate and Shell Theory
92(1)
3.3 General Behavior and Theory of Plates
93(1)
3.4 Strain-Curvature Relations
94(3)
3.4.1 Mohr's Circle of Curvature
96(1)
3.5 Stresses and Stress Resultants
97(2)
3.6 Equations for Transformation of Moment
99(2)
3.7 Variation of Stress within a Plate
101(2)
3.8 Governing Equation for Deflection of Plates
103(2)
3.8.1 Reduction of Plate-Bending Problem to That of Deflection of a Membrane
103(2)
3.9 Boundary Conditions
105(2)
3.10 Exact Theory of Plates
107(2)
3.11 Methods for Solution of Plate Deflections
109(7)
3.11.1 Cylindrical Bending of Plate Strips
110(3)
3.11.2 Variously Loaded Plates
113(3)
3.12 Strain Energy of Plates
116(1)
3.13 Energy Methods in Theory of Plates: Variational Principles
117(3)
3.13.1 The Principle of Virtual Work
117(1)
3.13.2 The Principle of Minimum Potential Energy
118(1)
3.13.3 The Ritz Method
119(1)
3.14 *Natural Frequencies of Plates by the Energy Method
120(1)
Problems
121(3)
References
124(3)
4 Circular Plates
127(40)
4.1 Introduction
127(1)
4.2 Basic Relations in Polar Coordinates
127(4)
4.3 The Axisymmetrical Bending
131(2)
4.4 Equations of Equilibrium for Axisymmetrically Loaded Circular Plates
133(1)
4.5 Uniformly Loaded Circular Plates
134(5)
4.5.1 Plate with Clamped Edge
134(2)
4.5.2 Plate with Simply Supported Edge
136(1)
4.5.3 Comparison of Deflections and Stresses in Built-in and Simply Supported Plates
137(2)
4.6 *Effect of Shear on the Plate Deflection
139(1)
4.7 Local Stresses at the Point of Application of a Concentrated Load
140(1)
4.8 Circular Plates under a Concentrated Load at the Center
141(2)
4.8.1 Plate with Clamped Edge
141(1)
4.8.2 Plate with Simply Supported Edge
142(1)
4.8.3 A Short Catalog of Solutions
143(1)
4.9 Annular Plates with Simply Supported Outer Edges
143(6)
4.9.1 Plate Loaded by Edge Moments
143(3)
4.9.2 Plate Loaded by Shear Force at Inner Edge
146(3)
4.10 Deflection and Stress by Superposition
149(4)
4.10.1 Design Tables for Annular Plates
149(4)
4.11 The Ritz Method Applied to Bending of Circular Plates
153(4)
4.12 Asymmetrical Bending of Circular Plates
157(2)
4.13 *Deflection by the Reciprocity Theorem
159(1)
Problems
160(6)
References
166(1)
5 Rectangular Plates
167(58)
5.1 Introduction
167(1)
5.2 Navier's Solution for Simply Supported Rectangular Plates
167(3)
5.3 Simply Supported Rectangular Plates under Various Loadings
170(6)
5.4 Levy's Solution for Rectangular Plates
176(9)
5.4.1 Simply Supported Rectangular Plate under Uniform Loading
178(7)
5.5 Levy's Method Applied to Rectangular Plates under Nonuniform Loading
185(5)
5.6 Rectangular Plates under Distributed Edge Moments
190(4)
5.7 Method of Superposition Applied to Bending of Rectangular Plates
194(3)
5.7.1 Rectangular Plate with Simple and Fixed Edges under Uniform Load
194(2)
5.7.2 Fixed-Edge Rectangular Plate Carries Uniform Load
196(1)
5.8 *The Strip Method
197(3)
5.9 *Simply Supported Continuous Rectangular Plates
200(3)
5.10 *Rectangular Plates Supported by Intermediate Columns
203(3)
5.11 Rectangular Plates on Elastic Foundation
206(11)
5.11.1 Simply Supported Plates
206(1)
5.11.2 Plates with Arbitrary Boundary Conditions
207(1)
5.12 The Ritz Method Applied to Bending of Rectangular Plates
208(9)
Problems
217(5)
References
222(3)
6 Plates of Various Geometrical Forms
225(16)
6.1 Introduction
225(1)
6.2 *Method of Images
225(3)
6.3 Equilateral Triangular Plate with Simply Supported Edges
228(2)
6.3.1 Equilateral Triangular Plate under Uniform Moment M0 along Its Boundary
228(1)
6.3.2 Equilateral Triangular Plate under Uniform Load P0
229(1)
6.4 Elliptical Plates
230(2)
6.4.1 Uniformly Loaded Elliptic Plate with Clamped Edge
230(2)
6.4.2 Uniformly Loaded Elliptic Plate with Simply Supported Edge
232(1)
6.5 Sector-Shaped Plates
232(3)
6.6 *Stress Concentration around Holes in a Plate
235(3)
Problems
238(1)
References
239(2)
7 Numerical Methods
241(52)
7.1 Introduction
241(1)
7.2 Finite Differences
241(5)
7.3 Solution of the Finite Difference Equations
246(10)
7.3.1 Load Representation
247(9)
7.4 *Plates with Curved Boundaries
256(3)
7.5 *The Polar Mesh
259(1)
7.6 *The Triangular Mesh
260(3)
7.7 The FEM
263(2)
7.8 Properties of a 2D Finite Element
265(2)
7.8.1 Displacement Matrix
265(1)
7.8.2 Strain, Stress, and Elasticity Matrices
265(2)
7.9 General Formulation of the FEM
267(3)
7.10 Beam Element
270(7)
7.10.1 Methods of Assemblage of the [ k]es
271(6)
7.11 Triangular Finite Element
277(4)
7.11.1 Displacement Function
277(2)
7.11.2 The Stiffness Matrix
279(1)
7.11.3 External Nodal Forces
279(2)
7.12 Rectangular Finite Element
281(5)
7.12.1 Displacement Function
281(1)
7.12.2 The Stiffness Matrix
282(1)
7.12.3 External Nodal Forces
282(4)
Problems
286(5)
References
291(2)
8 Anisotropic Plates
293(32)
8.1 Introduction
293(1)
8.2 Basic Relationships
293(3)
8.3 Determination of Rigidities
296(2)
8.4 Rectangular Orthotropic Plates
298(5)
8.4.1 Application of Navies Method
298(2)
8.4.2 Application of Levy's Method
300(1)
8.4.3 Application of the Finite Difference Method
301(2)
8.5 Elliptic and Circular Orthotropic Plates
303(1)
8.6 Deflection by the Energy Method
304(3)
8.7 *Plates of Isotropic Multilayers
307(2)
8.8 The Finite Element Solution
309(3)
8.9 A Typical Layered Orthotropic Plate
312(2)
8.10 Laminated Composite Plates
314(5)
8.11 Sandwich and Honeycomb Plates
319(2)
8.11.1 Design of Sandwich Type Beams and Plates
320(1)
Problems
321(2)
References
323(2)
9 Plates under Combined Loads
325(30)
9.1 Introduction
325(1)
9.2 Governing Equation for the Deflection Surface
325(4)
9.3 Buckling of Plates
329(4)
9.4 Application of the Energy Method
333(7)
9.5 *The Finite Difference Solution
340(4)
9.6 Plates with Small Initial Curvature
344(2)
9.7 *Bending to a Cylindrical Surface
346(4)
Problems
350(2)
References
352(3)
10 Large Deflection of Plates
355(18)
10.1 Introduction
355(1)
10.2 Plate Behavior When Deflections are Large
355(1)
10.3 Comparison of Small-and Large-Deflection Theories
356(4)
10.3.1 An Approximate Method for the Circular Plates
356(3)
10.3.2 Exact Solution for the Circular Plate Problem
359(1)
10.4 General Equations for Large Deflections of Plates
360(2)
10.5 Deflections by the Energy Method
362(4)
10.6 The Finite Element Solution
366(3)
10.6.1 Rectangular Finite Element
367(2)
Problems
369(2)
References
371(2)
11 Thermal Stresses in Plates
373(18)
11.1 Introduction
373(1)
11.2 Stress, Strain, and Displacement Relations
373(1)
11.3 Stress Resultants
374(2)
11.4 The Governing Differential Equations
376(1)
11.5 Simply Supported Rectangular Plate Subject to an Arbitrary Temperature Distribution
377(1)
11.6 Simply Supported Rectangular Plate with Temperature Distribution Varying over the Thickness
378(2)
11.7 Analogy between Thermal and Isothermal Plate Problems
380(2)
11.7.1 Plates with Clamped Edges
380(1)
11.7.2 Plates with Simply Supported or Free Edges
381(1)
11.8 Axisymmetrically Heated Circular Plates
382(4)
Problems
386(1)
References
387(4)
Section III: Shells
12 Membrane Stresses in Shells
391(48)
12.1 Introduction
391(1)
12.2 Theories and General Behavior of Shells
391(1)
12.3 Load Resistance Action of a Shell
392(3)
12.4 Geometry of Shells of Revolution
395(1)
12.5 Symmetrically Loaded Shells of Revolution
396(2)
12.6 Some Typical Cases of Shells of Revolution
398(15)
12.6.1 Spherical Shell
399(1)
12.6.2 Conical Shell
400(1)
12.6.3 Circular Cylindrical Shell
401(12)
12.7 Axially Symmetric Deformation
413(2)
12.8 Asymmetrically Loaded Shells of Revolution
415(2)
12.9 *Shells of Revolution under Wind Loading
417(2)
12.10 Cylindrical Shells of General Shape
419(5)
12.11 *Folded Structures
424(1)
12.12 *Shell of General Form
424(4)
12.13 *Breakdown of Elastic Action in Shells
428(2)
Problems
430(6)
References
436(3)
13 Bending Stresses in Shells
439(32)
13.1 Introduction
439(1)
13.2 Shell Stress Resultants
439(2)
13.3 Force, Moment, and Displacement Relations
441(2)
13.4 Compound Stresses in a Shell
443(1)
13.5 Strain Energy in the Bending and Stretching of Shells
444(1)
13.6 Axisymmetrically Loaded Circular Cylindrical Shells
444(4)
13.7 A Typical Case of the Axisymmetrically Loaded Cylindrical Shell
448(3)
13.8 Shells of Revolution under Axisymmetrical Loads
451(3)
13.8.1 Conical Shells
453(1)
13.8.2 Spherical Shells
453(1)
13.8.3 Cylindrical Shells
454(1)
13.9 Governing Equations for Axisymmetrical Displacements
454(2)
13.10 Spherical Shells under Axisymmetrical Load
456(2)
13.11 Comparison of Bending and Membrane Stresses
458(2)
13.12 *Simplified Theory of Spherical Shells under Axisymmetrical Load
460(3)
13.13 The Finite Element Representations of Shells of General Shape
463(1)
13.14 The Finite Element Solution of Axisymmetrically Loaded Shells
464(3)
Problems
467(1)
References
468(3)
14 Applications to Pipes, Tanks, and Pressure Vessels
471(32)
14.1 Introduction
471(1)
14.2 Pipes Subjected to Edge Forces and Moments
471(5)
14.2.1 Long Pipes
472(2)
14.2.2 Short Pipes
474(2)
14.3 Reinforced Cylinders
476(2)
14.3.1 Cylinders with Collars That Prohibit Deflection
477(1)
14.3.2 Cylinders with Collars That Resist Deflection
478(1)
14.3.3 Cylinders with Closed Ends
478(1)
14.4 Cylindrical Tanks
478(3)
14.5 Thermal Stresses in Cylinders
481(3)
14.5.1 Uniform Temperature Distribution
482(1)
14.5.2 Radial Temperature Gradient
482(2)
14.6 Thermal Stresses in Compound Cylinders
484(4)
14.7 Discontinuity Stresses in Pressure Vessels
488(1)
14.8 Cylindrical Vessel with Hemispherical Heads
489(4)
14.8.1 Cylinder with Semispherical and Heads of Equal Thickness
490(2)
14.8.2 Junction of a Cylinder and Sphere of Different Thickness
492(1)
14.9 Cylindrical Vessels with Ellipsoidal Heads
493(1)
14.10 Cylindrical Vessel with Flat Heads
493(2)
14.11 *Design Formulas for Conventional Pressure Vessels
495(3)
Problems
498(3)
References
501(2)
15 Cylindrical Shells under General Loads
503(36)
15.1 Introduction
503(1)
15.2 Differential Equations of Equilibrium
503(2)
15.3 Kinematic Relationships
505(2)
15.4 The Governing Equations for Deflections
507(1)
15.5 *Approximate Relations
508(1)
15.6 A Typical Case of Asymmetrical Loading
509(3)
15.7 Curved Circular Panels
512(2)
15.8 *A Simple Theory of Bending of Curved Circular Panels
514(3)
15.9 *Curved Circular Panels with Variously Supported Edges
517(4)
15.10 Inextensional Deformations
521(3)
15.11 A Typical Layered Orthotropic Cylindrical Shell
524(4)
15.12 Laminated Composite Cylindrical Shells
528(2)
15.13 *Symmetrical Buckling under Uniform Axial Pressure
530(3)
15.14 Nonsymmetrical Buckling under Uniform Compression
533(3)
15.15 Buckling of Conical Shells
536(1)
15.16 Buckling of Cylindrical and Spherical Pressure Vessels
536(1)
Problems
537(1)
References
538(1)
Appendix A: Fourier Series Expansions 539(6)
Appendix B: Tables 545(10)
Appendix C: Introduction to Finite Element Analysis 555(14)
Appendix D: Introduction to MATLAB® 569(4)
Answers to Selected Problems 573(4)
Index 577
Ansel C. Ugural, Ph.D., has been visiting and research professor at New Jersey Institute of Technology. He was a National Science Foundation (NSF) Fellow and taught at the University of Wisconsin - Madison. In addition, Dr. Ugural held positions for two decades as professor and chairman of the mechanical engineering department at Fairleigh Dickinson University. He has considerable and diverse industrial experience in mechanical and civil engineering in both full- time and consulting capacities. Professor Ugural received his M.S. in Mechanical Engineering and Ph.D. in Engineering Mechanics from the University of Wisconsin Madison. Dr. Ugural has been a member of several engineering and educational societies, and is listed in Who's Who in Engineering.
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