Discontinuous Solutions in the Statics of Deformable Bodies

CONTENTS:

Introduction 7

1. NOTIONS ABOUT DISCONTINUOUS SOLUTIONS 9
1.1. Discontinuous solutions for beams 9
1.2. Some applications 14
1.3. Discontinuous solutions for beams on elastic foundations 18

2. PLANE PROBLM OF THE THEORY OF ELASTICITY 33
2.1. Basic equations of the plane theory of elasticity 33
2.2. The infinite plane with discontinuous stresses and displacements 37
2.3. Discontinuous solutions for a defect of arbitrary form 46
2.4. The formulation of integral equations in the global system of coordinates 53
2.5. Some problems for the defects located on the coordinate lines 57
2.6. Discontinuous solutions in orthotropic body 81
2.7. Some applications 90
2.8. The periodic problems 94

3. THE THREE-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY 103
3.1. The basic equations of three-dimensional theory of elasticity 104
3.2. Solutions due to the discontinuous stresses 107
3.3. Solutions due to the discontinuous displacements 115
3.4. Application of discontinuous solutions in dislocations theory and cracks 120
3.5. Discontinuous solutions in cylindrical coordinates. Case I. 140
3.6. Some applications 155
3.7. Discontinuous solutions in cylindrical coordinates. Case II. 170
3.8. Formulation of integral equations in a global coordinate system 188

4. DISCONTINUOUS SOLUTIONS IN THE THEORY OF PLATES 195
4.1. Kirchhoff plates. The basic equations 195
4.2. Solutions due to the concentrated jumps 197
4.3. Discontinuous solutions 204
4.4. Some applications 209
4.5. Discontinuous solutions for the Kirchhoff plates on an elastic foundation 213
4.6. Some applications 225
4.7. Discontinuous solutions in the shear deformable plates 239
4.8. Some applications 254

5. DISCONTINUOUS SOLUTIONS IN SHALLOW SHELLS 262
5.1. Basic equations for the theory of shallow shells 262
5.2. The fundamental solution in Cartesian coordinates 268
5.3. The fundamental solution for a spherical shallow shell 272
5.4. A shallow shell under concentrated discontinuous efforts 275
5.5. A shallow shell under concentrated discontinuous displacements 281
5.6. Discontinuous solutions 296
5.7. Some applications 301

APPENDIX A. GENERALIZED FOURIER TRANSFORM 309

APPENDIX B. ON THE SOLUTION OF INTEGRAL EQUATIONS WITH SINGULAR AND HYPER-SINGULAR KERNELS 314

APPENDIX C. CALCULATION OF INTEGRALS OVER THE TRIANGULAR AREA 320

APPENDIX D. SUMMARY OF DISCONTINUOUS SOLUTIONS 327

Bibliography 374