实例介绍
【实例简介】高级力学：Advanced Mechanics
【实例截图】
【核心代码】
CONTENTS
CHAPTER 1 INTRODUCTION 1
1.1 Review of Elementary Mechanics of Materials 1
1.1.1
Axially Loaded Members 1
1.1.2
Torsionally Loaded Members 3
1.1.3
Bending of Beams 3
1.2.1
Method of Mechanics of Materials 6
1.2.2
1.2.3 Deflections by Energy Methods 7
1.3.1 Elastic and Inelastic Response of a Solid 8
1.3.2
Material Properties 10
1.4.1 Modes of Failure 19
Problems 22
References 24
1.2
Methods of Analysis 5
Method of Continuum Mechanics and the
Theory of Elasticity 7
1.3
Stress-Strain Relations 8
1.4
Failure and Limits on Design 16
CHAPTER 2 THEORIES OF STRESS AND STRAIN 25
~~~~~~
2.1
Definition of Stress at a Point 25
2.2
Stress Notation 26
2.3
Symmetry of the Stresshay and Stress on an Arbitrarily
Oriented Plane 28
2.3.1
Symmetry of Stress Components 28
2.3.2
Stresses Acting on Arbitrary Planes 29
2.3.3
Normal Stress and Shear Stress on an Oblique
Plane 30
Transformation of Stress, Principal Stresses, and Other
Properties 31
2.4.1
Transformation of Stress 31
2.4.2
Principal Stresses 32
2.4.3
Principal Values and Directions 33
2.4.4
Octahedral Stress 36
2.4.5
Mean and Deviator Stresses 37
2.4.6
Plane Stress 38
2.4.7
Mohr’s Circle in Two Dimensions 40
2.4.8
Mohr’s Circles in Three Dimensions 43
Differential Equations of Motion of a Deformable
Body 50
2.5.1
Specialization of Equations 2.46 52
2.4
2.5
2.6
Deformation of a Deformable Body 54
2.7
2.8
2.9
Strain Theory, Transformation of Strain, and Principal
Strains 55
2.7.1
Strain of a Line Element 55
2.7.2
Final Direction of a Line Element 57
2.7.3
Rotation Between Two Line Elements
(Definition of Shear Strain) 58
2.7.4
Principal Strains 60
Small-Displacement Theory 61
2.8.1
Strain Compatibility Relations 62
2.8.2
Strain-Displacement Relations for Orthogonal
Strain Measurement and Strain Rosettes 70
Problems 72
References 78
Curvilinear Coordinates 63
CHAPTER 3 LINEAR STRESS-STRAIN-TEMPERATURE
RELATIONS 79
3.1
First Law of Thermodynamics, Internal-Energy Density,
and Complementary Internal-Energy Density 79
3.1.1 Elasticity and Internal-Energy Density 81
3.1.2
Elasticity and Complementary Internal-Energy
Density 82
3.2 Hooke’s Law: Anisotropic Elasticity 84
3.3
Hooke’s Law: Isotropic Elasticity 85
3.3.1
Isotropic and Homogeneous Materials 85
3.3.2
Strain-Energy Density of Isotropic Elastic
Materials 85
Equations of Thennoelasticity for Isotropic
Materials 91
Problems 101
References 103
3.4
3.5 Hooke’s Law: Orthotropic Materials 93
CHAPTER 4 INELASTIC MATERIAL. BEHAVIOR 104
4.1
Limitations on the Use of Uniaxial Stress-Strain
Data 104
4.1.1
Rate of Loading 105
4.1.2
Temperature Lower Than Room
4.1.3
Temperature Higher Than Room
Temperature 105
Temperature 105
ix X
CONTENTS
4.1.4
Unloading and Load Reversal 105
4.1.5
Multiaxial States of Stress 106
4.2.1
Models of Uniaxial StressStrain Curves 108
4.3.1 Maximum Principal Stress Criterion 114
4.3.2
Maximum Principal Strain Criterion 116
4.3.3
Strain-Energy Density Criterion 116
4.4.1 Maximum Shear-Stress (Tresca) Criterion 118
4.4.2
4.4.3
4.2
Nonlinear Material Response 107
4.3
Yield Criteria: General Concepts 113
4.4
Yielding of Ductile Metals 117
Distortional Energy Density (von Mises)
Criterion 120
Effect of Hydrostatic Stress and the
z-Plane 122
4.5 Alternative Yield Criteria 126
4.5.1
Mohr-Coulomb Yield Criterion 126
4.5.2 Drucker-Prager Yield Criterion 128
4.5.3 Hill’s Criterion for Orthotropic Materials 128
4.6.1 Elastic-Plastic Bending 131
4.6.2 Fully Plastic Moment 132
4.6.3
Shear Effect on Inelastic Bending 134
4.6.4
Modulus of Rupture 134
4.6.5
Comparison of Failure Criteria 136
4.6.6
Problems 142
References 146
4.6
General Yielding 129
Interpretation of Failure Criteria for General
Yielding 137
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
CHAPTER 5 APPLICATIONS OF ENERGY METHODS 147
6.1
5.1
5.2
5.3
5.4
5.5
Principle of Stationary Potential Energy
Castigliano’s Theorem on Deflections 152
147
Castigliano’s Theorem on Deflections for Linear
Load-Deflection Relations 155
5.3.1
Strain Energy U, for Axial Loading 156
5.3.2 Strain Energies U, and Us for Beams 158
5.3.3
Strain Energy U, for Torsion 160
Deflections of Statically Determinate Structures
5.4.1
Curved Beams Treated as Straight Beams 165
5.4.2
Statically Indeterminate Structures 177
5.5.1 Deflections of Statically Indeterminate
Problems 187
References 199
163
Dummy Load Method and Dummy Unit Load
Method 170
Structures 180
6.2.2
Stresses at a Point and Equations of
Equilibrium 210
6.2.3
Boundary Conditions 211
Linear Elastic Solution 213
6.3.1
Elliptical Cross Section 214
6.3.2
Equilateral Triangle Cross Section 215
6.3.3
Other Cross Sections 216
The Prandtl Elastic-Membrane (Soap-Film) Analogy
6.4.1 Remark on Reentrant Corners 219
Narrow Rectangular Cross Section 219
6.5.1
216
Cross Sections Made Up of Long Narrow
Rectangles 221
Torsion of Rectangular Cross Section Members 222
Hollow Thin-Wall Torsion Members and Multiply
Connected Cross Sections 228
6.7.1 Hollow Thin-Wall Torsion Member Having
Several Compartments 230
Thin-Wall Torsion Members with Restrained
Ends 234
6.8.1
6.8.2
Numerical Solution of the Torsion Problem 239
Inelastic Torsion: Circular Cross Sections 243
6.10.1
Modulus of Rupture in Torsion 244
6.10.2
Elastic-Plastic and Fully Plastic
6.10.3
Residual Shear Stress 246
Fully Plastic Torsion: General Cross Sections 250
I-Section Torsion Member Having One End
Restrained from Warping 235
Various Loads and Supports for Beams in
Torsion 239
Torsion 244
Problems 254
References 262
CHAPTER 7
BENDING OF STRAIGHT BEAMS 263
7.1
Fundamentals of Beam Bending 263
7.1.1
Centroidal Coordinate Axes 263
7.1.2
7.1.3
Symmetrical Bending 265
7.1.4
Nonsymmetrical Bending 268
7.1.5
Plane of Loads: Symmetrical and
Nonsymmetrical Loading 268
Bending Stresses in Beams Subjected to Nonsymmetrical
Bending 272
7.2.1
Equations of Equilibrium 272
7.2.2
Geometry of Deformation 273
7.2.3
StressStrain Relations 273
Shear Loading of a Beam and Shear Center
Defined 264
7.2
CHAPTER 6
TORSION 200
7.2.4
Load-Stress Relation for Nonsymmetrical
6.1 Torsion of a Prismatic Bar of Circular Cross Section 200
7.2.5
Neutral Axis 274
6.2
Saint-Venant’s Semiinverse Method 209
O,, 275
Bending 273
6.1.1 Design of Transmission Shafts 204
7.2.6
More Convenient Form for the Flexure Stress
6.2.1
Geometry of Deformation 209
7.3
Deflections of Straight Beams Subjected to
Nonsymmetrical Bending 280 CONTENTS xi
7.4 Effect of Inclined Loads 284
7.5 Fully Plastic Load for Nonsymmetrical Bending 285
Problems 287
References 294
CHAPTER 8
SHEAR CENTER FOR THIN-WALL BEAM
CROSS SECTIONS 295
8.1
Approximations for Shear in Thin-Wall Beam Cross
Sections 295
8.2 Shear Flow in Thin-Wall Beam Cross Sections 296
8.3
Shear Center for a Channel Section 298
8.4
8.5
Shear Center of Box Beams 306
Shear Center of Composite Beams Formed from
Stringers and Thin Webs 303
Problems 312
References 318
CHAPTER 9 CURVED BEAMS 319
9.1
Introduction 319
9.2
Circumferential Stresses in a Curved Beam 320
9.2.1 Location of Neutral Axis of Cross Section 326
9.3
Radial Stresses in Curved Beams 333
9.3.1 Curved Beams Made from Anisotropic
Materials 334
Correction of Circumferential Stresses in Curved Beams
Having I, T, or Similar Cross Sections 338
9.4.1
Bleich's Correction Factors 340
9.5.1
Statically Indeterminate Curved Beams: Closed Ring
Subjected to a Concentrated Load 348
9.7.1
Problems 352
References 356
9.4
9.5 Deflections of Curved Beams 343
9.6
9.7 Fully Plastic Loads for Curved Beams 350
Fully Plastic Versus Maximum Elastic Loads for
Curved Beams 351
Cross Sections in the Form of an I, T, etc. 346
CHAPTER 10 BEAMS ON ELASTIC FOUNDATIONS 357
10.1
10.2
10.3
10.4
General Theory 357
Infinite Beam Subiected to a Concentrated Load:
10.5
Semiinfinite Beam with Concentrated Load Near Its
End 376
10.6
ShortBeams 377
10.7 Thin-Wall Circular Cylinders 378
Problems 384
References 388
CHAPTER 1'1 THE THICK-WALL CYLINDER 389
1 1.1
Basic Relations 389
1 1.1.1
Equation of Equilibrium 391
1 1.1.2
Strain-Displacement Relations and
Compatibility Condition 391
1 1.1.3
Stress-Strain-Temperature Relations 392
1 1.1.4
Material Response Data 392
Stress Components at Sections Far from Ends for a
Cylinder with Closed Ends 392
1 1.2.1
Open Cylinder 394
Stress Components and Radial Displacement for
Constant Temperature 395
1 1.3.1
Stress Components 395
11.3.2
Radial Displacement for a Closed
Cylinder 396
11.3.3 Radial Displacement for an Open
Cylinder 396
1 1.4
Criteria of Failure 399
11.2
11.3
11.4.1
Failure of Brittle Materials 399
1 1.4.2
Failure of Ductile Materials 400
1 1.4.3
Material Response Data for Design 400
11.4.4
Ideal Residual Stress Distributions for
Composite Open Cylinders 401
11.5
Fully Plastic Pressure and Autofrettage 405
11.6
Cylinder Solution for Temperature Change Only 409
11.6.1
Steady-State Temperature Change
11.6.2
Stress Components 410
1 1.7
Rotating Disks of Constant Thickness 41 1
Problems 419
References 422
(Distribution) 409
CHAPTER 12
COLUMNS 423
ELASTIC AND INELASTIC STABILITY OF
Boundary Conditions 360
12.1
10.2.1
Method of Superposition 363
12.2
10.2.2
Infinite Beam Subjected to a Distributed Load
Segment 369
10.3.1
Uniformly Distributed Load 369
12.3
10.3.2
PL'Iz 371
10.3.3 PL' m 371
10.3.4
Intermediate Values of PL' 371
10.3.5
Triangular Load 371
Semiinfinite Beam Subjected to Loads at Its End 374
Beam Supported on Equally Spaced Discrete
Elastic Supports 364
Introduction to the Concept of Column Buckling 424
Deflection Response of Columns to Compressive
Loads 425
12.2.1
12.2.2
Imperfect Slender Columns 427
The Euler Formula for Columns with Pinned Ends 428
12.3.1
The Equilibrium Method 428
12.3.2
Higher Buckling Loads; n > 1 431
12.3.3
The Imperfection Method 432
12.3.4
The Energy Method 433
Elastic Buckling of an Ideal Slender
Column 425 xii CONTENTS
12.4
12.5
Local Buckling of Columns 440
12.6
Inelastic Buckling of Columns 442
12.6.1
Inelastic Buckling 442
12.6.2
12.6.3
12.6.4
Direct Tangent-Modulus Method 446
Problems 450
References 455
Euler Buckling of Columns with Linearly Elastic End
Constraints 436
Two Formulas for Inelastic Buckling of an
Ideal Column 443
Tangent-Modulus Formula for an Inelastic
Buckling Load 444
CHAPTER 13 FLAT PLATES 457
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
Introduction 457
Stress Resultants in a Flat Plate 458
Kinematics: Strain-Displacement Relations for
Plates 461
13.3.1 Rotation of a Plate Surface Element 464
Equilibrium Equations for Small-Displacement Theory
of Flat Plates 466
Stress-Strain-Temperature Relations for Isotropic
Elastic Plates 469
13.5.1
Stress Components in Terms of Tractions
and Moments 472
13.5.2
Pure Bending of Plates 472
Strain Energy of a Plate 472
Boundary Conditions for Plates 473
Solution of Rectangular Plate Problems 476
13.8.1
13.8.2
Westergaard Approximate Solution for
13.8.3
Solution of Circular Plate Problems 486
Solution of vzvZw = g for a Rectangular
Plate 477
D
Rectangular Plates: Uniform Load 479
Deflection of a Rectangular Plate:
Uniformly Distributed Load 482
13.9.1
13.9.2
13.9.3
13.9.4
13.9.5
13.9.6
13.9.7
13.9.8
Solution of v2v2W = g for a Circular
Plate 486
D
Circular Plates with Simply Supported
Edges 488
Circular Plates with Fixed Edges 488
Circular Plate with a Circular Hole at the
Center 489
Summary for Circular Plates with Simply
Supported Edges 490
Summary for Circular Plates with Fixed
Edges 491
Summary for Stresses and Deflections in
Flat Circular Plates with Central Holes
Summary for Large Elastic Deflections of
Circular Plates: Clamped Edge and
Uniformly Distributed Load 492
492
13.9.9
13.9.10
13.9.1 1
Significant Stress When Edges Are
Clamped 495
Load on a Plate When Edges Are
Clamped 496
Summary for Large Elastic Deflections of
Circular Plates: Simply Supported Edge and
Uniformly Distributed Load 497
Rectangular or Other Shaped Plates with
Large Deflections 498
13.9.12
Problems 500
References 501
CHAPTER 14 STRESS CONCENTRATIONS 502
14.1
Nature of a Stress Concentration Problem and the Stress
Concentration Factor 504
14.2
Stress Concentration Factors: Theory of Elasticity 507
14.2.1
14.2.2
Circular Hole in an Infinite Plate Under
Uniaxial Tension 507
Elliptic Hole in an Infinite Plate Stressed in a
Direction Perpendicular to the Major Axis of
the Hole 508
Elliptical Hole in an Infinite Plate Stressed in
the Direction Perpendicular to the Minor Axis
of the Hole 511
14.2.3
14.2.4 Crack in a Plate 512
14.2.5
Ellipsoidal Cavity 512
14.2.6 Grooves and Holes 513
14.3.1
Infinite Plate with a Circular Hole 515
14.3.2
14.3
Stress Concentration Factors: Combined Loads 515
Elliptical Hole in an Infinite Plate Uniformly
Stressed in Directions of Major and Minor
Axes of the Hole 516
Pure Shear Parallel to Major and Minor Axes
of the Elliptical Hole 516
Elliptical Hole in an Infinite Plate with
Different Loads in Two Perpendicular
Directions 517
Stress Concentration at a Groove in a Circular
Shaft 520
14.3.3
14.3.4
14.3.5
14.4
Stress Concentration Factors: Experimental
Techniques 522
14.4.1
Photoelastic Method 522
14.4.2
Strain-Gage Method 524
14.4.3
14.4.4
14.4.5 Beams with Rectangular Cross Sections 527
14.5.1 Definition of Effective Stress Concentration
Factor 530
14.5.2
Static Loads 532
14.5.3 Repeated Loads 532
Elastic Torsional Stress Concentration at a
Fillet in a Shaft 525
Elastic Membrane Method: Torsional Stress
concentration 525
14.5 Effective Stress Concentration Factors 530 CONTENTS xiii
14.5.4
Residual Stresses 534
14.5.5
Very Abrupt Changes in Section: Stress
Gradient 534
14.5.6
Significance of Stress Gradient 535
14.5.7
Impact or Energy Loading 536
Effective Stress Concentration Factors: Inelastic
Strains 536
14.6.1 Neuber’s Theorem 537
Problems 539
References 541
14.6
CHAPTER 15 FRACTURE MECHANICS 543
15.1
Failure Criteria and Fracture 544
15.1.1
15.1.2
Brittle Fracture of Members Free of Cracks
andFlaws 545
Brittle Fracture of Cracked or Flawed
Members 545
15.2
The Stationary Crack 551
15.2.1 Blunt Crack 553
15.2.2
Sharpcrack 554
15.3.1
15.3.2
15.3.3 Derivation of Crack Extension Force G 556
15.3.4
Critical Value of Crack Extension Force 558
15.4.1 Elastic-Plastic Fracture Mechanics 562
15.4.2
Crack-Growth Analysis 562
15.4.3 Load Spectra and Stress History 562
15.4.4 Testing and Experimental Data
Problems 564
References 565
15.3
Crack Propagation and the Stress Intensity Factor 555
Elastic Stress at the Tip of a Sharp
Crack 555
Stress Intensity Factor: Definition and
Derivation 556
15.4
Fracture: Other Factors 561
Interpretation 563
CHAPTER 16 FATIGUE: PROGRESSNE FRACTURE 567
16.1
Fracture Resulting from Cyclic Loading 568
16.1.1
Stress Concentrations 573
16.2 Effective Stress Concentration Factors: Repeated
Loads 575
16.3
Effective Stress Concentration Factors: Other
Influences 575
16.3.1
Corrosion Fatigue 575
16.3.2 Effect of Range of Stress 577
16.3.3 Methods of Reducing Harmful Effects of
Stress Concentrations 577
16.4
Low Cycle Fatigue and the E-N Relation 580
16.4.1
Hysteresis Loop 580
16.4.2
Problems 585
References 588
Fatigue-Life Curve and the E-N
Relation 581
CHAPTER 17 CONTACT STRESSES 589
17.1
Introduction 589
17.2 The Problem of Determining Contact Stresses 590
17.3
Geometry of the Contact Surface 591
17.3.1 Fundamental Assumptions 591
17.3.2
Contact Surface Shape After Loading 592
17.3.3
Justification of Eq. 17.1 592
17.3.4 Brief Discussion of the Solution 595
17.4
Notation and Meaning of Terms 596
17.5
Expressions for Principal Stresses 597
17.6
Method of Computing Contact Stresses 598
17.6.1
Principal Stresses 598
17.6.2
Maximum Shear Stress 599
17.6.3 Maximum Octahedral Shear Stress 599
17.6.4
Maximum Orthogonal Shear Stress 599
17.6.5
Curves for Computing Stresses for Any Value
of BIA 605
17.7 Deflection of Bodies in Point Contact 607
17.8
17.7.1
Significance of Stresses 611
Stress for Two Bodies in Line Contact: Loads Normal to
Contact Area 61 1
17.8.1 Maximum Principal Stresses: k = 0 613
17.8.2 Maximum Shear Stress: k = 0 613
17.8.3
Maximum Octahedral Shear Stress:
Stresses for Two Bodies in Line Contact: Loads Normal
and Tangent to Contact Area 613
17.9.1
Roller on Plane 614
17.9.2
Principal Stresses 616
17.9.3 Maximum Shear Stress 617
17.9.4
Maximum Octahedral Shear Stress 617
17.9.5
Effect of Magnitude of Friction
Coefficient 618
17.9.6 Range of Shear Stress for One Load
Cycle 619
Problems 622
References 623
k=O 613
17.9
CHAPTER 18 CREEP: TIME-DEPENDENT
DEFORMATION 624
18.1 Definition of Creep and the Creep Curve 624
18.2
The Tension Creep Test for Metals 626
18.3 One-Dimensional Creep Formulas for Metals Subjected
to Constant Stress and Elevated Temperature 626 XiV
CONTENTS
18.4
One-Dimensional Creep of Metals Subjected to
Variable Stress and Temperature 631
18.4.1
Preliminary Concepts 631
18.4.2
Similarity of Creep Curves 633
18.4.3 Temperature Dependency 635
18.4.4 Variable Stress and Temperature 635
18.5.1
General Discussion 640
Flow Rule for Creep of Metals Subjected to Multiaxial
States of stress 643
18.6.1
Steady-State Creep 644
18.6.2 Nonsteady Creep 648
18.7
An Application of Creep of Metals 649
18.7.1
Summary 650
18.8
Creep of Nonmetals 650
18.8.1
Asphalt 650
18.8.2
Concrete 651
18.8.3
Wood 652
References 654
18.5
Creep Under Multiaxial States of Stress 640
18.6
APPENDIX A
SELECTED MATERIALS 657
AVERAGE MECHANICAL PROPERTIES OF
APPENDIX 8
OF A PLANE AREA 660
SECOND MOMENT (MOMENT OF INERTIA)
B. 1 Moments of Inertia of a Plane Area 660
B.2
Parallel Axis Theorem 661
B.3
Transformation Equations for Moments and Products of
Inertia 664
B.3.1
Principal Axes of Inertia 665
Problems 666
APPENDIX C
SECTIONS 668
PROPERTIES OF STEEL CROSS
AUTHOR tNDEX 673
SUBJECT INDEX 676
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