Theory of Elasticity and Stress Concentration

1 - Title Page [Seite 5]
2 - Copyright [Seite 6]
3 - Contents [Seite 7]
4 - Preface [Seite 15]
5 - Preface for Part I: Theory of Elasticity [Seite 17]
6 - Part I Nomenclature [Seite 19]
7 - Preface for Part II: Stress Concentration [Seite 21]
8 - Part II Nomenclature [Seite 25]
9 - Acknowledgments [Seite 27]
10 - Part I Theory of Elasticity [Seite 29]
10.1 - Chapter 1 Stress [Seite 31]
10.1.1 - 1.1 Stress at the Surface of a Body [Seite 31]
10.1.1.1 - 1.1.1 Normal Stress [Seite 31]
10.1.1.2 - 1.1.2 Shear Stress [Seite 31]
10.1.2 - 1.2 Stress in the Interior of a Body [Seite 32]
10.1.3 - 1.3 Two Dimensional Stress, Three Dimensional Stress and Stress Transformation [Seite 33]
10.1.3.1 - 1.3.1 Normal Stress [Seite 33]
10.1.3.2 - 1.3.2 Shear Stress [Seite 34]
10.1.3.3 - 1.3.3 Stress in an Arbitrary Direction [Seite 35]
10.1.3.4 - 1.3.4 Principal Stresses [Seite 42]
10.1.3.5 - 1.3.5 Principal Shear Stresses [Seite 46]
10.1.4 - Problems of Chapter 1 [Seite 47]
10.2 - Chapter 2 Strain [Seite 49]
10.2.1 - 2.1 Strains in Two Dimensional Problems [Seite 49]
10.2.2 - 2.2 Strains in Three Dimensional Problems [Seite 52]
10.2.3 - 2.3 Strain in an Arbitrary Direction [Seite 52]
10.2.3.1 - 2.3.1 Two Dimensional Case [Seite 52]
10.2.3.2 - 2.3.2 Three Dimensional Case [Seite 54]
10.2.4 - 2.4 Principal Strains [Seite 54]
10.2.5 - 2.5 Conditions of Compatibility [Seite 56]
10.2.6 - Problems of Chapter 2 [Seite 58]
10.2.7 - Reference [Seite 59]
10.3 - Chapter 3 Relationship between Stresses and Strains: Generalized Hooke´s Law [Seite 61]
10.3.1 - Problems of Chapter 3 [Seite 66]
10.4 - Chapter 4 Equilibrium Equations [Seite 69]
10.4.1 - Problems of Chapter 4 [Seite 72]
10.5 - Chapter 5 Saint Venant´s Principle and Boundary Conditions [Seite 73]
10.5.1 - 5.1 Saint Venant´s Principle [Seite 73]
10.5.2 - 5.2 Boundary Conditions [Seite 75]
10.5.2.1 - 5.2.1 Stress Boundary Conditions [Seite 75]
10.5.2.2 - 5.2.2 Displacement Boundary Conditions [Seite 76]
10.5.2.3 - 5.2.3 Mixed Boundary Conditions [Seite 76]
10.5.3 - Problems of Chapter 5 [Seite 77]
10.6 - Chapter 6 Two Dimensional Problems [Seite 81]
10.6.1 - 6.1 Plane Stress and Plane Strain [Seite 81]
10.6.1.1 - 6.1.1 Plane Stress [Seite 81]
10.6.1.2 - 6.1.2 Plane Strain [Seite 82]
10.6.2 - 6.2 Basic Conditions for Exact Solutions: Nature of Solutions [Seite 84]
10.6.3 - 6.3 Airy´s Stress Function [Seite 86]
10.6.4 - 6.4 Hollow Cylinder [Seite 88]
10.6.5 - 6.5 Stress Concentration at a Circular Hole [Seite 91]
10.6.6 - 6.6 Stress Concentration at an Elliptical Hole [Seite 97]
10.6.7 - 6.7 Stress Concentration at a Hole in a Finite Width Plate [Seite 101]
10.6.8 - 6.8 Stress Concentration at a Crack [Seite 103]
10.6.9 - 6.9 Stress Field due to a Point Force Applied at the Edge of a Semi-Infinite Plate [Seite 110]
10.6.10 - 6.10 Circular Disk Subjected to Concentrated Force [Seite 115]
10.6.11 - Problems of Chapter 6 [Seite 116]
10.6.12 - Appendix of Chapter 6 [Seite 119]
10.6.13 - References [Seite 120]
10.7 - Chapter 7 Torsion of a Bar with Uniform Section [Seite 123]
10.7.1 - 7.1 Torsion of Cylindrical Bars [Seite 123]
10.7.2 - 7.2 Torsion of Bars Having Thin Closed Section [Seite 125]
10.7.3 - 7.3 Saint Venant´s Torsion Problems [Seite 127]
10.7.4 - 7.4 Stress Function in Torsion [Seite 128]
10.7.4.1 - 7.4.1 Equilibrium Condition [Seite 129]
10.7.4.2 - 7.4.2 Compatibility Equation [Seite 129]
10.7.4.3 - 7.4.3 Boundary Conditions [Seite 130]
10.7.5 - 7.5 Membrane Analogy: Solution of Torsion Problems by Using the Deformation of Pressurized Membrane [Seite 133]
10.7.6 - 7.6 Torsion of Bars Having a Thin Unclosed Cross Section [Seite 135]
10.7.7 - 7.7 Comparison of Torsional Rigidity between a Bar with an Open Section and a Bar with a Closed Section [Seite 140]
10.7.8 - Problems of Chapter 7 [Seite 142]
10.7.9 - Reference [Seite 143]
10.8 - Chapter 8 Energy Principles [Seite 145]
10.8.1 - 8.1 Strain Energy [Seite 145]
10.8.2 - 8.2 Uniqueness of the Solutions of Elasticity Problems [Seite 150]
10.8.3 - 8.3 Principle of Virtual Work [Seite 151]
10.8.4 - 8.4 Principle of Minimum Potential Energy [Seite 154]
10.8.5 - 8.5 Castigliano´s Theorem [Seite 157]
10.8.6 - 8.6 The Reciprocal Theorem [Seite 161]
10.8.7 - Problems of Chapter 8 [Seite 164]
10.8.8 - Reference [Seite 164]
10.9 - Chapter 9 Finite Element Method [Seite 165]
10.9.1 - 9.1 FEM for One Dimensional Problems [Seite 166]
10.9.2 - 9.2 Analysis of Plane Stress Problems by the Finite Element Method [Seite 170]
10.9.2.1 - 9.2.1 Approximation of 2D Plate Problems by a Set of Triangular Elements [Seite 170]
10.9.2.2 - 9.2.2 Relationship between Stress and Strain in Plane Stress Problem [Seite 173]
10.9.2.3 - 9.2.3 Stiffness Matrix of a Triangular Plate Element [Seite 173]
10.9.2.4 - 9.2.4 Stiffness Matrix of the Total Structure [Seite 180]
10.9.2.5 - 9.2.5 Expression of Boundary Conditions and Basic Knowledge for Element Meshing [Seite 183]
10.9.3 - Problems of Chapter 9 [Seite 185]
10.10 - Chapter 10 Bending of Plates [Seite 189]
10.10.1 - 10.1 Simple Examples of Plate Bending [Seite 189]
10.10.2 - 10.2 General Problems of Plate Bending [Seite 193]
10.10.3 - 10.3 Transformation of Bending Moment and Torsional Moment [Seite 194]
10.10.4 - 10.4 Differential Equations for a Plate Subjected to Surface Loads and their Applications [Seite 197]
10.10.5 - 10.5 Boundary Conditions in Plate Bending Problems [Seite 201]
10.10.6 - 10.6 Polar Coordinate Expression of the Quantities of Plate Bending [Seite 204]
10.10.7 - 10.7 Stress Concentration in Plate Bending Problems [Seite 205]
10.10.7.1 - 10.7.1 Stress Concentration at a Circular Hole in Bending a Wide Plate [Seite 205]
10.10.7.2 - 10.7.2 Stress Concentration at an Elliptical Hole in Bending a Wide Plate [Seite 205]
10.10.8 - 10.8 Bending of a Circular Plate [Seite 206]
10.10.9 - Problems of Chapter 10 [Seite 213]
10.10.10 - References [Seite 214]
10.11 - Chapter 11 Deformation and Stress in Cylindrical Shells [Seite 215]
10.11.1 - 11.1 Basic Equations [Seite 215]
10.11.1.1 - 11.1.1 Equilibrium Condition [Seite 215]
10.11.1.2 - 11.1.2 Forces and Deformations [Seite 217]
10.11.1.3 - 11.1.3 Basic Differential Equation [Seite 219]
10.11.2 - 11.2 Various Problems of Cylindrical Shells [Seite 220]
10.11.3 - Problems of Chapter 11 [Seite 222]
10.12 - Chapter 12 Thermal Stress [Seite 225]
10.12.1 - 12.1 Thermal Stress in a Rectangular Plate - Simple Examples of Thermal Stress [Seite 225]
10.12.1.1 - 12.1.1 Constant Temperature Rise ?T(x,y) = T0 (Constant) [Seite 225]
10.12.1.2 - 12.1.2 Linear Temperature Distribution ?T(x,y) = 2T0y/h [Seite 226]
10.12.1.3 - 12.1.3 Quadratic Temperature Distribution ?T(x,y) = 2T0(y/h)2 [Seite 227]
10.12.2 - 12.2 Thermal Stress in a Circular Plate [Seite 229]
10.12.3 - 12.3 Thermal Stress in a Cylinder [Seite 232]
10.12.4 - Problems of Chapter 12 [Seite 233]
10.13 - Chapter 13 Contact Stress [Seite 235]
10.13.1 - 13.1 2D Contact Stress [Seite 236]
10.13.1.1 - 13.1.1 Stress and Deformation for Uniform Pressure Distribution [Seite 236]
10.13.1.2 - 13.1.2 Contact Stress by a Rigid Punch [Seite 239]
10.13.1.3 - 13.1.3 Stress Field by Elliptical Contact Stress Distribution [Seite 240]
10.13.2 - 13.2 3D Contact Stress [Seite 241]
10.13.2.1 - 13.2.1 Stress and Displacement Due to a Constant Distributed Loading [Seite 242]
10.13.2.2 - 13.2.2 Contact Stress Due to a Rigid Circular Punch [Seite 244]
10.13.2.3 - 13.2.3 Contact Between Two Spheres [Seite 244]
10.13.2.4 - 13.2.4 Contact Between Two Cylinders [Seite 245]
10.13.3 - Problems of Chapter 13 [Seite 246]
10.13.4 - References [Seite 247]
10.14 - Answers and Hints for Part I Problems [Seite 249]
10.15 - Appendix for Part I [Seite 269]
10.15.1 - A.1 Rule of Direction Cosines [Seite 269]
10.15.2 - A.2 Green's Theorem and Gauss' Divergence Theorem [Seite 269]
10.15.2.1 - A.2.1 2D Green's Theorem [Seite 269]
10.15.2.2 - A.2.2 3D Green's Theorem [Seite 272]
11 - Part II Stress Concentration [Seite 273]
11.1 - Chapter 1 Stress Concentration in Two Dimensional Problems [Seite 275]
11.1.1 - 1.1 Stress Concentration at a Circular Hole [Seite 275]
11.1.2 - 1.2 Stress Concentration at an Elliptical Hole [Seite 281]
11.1.2.1 - 1.2.1 Stress Distribution and Stress Concentration Under Remote Stress ?y or ?x [Seite 281]
11.1.2.2 - 1.2.2 Stress Concentration and Stress Distribution Under Remote Shear Stress ?xy [Seite 285]
11.1.3 - 1.3 Stress Concentration at a Hole in a Finite Width Plate [Seite 288]
11.1.4 - 1.4 Concept of Equivalent Ellipse [Seite 291]
11.1.4.1 - 1.4.1 Basic Concept [Seite 291]
11.1.4.2 - 1.4.2 Difference of Stress Concentration at a Circular Hole in an Infinite Plate and at a Semi-Circular Hole on the Edge of... [Seite 295]
11.1.4.3 - 1.4.3 Limitation of Applicability of the Concept of the Equivalent Ellipse [Seite 296]
11.1.5 - 1.5 Stress Concentration at Inclusions [Seite 298]
11.1.6 - Problems of Chapter 1 [Seite 302]
11.1.7 - References [Seite 306]
11.2 - Chapter 2 Stress Concentration at Cracks [Seite 307]
11.2.1 - 2.1 Singular Stress Distribution in the Neighborhood of a Crack Tip [Seite 307]
11.2.2 - 2.2 Stress Distribution Near Crack Tip Under Biaxial Stress Field [Seite 309]
11.2.3 - 2.3 Distribution of Shear Stress Near Crack Tip [Seite 310]
11.2.4 - 2.4 Short Cracks and Long Cracks [Seite 311]
11.2.5 - 2.5 Plastic Zone Ahead of Crack Tip: Dugdale Model [Seite 312]
11.2.6 - 2.6 Approximate Estimation Method of KI [Seite 314]
11.2.7 - 2.7 Crack Propagation Path [Seite 316]
11.2.7.1 - 2.7.1 Propagation Direction of Mode I Crack [Seite 318]
11.2.7.2 - 2.7.2 Propagation Direction of Mode II Crack [Seite 322]
11.2.7.3 - 2.7.3 Propagation Direction of Mode III Crack [Seite 322]
11.2.8 - Problems of Chapter 2 [Seite 324]
11.2.9 - References [Seite 327]
11.3 - Chapter 3 Stress Concentration in Three Dimensional Problems [Seite 329]
11.3.1 - 3.1 Stress Concentration at a Spherical Cavity [Seite 329]
11.3.2 - 3.2 Stress Concentration at a Spherical Inclusion [Seite 330]
11.3.3 - 3.3 Stress Concentration at an Axially Symmetric Ellipsoidal Inclusion [Seite 331]
11.3.4 - 3.4 Stress Concentration at a Surface Pit [Seite 331]
11.3.5 - 3.5 Stress Concentration at a 3D Crack [Seite 338]
11.3.5.1 - 3.5.1 Basic Problems [Seite 338]
11.3.5.2 - 3.5.2 Approximate Equation for the Stress Intensity Factor KI for a Crack of Arbitrary Shape in an Infinite Body [Seite 340]
11.3.5.3 - 3.5.3 Approximate Formula of the Stress Intensity Factor KI for a Crack of Arbitrary Shape at the Surface of a Semi-Infinit... [Seite 342]
11.3.6 - Problems of Chapter 3 [Seite 343]
11.3.7 - References [Seite 344]
11.4 - Chapter 4 Interaction Effects of Stress Concentration [Seite 347]
11.4.1 - 4.1 Interaction Effect which Enhances Stress Concentration [Seite 347]
11.4.2 - 4.2 Interaction Effect which Mitigates Stress Concentration [Seite 350]
11.4.3 - 4.3 Stress Concentration at Bolt Threads [Seite 352]
11.4.4 - Problems of Chapter 4 [Seite 360]
11.4.5 - References [Seite 362]
11.5 - Chapter 5 Notch Effect and Size Effect in Fatigue: Viewpoint from Stress Concentration [Seite 363]
11.5.1 - Problem of Chapter 5 [Seite 368]
11.5.2 - References [Seite 369]
11.6 - Chapter 6 Stress Concentration in Plate Bending [Seite 371]
11.6.1 - 6.1 Stress Concentration at a Circular Hole in a Wide Plate Under Bending [Seite 371]
11.6.2 - 6.2 Stress Concentration at an Elliptical Hole in a Wide Plate Under Bending [Seite 373]
11.6.3 - Problems of Chapter 6 [Seite 373]
11.6.4 - References [Seite 374]
11.7 - Chapter 7 Relevant Usage of Finite Element Method [Seite 375]
11.7.1 - 7.1 Fundamentals for Element Meshing [Seite 375]
11.7.2 - 7.2 Elastic-Plastic Analysis [Seite 376]
11.7.3 - 7.3 Element Meshing for Cracks and Very Sharp Notches [Seite 378]
11.7.4 - Problems of Chapter 7 [Seite 380]
11.7.5 - References [Seite 383]
11.8 - Chapter 8 Hollow Cylinder Subjected to Internal or External Pressure [Seite 385]
11.8.1 - 8.1 Basic Solution [Seite 385]
11.8.2 - 8.2 Crack at Inner Wall of Hollow Cylinder Under Internal Pressure [Seite 386]
11.8.3 - 8.3 Shrink Fit Problems [Seite 387]
11.8.3.1 - 8.3.1 Shrink Fit of Shaft and Hollow Cylinder [Seite 391]
11.8.4 - 8.4 Other Related Problems [Seite 391]
11.8.5 - Problem of Chapter 8 [Seite 401]
11.8.6 - Reference [Seite 402]
11.9 - Chapter 9 Circular Disk Subjected to Concentrated Point Forces [Seite 403]
11.9.1 - 9.1 Basic Solution [Seite 403]
11.9.2 - 9.2 Circular Hole in Circular Disk [Seite 404]
11.9.3 - 9.3 Various Concentrated Forces [Seite 406]
11.9.4 - Problems of Chapter 9 [Seite 409]
11.9.5 - Reference [Seite 410]
11.10 - Chapter 10 Stress Concentration by Point Force [Seite 411]
11.10.1 - 10.1 Point Force Acting at the Edge of Semi-Infinite Plate [Seite 411]
11.10.2 - 10.2 Point Force Acting in Infinite Plate [Seite 413]
11.10.3 - 10.3 Point Force Acting at the Inner Edge of a Circular Hole [Seite 413]
11.10.4 - 10.4 Applications of Solutions [Seite 414]
11.10.5 - 10.5 Point Force Acting on the Surface of Semi-Infinite Body [Seite 417]
11.10.6 - References [Seite 417]
11.11 - Chapter 11 Stress Concentration by Thermal Stress [Seite 419]
11.11.1 - 11.1 Thermal Residual Stress Around a 2D Circular Inclusion [Seite 419]
11.11.2 - 11.2 Stress Concentration Due to Thermal Shock [Seite 422]
11.11.3 - 11.3 Thermal Residual Stress Around a Spherical Inclusion [Seite 422]
11.11.4 - Reference [Seite 424]
11.12 - Chapter 12 Stress Concentration Due to Dislocations [Seite 425]
11.12.1 - 12.1 Basic Equations [Seite 425]
11.12.2 - 12.2 Stress Concentration Due to Slip Bands [Seite 426]
11.12.3 - References [Seite 428]
11.13 - Chapter 13 Stress Concentration Due to Contact Stress [Seite 429]
11.13.1 - 13.1 Basic Nature of Contact Stress Field [Seite 429]
11.13.2 - 13.2 Stress Concentration Due to 2D Rigid Punch [Seite 431]
11.13.3 - 13.3 Stress Concentration Due to 3D Circular Rigid Punch [Seite 432]
11.13.4 - 13.4 Stress Concentration Due to Contact of Two Elastic Bodies [Seite 433]
11.13.5 - Reference [Seite 434]
11.14 - Chapter 14 Strain Concentration [Seite 435]
11.14.1 - References [Seite 443]
11.15 - Answers and Hints for Part II Problems [Seite 445]
11.16 - Appendices for Part II [Seite 453]
11.16.1 - A.1 Basis of the Theory of Elasticity [Seite 453]
11.16.1.1 - A.1.1 Rule of Shear Stress [Seite 453]
11.16.1.2 - A.1.2 Stress Transformation Equations [Seite 454]
11.16.1.3 - A.1.3 Principal Stresses [Seite 455]
11.16.1.4 - A.1.4 Stress in a Plate of Arbitrary Shape Subjected to External Pressure p along the Outer Periphery [Seite 456]
11.16.1.5 - A.1.5 Relationship between Strains and Displacements in Axially Symmetric Problems [Seite 458]
11.16.1.6 - A.1.6 Hooke´s Law of Isotropic and Homogeneous Elastic Material [Seite 459]
11.16.2 - A.2 Stress Field at Crack Tip [Seite 461]
11.16.2.1 - A.2.1 Expression of Stresses and Displacements (u, v) in x, y, z Orthogonal Coordinate System [Seite 461]
11.16.3 - A.3 Stress Concentration for a Circular or an Elliptical Hole with Diameter Approaching to Width of Strip (a/W1.0) [Seite 463]
11.16.4 - A.4 Stress Concentration and Stress Distribution Due to Elliptic Hole in Infinite Plate Under Remote Stress (?x?y?xy) = (?x?y?xy) [Seite 465]
11.16.5 - A.5 Verification of Stress ?x*, ?y*, ?xy* at a Disk Center Subjected to Periodical Point Forces Around the Outer Periphery [Seite 466]
11.16.6 - References [Seite 469]
12 - Index [Seite 471]