高等材料力学和实用应力分析 第2版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

高等材料力学和实用应力分析 第2版PDF格式电子书版下载

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CHAPTER ONE BASIC CONCEPTS OF FORCE,STRESS,STRAIN,AND DISPLACEMENT1

1．0 Introduction1

1．1 Force Diagrams2

1．2 Force Distributions2

1．3 Stress10

1．4 Strain,Stress—Strain Relations20

1．4．1 Normal Strains20

1．4．2 Shear Strains23

1．4．3 Thermal Strains24

1．5 Displacements, Strain-Displacement Relations24

1．5．1 Rectangular Coordinates24

1．5．2 Cylindrical Coordinates29

1．6 Summary of Important Relationships33

1．7 Problems37

CHAPTER TWO STRESS AND STRAIN.TRANSFORMATIONS,EQUILIBRIUM,AND COMPATIBILITY46

2．0 Introduction46

2．1．1 General Three-Dimensional Stress Transformations47

2．1 Stress Transformations47

2．1．2 Plans Stress Transformations56

2．1．3 Mohr s Circle for Plane Stress57

2．1．4 Three-Dimensional Stress Transformation Simplified62

2．1．5 Principal Stresses66

2．1．6 Mohr s Circles in Three Dimensions72

2．1．7 Maximum Shear Stress75

2．2．1 Strain Transformations,General78

2．2 Strain Transformations78

2．2．2 Principal Strains81

2．3 Generalized Stress-Strain Relations82

2．4 The Equilibrium Equations86

2．5 Compatibility89

2．6 Summary of Important Equations97

2．7 Problems101

CHAPTER THREE A REVIEW OF THE FUNDAMENTAL FORMULATIONS OF STRESS,STRAIN,AND DEFLECTION113

3．0 Introduction113

3．2 Axial Loading114

3．2．1 Axial Stresses114

3．1 Assumptions and Limitations114

3．2．2 Axial Strains and Deflections117

3．3 Torsion of Circular Shafts129

3．3．1 Torsional Stresses129

3．3．2 Torsional Strains and Deflections130

3．4 Beams in Bending132

3．4．1 Shear Force and Bending Moment Equations and Diagrams132

3．4．2 Bending Stresses138

3．4．3 Transverse Shear Stresses143

3．4．4 Bending Strains and Deflections152

3．5 Bending of Symmetric Beams in Two Planes158

3．6 Thin-Walled Pressure Vessels162

3．6．1 Stresses162

3．6．2 Strains and Deflections in a Circular Cylinder166

3．7 Superposition166

3．8 Statically Indeterminate Problems175

3．9 Stress and Strain Transformations185

3．9．1 Plane Stress185

3．9．2 Principal Stress186

3．9．3 Maximum In-Plane Shear Stress189

3．9．4 Strain Transformations191

3．10 Buckling Instability of Columns in Compression192

3．11 Problems199

3．12References219

CHAPTER FOUR CONCEPTS FROM THE THEORY OF ELASTICITY220

4．0 Introduction220

4．1．1 Definition221

4．1 Plane Elastic Problems221

4．1．2 Governing Equations222

4．1．3 Conversion between Plane Stress and Plane Strain Problems224

4．2 The Airy Stress Function225

4．2．1 Rectangular Coordinates225

4．2．2 Polar Coordinates230

4．2．3 Curved Beam in Bending233

4．2．4 Circular Hole in a Plate Loaded in Tension235

4．2．5 Concentrated Force on a Flat Boundary (Flamant Solution)238

4．2．6 Disk with Opposing Concentrated Forces240

4．3．1 General Formulation244

4．3 Prandtl s Stress Function for Torsion244

4．3．2 Torsion on a Rectangular Cross Section251

4．4 Discussion255

4．5 Problems255

4．6 References260

CHAPTER FIVE TOPICS FROM ADVANCED MECHANICS OF MATERIALS261

5．0 Introduction261

5．1 Shear Flow261

5．2 Torsion of Closed Thin-Walled Tubes262

5．2．1 Single Cell Sections in Torsion263

5．2．2 Multiple Cell Sections in Torsion267

5．3 Bending of Unsymmetrical Beams272

5．3．1 Stresses272

5．3．2 Deflections279

5．4 Further Discussion of Transverse Shear Stresses280

5．4．1 Shear Flow in Open Thin-Walled Beams280

5．4．2 Shear Center for Open Thin-Walled Beams with One Axis of Symmetry283

5．4．3 Shear Center for Open Unsymmetric Thin-Walled Beams291

5．4．4 Shear in Closed Thin-Walled Sections296

5．5 Composite Beams in Bending302

5．6 Curved Beams309

5．6．1 Tangential Stresses309

5．6．2 Approximate and Numerical Calculations of e317

5．6．3 Radial Stresses322

5．7 Bending of Thin Flat Plates324

5．7．1 Governing Equations in Rectangular Coordinates324

5．7．2 Tabulated Solutions of Uniformly Loaded Rectangular Plates329

5．7．3 Governing Equations for Axisymmetric Circular Plates in Bending330

5．7．4 Tabulated Solutions of Circular Plates336

5．7．5 Superposition341

5．8 Thick-Walled Cylinders and Rotating Disks348

5．9 Contact Stresses357

5．9．1 Distributed Contact Loading357

5．9．2 Contact Between Curved Surfaces361

5．10 Stress Concentrations364

5．11 Problems371

5．12 References403

6．0 Introduction404

CHAPTER SIX ENERGY TECHNIQUES IN STRESS ANALYSIS404

6．1 Work409

6．2 Strain Energy410

6．2．1 Uniaxial Case410

6．2．2 Additional Normal Stresses411

6．2．3 Shear Stress411

6．2．4 General State of Stress412

6．2．5 Plane Stress413

6．3．2 Torsional Loading of a Solid Circular Bar414

6．3．1 Axial Loading414

6．3 Total Strain Energy in Bars with Simple Loading Conditions414

6．3．3 Transverse Loading415

6．4 Castigliano s First Theorem419

6．5 The Complementary-Energy Theorem424

6．6 Castigliano s Second Theorem428

6．6．1 Deflections of Statically Determinate Problems428

6．6．2 Deflections Due to Temperature Changes445

6．7 Deflections of Thick-Walled Curved Beams446

6．8 Castigliano s Second Theorem Applied to Statically Indeterminate Problems450

6．9 The Virtual Load Method456

6．9．1 Axial Loading458

6．9．2 Torsional Loading459

6．9．3 Bending460

6．10 The Virtual Load Method Applied to Statically Indeterminate Problems462

6．11 Rayleigh s Method Applied to Beams in Bending464

6．12 The Rayleigh-Ritz Technique Applied to Beams in Bending469

6．13 Straight Beams Undergoing the Combined Effects of Axial and Transverse Loading471

6．13．1 Unconstrained Beams471

6．13．2 Constrained Beams479

6．14 Problems483

CHAPTER SEVEN STRENGTH，FAILURE MODES，AND DESIGN CONSIDERATIONS498

7．0 Introduction498

7．1 Strength498

7．2 The Design Factor500

7．3 Strength Theories505

7．3．1 Basis of Theories505

7．3．2 Tresca （Maximum-Shear-Stress）Theory for Ductile Materials509

7．3．3 von Mises （Maximum-Energy-of-Distortion）Theory for Ductile Materials509

7．3．4 Comparison between the Tresca and von Mises Theories（Plane Stress）512

7．3．5 Coulomb-Mohr Theory for Brittle Materials513

7．3．6 Design Equations515

7．4 Fracture Mechanics518

7．4．1 Introduction518

7．4．2 Crack Modes and the Stress Intensity Factor520

7．4．3 The Plastic Zone Correction526

7．5 Fatigue Analysis532

7．5．1 Fatigue Strength and Endurance Limit532

7．5．2 Cyclic Stress with a Static Component534

7．5．3 Fatigue Strength Reduction Factors538

7．5．4 Equivalent Stresses（Plane Stress）541

7．5．5 Estimating Life for Nonreversing or Nonrepetitive Stress Cycles543

7．6 Structural Stability546

7．6．1 Column Buckling547

7．6．2 Buckling of Plates556

7．7 Inelastic Behavior561

7．7．1 EPP Materials561

7．7．2 Plastic Behavior of Straight Beams in Bending564

7．7．3 Depth of the Plastic Zone（Rectangular Beam）568

7．7．4 Residual Stresses（Rectangular Beam）569

7．7．5 Residual Stresses and Fatigue（Rectangular Beam）571

7．8 Engineering Approximations Used in Statically Indeterminate Problems573

7．8．1 Considering Deflections of Flexible Elements Only573

7．8．2 Limit Analysis579

7．9 Problems584

7．10 References596

8．0 Introduction597

CHAPTER EIGHT EXPERIMENTAL STRESS ANALYSIS597

8．1 Dimensional Analysis598

8．2 Analysis Techniques601

8．2．1 Symmetry601

8．2．2 When a Surface Perpendicular to a Free Surface Exists Without Shear Stress602

8．3 Strain Gages,General604

8．4 Strain Gage Configurations607

8．5 Strain Gage Instrumentation610

8．5．1 The Wheatstone Bridge610

8．5．2 Commercial Strain Gage Indicator Systems613

8．6 Characteristics of Strain Gage Measurements616

8．6．1 Linearity of the Grid Material617

8．6．2 Transverse Sensitivity of the Gage617

8．6．3 Temperature Effects620

8．6．4 Lead-Wire Connection623

8．6．5 Strain Gradient624

8．6．6 Zero Shift and Hysteresis Effects624

8．6．7 Dynamic Response624

8．6．8 Gage-Current Heating Effects625

8．7．1 Electromagnetic Wave Representation of Light626

8．6．9 Noise from Electric and/or Magnetic Fields626

8．7 The Theory of Photoelasticity626

8．7．2 Polarization628

8．7．3 Refraction630

8．7．4 Birefringence631

8．7．5 Stress and Birefringence634

8．7．6 Isoclinic Fringe Analysis637

8．7．7 Isochromatic Fringe Analysis642

8．8．1 Photoelastic Material Calibrations645

8．8 Techniques Used in Photoelastic Applications645

8．8．2 Fractional Fringe Orders647

8．8．3 Separation of the Principal Stresses,σ1 andσ2650

8．8．4 Reflection Photoelasticity654

8．8．5 Stress Freezing in Three-Dimensional Photoelasticity660

8．9 Problems662

8．10 References672

CHAPTER NINE INTRODUCTION TO THE FINITE ELEMENT METHOD673

9．0 Introduction673

9．2 The Truss Element677

9．1 Node and Element Subscript Notation677

9．2．1 The One-Dimensional Truss Element-Direct Stiffness Method678

9．2．2 The One-Dimensional Truss Element-The Rayleigh-Ritz Method681

9．2．3 The Assembly Process683

9．2．4 Distributed Loads692

9．2．5 Thermal Stress694

9．2．6 The Two-Dimensional Truss Element698

9．2．7 Skew Supports708

9．2．8 The Three-Dimensional Truss Element711

9．3 Beam and Frame Elements718

9．3．1 The Planar Beam Element718

9．3．2 Distributed Loading727

9．3．3 Pin Releases(Hinges)in Beam Elements736

9．3．4 Beams in Two-Plane Bending741

9．3．5 The Frame Element742

9．3．6 Three-Dimensional Transformation of the Frame Element743

9．3．7 Load-Stiffening and Buckling of Beams747

9．4 Two-Dimensional Elastic Elements757

9．4．1 The Two-Dimensional Constant Strain Triangle(CST)Element758

9．4．2 The Two-Dimensional Isoparametric Quadrilateral Element767

9．5 Higher-Order and Three-Dimensional Elastic Elements777

9．6 Problems778

9．7 References788

CHAPTER TEN FINITE ELEMENT MODELING TECHNIQUES789

10．0 Introduction789

10．1 Planning and Creating the Finite Element Model(Preprocessing)791

10．2．1 Introductory Remarks792

10．2 Element Selection and Mesh Strategy792

10．2．2 Element Selection796

10．2．3 Element Input Information802

10．2．4 Mesh Generation803

10．2．5 Two-Dimensional Meshing Strategies808

10．2．6 Submodeling811

10．2．7 Symmetry812

10．3 Load Application818

10．3．1 Nodal Loads819

10．3．3 Forcing Specified Nonzero Boundary Conditions with Boundary Elements820

10．3．2 Element Loads820

10．3．4 Multiple Load Cases822

10．3．5 Load Scale Factors823

10．4 Constraints823

10．5 Preprocessing Checks829

10．6 Processing the Model830

10．7 Postprocessing830

10．7．1 Graphic Output831

10．8 Closure834

10．7．2 Text Output834

10．9 Problems835

10．10 References842

APPENDIX A SI AND USCU CONVERSIONS843

APPENDIX B PROPERTIES OF CROSS SECTIONS845

B．1 Tables845

B．2 Combinations of Sections847

APPENDIX C BEAMS IN BENDING849

D．0 Introduction858

APPENDIX D SINGULARITY FUNCTIONS858

D．1 Integral Relations for Beams in Bending859

D．2 Singularity Functions860

APPENDIX E PRINCIPAL SECOND-AREA MOMENTS868

E．1 Second-Area Moments868

E．2 Principal Second-Area Moments870

APPENDIX F STRESS CONCENTRATION FACTORS873

APPENDIX G STRAIN GAGE ROSETTE EQUATIONS879

G．1 Three-Element Rectangular Rosette879

G．2 Three-Element Delta Rosette881

H．0 Introduction883

APPENDIX H CORRECTIONS FOR THE TRANSVERSE SENSITIVITY OF STRAIN GAGES883

H．1 Corrections for the Two-Gage Rectangular Rosette884

H．2 Corrections for the Three-Gage Rectangular Rosette885

H．3 Corrections for the Three-Gage Delta(120°)Rosette887

APPENDIX I MATRIX ALGEBRA AND CARTESIAN TENSORS889

I．0 Introduction889

I．1 Matrix Algebra890

I．1．1 Addition890

I．1．3 Matrix Multiplication891

I ．1．2 Scalar Multiplication891

I．1．4 Transposition892

I．1．5 Determinant of a Matrix892

I．1．6 Cofactor Matrix893

I．1．7 Matrix Inversion894

I．1．8 Eigenvalues and Eigenvectors895

I．2 Cartesian Tensors896

APPENDIX J ANSWERS TO MOST ODD-NUMBERED PROBLEMS900

INDIX913