Elasticity: Theory, Applications, and Numerics, Fifth Edition continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods.
Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples, exercises, and new or expanded coverage in recent areas of interest. Using MATLAB® software, numerical activities in the text are integrated with analytical problem solutions, and new symbolic software has now been introduced.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Preface - p. xi 7. Acknowledgments - p. xvii 8. About the Author - p. xix 9. Part 1. Foundations and elementary applications - p. P1 10. Chapter 1. Mathematical preliminaries - p. 3 11. 1.1 Scalar, vector, matrix, and tensor definitions - p. 3 12. 1.2 Index notation - p. 4 13. 1.3 Kronecker delta and alternating symbol - p. 7 14. 1.4 Coordinate transformations - p. 8 15. 1.5 Cartesian tensors - p. 10 16. 1.6 Principal values and directions for symmetric second-order tensors - p. 12 17. 1.7 Vector, matrix, and tensor algebra - p. 16 18. 1.8 Calculus of Cartesian tensors - p. 17 19. 1.9 Orthogonal curvilinear coordinates - p. 21 20. Chapter 2. Deformation: displacements and strains - p. 31 21. Chapter 3. Stress and equilibrium - p. 57 22. Chapter 4. Material behavior—linear elastic solids - p. 83 23. Chapter 5. Formulation and solution strategies - p. 97 24. Chapter 6. Strain energy and related principles - p. 125 25. Chapter 7. Two-dimensional formulation - p. 147 26. Chapter 8. Two-dimensional problem solution - p. 165 27. 8.1 Cartesian coordinate solutions using polynomials - p. 165 28. 8.2 Cartesian coordinate solutions using Fourier methods - p. 177 29. 8.3 General solutions in polar coordinates - p. 186 30. 8.4 Example polar coordinate solutions - p. 189 31. 8.4.1 Pressurized hole in an infinite medium - p. 191 32. 8.4.2 Stress-free hole in an infinite medium under equal biaxial loading at infinity - p. 191 33. 8.4.3 Biaxial and shear loading cases - p. 196 34. 8.4.4 Quarter-plane example - p. 197 35. 8.4.5 Half-space examples - p. 199 36. 8.4.6 Half-space under uniform normal stress over x≤0 - p. 199 37. 8.4.7 Half-space under concentrated surface force system (Flamant problem) - p. 200 38. 8.4.8 Half-space under a surface concentrated moment - p. 205 39. 8.4.9 Half-space under uniform normal loading over −a≥x≥a - p. 205 40. 8.4.10 Notch and crack problems - p. 209 41. 8.4.11 Pure bending example - p. 212 42. 8.4.12 Curved cantilever under end loading - p. 213 43. 8.5 Simple plane contact problems - p. 222 44. Chapter 9. Extension, torsion, and flexure of elastic cylinders - p. 245 45. 9.1 General formulation - p. 246 46. 9.2 Extension formulation - p. 246 47. 9.3 Torsion formulation - p. 247 48. 9.4 Torsion solutions derived from boundary equation - p. 257 49. 9.5 Torsion solutions using Fourier methods - p. 263 50. 9.6 Torsion of cylinders with hollow sections - p. 268 51. 9.7 Torsion of circular shafts of variable diameter - p. 271 52. 9.8 Flexure formulation - p. 274 53. 9.9 Flexure problems without twist - p. 278 54. Part 2. Advanced applications - p. P2 55. Chapter 10. Complex variable methods - p. 295 56. 10.1 Review of complex variable theory - p. 295 57. 10.2 Complex formulation of the plane elasticity problem - p. 302 58. 10.3 Resultant boundary conditions - p. 305 59. 10.4 General structure of the complex potentials - p. 307 60. 10.5 Circular domain examples - p. 309 61. 10.6 Plane and half-plane problems - p. 314 62. 10.7 Applications using the method of conformal mapping - p. 319 63. 10.8 Applications to fracture mechanics - p. 324 64. 10.9 Westergaard method for crack analysis - p. 327 65. Chapter 11. Anisotropic elasticity - p. 335 66. 11.1 Basic concepts - p. 335 67. 11.2 Material symmetry - p. 337 68. 11.3 Restrictions on elastic moduli - p. 344 69. 11.4 Torsion of a solid possessing a plane of material symmetry - p. 346 70. 11.5 Plane deformation problems - p. 353 71. 11.6 Applications to fracture mechanics - p. 365 72. 11.7 Curvilinear anisotropic problems - p. 369 73. Chapter 12. Thermoelasticity - p. 383 74. 12.1 Heat conduction and the energy equation - p. 383 75. 12.2 General uncoupled formulation - p. 385 76. 12.3 Two-dimensional formulation - p. 385 77. 12.4 Displacement potential solution - p. 388 78. 12.5 Stress function formulation - p. 389 79. 12.6 Polar coordinate formulation - p. 392 80. 12.7 Radially symmetric problems - p. 393 81. 12.8 Complex variable methods for plane problems - p. 398 82. Chapter 13. Displacement potentials and stress functions: applications to three-dimensional problems - p. 411 83. 13.1 Helmholtz displacement vector representation - p. 411 84. 13.2 Lamé's strain potential - p. 412 85. 13.3 Galerkin vector representation - p. 413 86. 13.4 Papkovich–Neuber and Naghdi–Hsu representation - p. 418 87. 13.5 Spherical coordinate formulations - p. 422 88. 13.6 Stress functions - p. 429 89. Chapter 14. Nonhomogeneous elasticity - p. 441 90. 14.1 Basic concepts - p. 441 91. 14.2 Plane problem of a hollow cylindrical domain under uniform pressure - p. 445 92. 14.3 Rotating disk problem - p. 452 93. 14.4 Point force on the free surface of a half-space - p. 457 94. 14.5 Antiplane strain problems - p. 466 95. 14.6 Torsion problem - p. 470 96. Chapter 15. Micromechanics applications - p. 485 97. 15.1 Dislocation modeling - p. 486 98. 15.2 Singular stress states - p. 490 99. 15.3 Elasticity theory with distributed cracks - p. 499 100. 15.4 Micropolar/couple-stress elasticity - p. 502 101. 15.5 Elasticity theory with voids - p. 511 102. 15.6 Doublet mechanics - p. 516 103. 15.7 Higher gradient elasticity theories - p. 521 104. 15.8 Meta and auxetic materials - p. 526 105. Chapter 16. Numerical finite and boundary element methods - p. 537 106. Appendix A. Basic field equations in Cartesian, cylindrical, and spherical coordinates - p. 563 107. Appendix B. Transformation of field variables between Cartesian, cylindrical, and spherical components - p. 569 108. Appendix C. MATLAB® Primer - p. 573 109. Appendix D. Review of mechanics of materials - p. 597 110. Index - p. 613
Elasticity: Theory, Applications, and Numerics, Fifth Edition continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods.
Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples, exercises, and new or expanded coverage in recent areas of interest. Using MATLAB® software, numerical activities in the text are integrated with analytical problem solutions, and new symbolic software has now been introduced.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Preface - p. xi 7. Acknowledgments - p. xvii 8. About the Author - p. xix 9. Part 1. Foundations and elementary applications - p. P1 10. Chapter 1. Mathematical preliminaries - p. 3 11. 1.1 Scalar, vector, matrix, and tensor definitions - p. 3 12. 1.2 Index notation - p. 4 13. 1.3 Kronecker delta and alternating symbol - p. 7 14. 1.4 Coordinate transformations - p. 8 15. 1.5 Cartesian tensors - p. 10 16. 1.6 Principal values and directions for symmetric second-order tensors - p. 12 17. 1.7 Vector, matrix, and tensor algebra - p. 16 18. 1.8 Calculus of Cartesian tensors - p. 17 19. 1.9 Orthogonal curvilinear coordinates - p. 21 20. Chapter 2. Deformation: displacements and strains - p. 31 21. Chapter 3. Stress and equilibrium - p. 57 22. Chapter 4. Material behavior—linear elastic solids - p. 83 23. Chapter 5. Formulation and solution strategies - p. 97 24. Chapter 6. Strain energy and related principles - p. 125 25. Chapter 7. Two-dimensional formulation - p. 147 26. Chapter 8. Two-dimensional problem solution - p. 165 27. 8.1 Cartesian coordinate solutions using polynomials - p. 165 28. 8.2 Cartesian coordinate solutions using Fourier methods - p. 177 29. 8.3 General solutions in polar coordinates - p. 186 30. 8.4 Example polar coordinate solutions - p. 189 31. 8.4.1 Pressurized hole in an infinite medium - p. 191 32. 8.4.2 Stress-free hole in an infinite medium under equal biaxial loading at infinity - p. 191 33. 8.4.3 Biaxial and shear loading cases - p. 196 34. 8.4.4 Quarter-plane example - p. 197 35. 8.4.5 Half-space examples - p. 199 36. 8.4.6 Half-space under uniform normal stress over x≤0 - p. 199 37. 8.4.7 Half-space under concentrated surface force system (Flamant problem) - p. 200 38. 8.4.8 Half-space under a surface concentrated moment - p. 205 39. 8.4.9 Half-space under uniform normal loading over −a≥x≥a - p. 205 40. 8.4.10 Notch and crack problems - p. 209 41. 8.4.11 Pure bending example - p. 212 42. 8.4.12 Curved cantilever under end loading - p. 213 43. 8.5 Simple plane contact problems - p. 222 44. Chapter 9. Extension, torsion, and flexure of elastic cylinders - p. 245 45. 9.1 General formulation - p. 246 46. 9.2 Extension formulation - p. 246 47. 9.3 Torsion formulation - p. 247 48. 9.4 Torsion solutions derived from boundary equation - p. 257 49. 9.5 Torsion solutions using Fourier methods - p. 263 50. 9.6 Torsion of cylinders with hollow sections - p. 268 51. 9.7 Torsion of circular shafts of variable diameter - p. 271 52. 9.8 Flexure formulation - p. 274 53. 9.9 Flexure problems without twist - p. 278 54. Part 2. Advanced applications - p. P2 55. Chapter 10. Complex variable methods - p. 295 56. 10.1 Review of complex variable theory - p. 295 57. 10.2 Complex formulation of the plane elasticity problem - p. 302 58. 10.3 Resultant boundary conditions - p. 305 59. 10.4 General structure of the complex potentials - p. 307 60. 10.5 Circular domain examples - p. 309 61. 10.6 Plane and half-plane problems - p. 314 62. 10.7 Applications using the method of conformal mapping - p. 319 63. 10.8 Applications to fracture mechanics - p. 324 64. 10.9 Westergaard method for crack analysis - p. 327 65. Chapter 11. Anisotropic elasticity - p. 335 66. 11.1 Basic concepts - p. 335 67. 11.2 Material symmetry - p. 337 68. 11.3 Restrictions on elastic moduli - p. 344 69. 11.4 Torsion of a solid possessing a plane of material symmetry - p. 346 70. 11.5 Plane deformation problems - p. 353 71. 11.6 Applications to fracture mechanics - p. 365 72. 11.7 Curvilinear anisotropic problems - p. 369 73. Chapter 12. Thermoelasticity - p. 383 74. 12.1 Heat conduction and the energy equation - p. 383 75. 12.2 General uncoupled formulation - p. 385 76. 12.3 Two-dimensional formulation - p. 385 77. 12.4 Displacement potential solution - p. 388 78. 12.5 Stress function formulation - p. 389 79. 12.6 Polar coordinate formulation - p. 392 80. 12.7 Radially symmetric problems - p. 393 81. 12.8 Complex variable methods for plane problems - p. 398 82. Chapter 13. Displacement potentials and stress functions: applications to three-dimensional problems - p. 411 83. 13.1 Helmholtz displacement vector representation - p. 411 84. 13.2 Lamé's strain potential - p. 412 85. 13.3 Galerkin vector representation - p. 413 86. 13.4 Papkovich–Neuber and Naghdi–Hsu representation - p. 418 87. 13.5 Spherical coordinate formulations - p. 422 88. 13.6 Stress functions - p. 429 89. Chapter 14. Nonhomogeneous elasticity - p. 441 90. 14.1 Basic concepts - p. 441 91. 14.2 Plane problem of a hollow cylindrical domain under uniform pressure - p. 445 92. 14.3 Rotating disk problem - p. 452 93. 14.4 Point force on the free surface of a half-space - p. 457 94. 14.5 Antiplane strain problems - p. 466 95. 14.6 Torsion problem - p. 470 96. Chapter 15. Micromechanics applications - p. 485 97. 15.1 Dislocation modeling - p. 486 98. 15.2 Singular stress states - p. 490 99. 15.3 Elasticity theory with distributed cracks - p. 499 100. 15.4 Micropolar/couple-stress elasticity - p. 502 101. 15.5 Elasticity theory with voids - p. 511 102. 15.6 Doublet mechanics - p. 516 103. 15.7 Higher gradient elasticity theories - p. 521 104. 15.8 Meta and auxetic materials - p. 526 105. Chapter 16. Numerical finite and boundary element methods - p. 537 106. Appendix A. Basic field equations in Cartesian, cylindrical, and spherical coordinates - p. 563 107. Appendix B. Transformation of field variables between Cartesian, cylindrical, and spherical components - p. 569 108. Appendix C. MATLAB® Primer - p. 573 109. Appendix D. Review of mechanics of materials - p. 597 110. Index - p. 613
