Title:
Handbook of Green's functions and matrices
Personal Author:
Publication Information:
Southhampton ; Boston : WIT Press, c2003
Physical Description:
1 CD-ROM ; 12 cm.
ISBN:
9781853129339
General Note:
Accompanies text of the same title : QA371 S47 2003
Available:*
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Summary
Summary
In this book the author describes his own technique of constructing Green's functions and matrices for the elastostatic Lame's equations and provides examples of applications in applied mathematical physics.
Table of Contents
| Preface | p. 9 |
| Introduction | p. 15 |
| Part I The Basis of Incompressible Influence Elements Method (Theoretical Basis of the Handbook) | p. 26 |
| Chapter I Integral Representations of Solutions in the Theory of Elasticity | p. 27 |
| 1. Boundary-value Problem for the General Incompressible Element | p. 27 |
| 1.1 A Concept of General Incompressible Influence Element | p. 27 |
| 1.2 Green's Function and Formula for the Poisson's Equation | p. 30 |
| 1.3 Methods Applied to Construct Green's Functions | p. 32 |
| 2. Integral Representations of Solutions in Terms of Green's Functions | p. 38 |
| 2.1 General Integral Representations | p. 38 |
| 2.2 Integral Representations for Green's Matrices | p. 42 |
| 2.2.1 On the Green's Matrix and Green's Formula in Elastostatics | p. 42 |
| 2.2.2 General Constructive Formulae for Green's Matrices | p. 44 |
| 2.3 Integral Representations for the Basic Problems of the Theory of Elasticity | p. 47 |
| 2.3.1 First Basic Problem | p. 47 |
| 2.3.2 Second Basic Problem | p. 50 |
| 2.3.3 Basic Mixed Problem | p. 51 |
| Chapter II Constructive Solutions for Green's Matrices in the form of Integrals | p. 57 |
| 3. First Theorem for Locally Mixed Problems | p. 57 |
| 3.1 Concept of Generalised Rectangular Influence Element | p. 57 |
| 3.2 First Theorem on Green's Matrix | p. 61 |
| 4. Second Theorem on Green's Matrix for the Partially Restrained Influence Element | p. 64 |
| 5. Third Theorem on Green's Matrix for Partially Free Influence Element | p. 69 |
| 6. Main Corollaries of Theorems Used to Construct Green's Matrices | p. 75 |
| 7. Generalised Green's Functions and Formulae in Uncoupled Thermoelastostatics | p. 91 |
| 7.1 Generalised Green's Functions and Some Other Integral Formulae | p. 91 |
| 7.2 On Proprieties and Possibilities of Definition of the Introduced Influence Functions | p. 94 |
| Part II Handbook on Green's Functions and Matrices (List of Green's Functions and Matrices) | p. 99 |
| Chapter III Green's Functions and Matrices for Two-Dimensional Domains | p. 101 |
| 8. Plane (- [infinity] [less than or equal] x[subscript 1],x[subscript 2] [less than or equal] [infinity]) | p. 101 |
| 8.P Green's Function for Poisson's Equation. Problem 8.P.1 with Answer | p. 102 |
| 8.L Green's Matrix for Lame's Equations | p. 102 |
| Problem 8.L.1 | p. 102 |
| Answer to Problem 8.L.1 | p. 103 |
| 9. Half - Plane (0 [less than or equal] x[subscript 1] [less than or equal] [infinity], - [infinity] [less than or equal] x[subscript 2] [less than or equal] [infinity]) | p. 103 |
| 9.P Green's Functions for Poisson's Equation | p. 104 |
| Problems 9.L.1 and 9.L.2 | p. 104 |
| Answers to Problems 9.P.1-9.P.2 | p. 104 |
| 9.L Green's Matrices for Lame's Equations | p. 104 |
| Problems of First Type. Problems 9.L.1-9.L.2 | p. 104 |
| Answers to Problems 9.L.1-9.L.2 | p. 104 |
| A Problem of Second Type | p. 105 |
| Problem 9.L.3 with Answer | p. 105 |
| A Problem of Third Type | p. 105 |
| Problem 9.L.4 with Answer | p. 105 |
| 10. Quadrant (0 [less than or equal] x[subscript 1],x[subscript 2] [less than or equal] [infinity]) | p. 106 |
| 10.P Green's Functions for Poisson's Equation | p. 107 |
| Problems 10.P.1-10.P.4 | p. 107 |
| Answers to Problems 10.P.1-10.P.4 | p. 108 |
| 10.L Green's Matrices for Lame's Equations | p. 108 |
| Problems of First Type | p. 108 |
| Problems 10.L.1-10.L.4 | p. 108 |
| Answers to Problems 10.L.1-10.L.4 | p. 108 |
| Problems of Second Type | p. 109 |
| Problems 10.L.5 and 10.L.6 | p. 109 |
| Answers to Problems 10.L.5 and 10.L.6 | p. 109 |
| Problems of Third Type | p. 110 |
| Problems 10.L.7 and 10.L.8 | p. 110 |
| Answers to Problems 10.7 and 10.8 | p. 110 |
| 11. Strip (- [infinity] [less than or equal] x[subscript 1] [less than or equal] [infinity],0 [less than or equal] x[subscript 2] [less than or equal] a[subscript 2]) | p. 111 |
| 11.P Green's Functions for Poisson's Equation | p. 111 |
| Problems 11.P.1 to 11.P.4 | p. 111 |
| Answers to Problems 11.P.1 to 11.P.4 | p. 112 |
| 11.L Green's Matrices for Lame's Equations | p. 113 |
| Problems of First Type | p. 113 |
| Problems 11.L.1-11.L.4 | p. 113 |
| Answers to Problems 11.L.1-11.L.4 | p. 113 |
| 12. Half-Strip (0 [less than or equal] x[subscript 1] [less than or equal] [infinity],0 0 [less than or equal] x[subscript 2] [less than or equal] a[subscript 2]) | p. 114 |
| 12.P Green's Functions for Poisson's Equation | p. 114 |
| Problems 12.P.1-12.P.8 | p. 114 |
| Answers to Problems 12.P.1-12.P.8 | p. 115 |
| 12.L Green's Matrices for Lame's Equations | p. 116 |
| Problems of First Type | p. 116 |
| Problems 12.L.1-12.L.8 | p. 116 |
| Answers to Problems 12.L.1-12.L.8 | p. 117 |
| Problems of Second Type | p. 118 |
| Problems 12.L.9-12.L.12 | p. 118 |
| Answers to Problems 12.L.9-12.L.12 | p. 118 |
| Problems of Third Type | p. 119 |
| Problems 12.L.13-12.L.16 | p. 119 |
| Answers to Problems 12.L.13-12.L.16 | p. 119 |
| 13. Rectangular (0 [less than or equal] x[subscript 1] [less than or equal] a[subscript 1],0 [less than or equal] x[subscript 2] [less than or equal] a[subscript 2]) | p. 121 |
| 13.P Green's Functions for Poisson's Equation | p. 122 |
| Problems 13.P.1-13.P.16 | p. 122 |
| Answers to Problems 13.P.1-13.P.16 | p. 123 |
| 13.L Green's Matrices for Lame's Equations | p. 125 |
| Problem of First Type | p. 125 |
| Problems 13.L.1-13.L.14 | p. 125 |
| Answers to Problems 13.L.1-13.L.14 | p. 127 |
| Chapter IV Green's Functions and Matrices for Three-Dimensional Domains | p. 131 |
| 14. Space (- [infinity] [less than or equal] x[subscript 1],x[subscript 2],x[subscript 3] [less than or equal] [infinity]) | p. 131 |
| 14.P Green's Functions for the Poisson's Equation | p. 132 |
| Problem 14.P.1 with Answer | p. 132 |
| 14.L Green's Matrix for Lame's Equations | p. 132 |
| Problem of First Type | p. 132 |
| Problem 14.L.1 with Answer | p. 132 |
| 15. Half-space (0 [less than or equal] x[subscript 1] [less than or equal] [infinity], - [infinity] [less than or equal] x[subscript 2],x[subscript 3] [less than or equal] [infinity]) | p. 133 |
| 15.P Green's Functions for Poisson's Equation | p. 134 |
| Problems 15.P.1 and 15.P.2 | p. 134 |
| Answers to Problems 15.P.1 and 15.2 | p. 134 |
| 15.L Green's Matrices for Lame's Equations | p. 134 |
| Problems of First Type | p. 134 |
| Problems 15.L.1 and 15.L.2 | p. 134 |
| Answers to Problems 15.L.1 and 15.L.2 | p. 135 |
| A Problem of Second Type. Problem 15.L.3 with Answer | p. 135 |
| A Problem of Third Type. Problem 15.L.4 with Answer | p. 136 |
| 16. Quarter-space (0 [less than or equal] x[subscript 1],x[subscript 2] [less than or equal] [infinity], - [infinity] [less than or equal] x[subscript 3] [less than or equal] [infinity]) | p. 137 |
| 16.P Green's Functions for Poisson's Equation | p. 137 |
| Problems 16.P.1-16.P.4 | p. 137 |
| Answers to Problems 16.P.1-16.P.4 | p. 138 |
| 16.L Green's Matrices for Lame's Equations | p. 138 |
| Problems of First Type | p. 138 |
| Problems 16.L.1-16.L.4 | p. 138 |
| Answers to Problems 16.L.1-16.L.4 | p. 139 |
| Problems of Second Type | p. 139 |
| Problems 16.L.5-16.L.6 | p. 139 |
| Answers to Problems 16.L.5-16.L.6 | p. 140 |
| Problems of Third Type | p. 140 |
| Problems 16.L.7-16.L.8 | p. 140 |
| Answers to Problems 16.L.7-16.L.8 | p. 141 |
| 17. Octant (0 [less than or equal] x[subscript 1],x[subscript 2],x[subscript 3] [less than or equal] [infinity]) | p. 142 |
| 17.P Green's Functions for Poisson's Equation | p. 143 |
| Problems 17.P.1-17.P.8 | p. 143 |
| Answers to Problems 17.P.1-17.P.8 | p. 144 |
| 17.L Green's Matrices for Lame's Equations | p. 145 |
| Problems of First Type | p. 145 |
| Problems 17.L.1-17.L.8 | p. 145 |
| Answers to Problems 17.L.1-17.L.8 | p. 146 |
| Problems of Second Type | p. 147 |
| Problems 17.L.9-17.L.12 | p. 147 |
| Answers to Problems 17.L.9-17.L.12 | p. 147 |
| Problems of Third Type | p. 148 |
| Problems 17.L.13-17.L.16 | p. 148 |
| Answers to Problems 17.L.13-17.L.16 | p. 149 |
| 18. Layer (- [infinity] [less than or equal] x[subscript 1],x[subscript 2] [less than or equal] [infinity], 0 [less than or equal] x[subscript 3] [less than or equal] a[subscript 3]) | p. 151 |
| 18.P Green's Functions for Poisson's Equation | p. 151 |
| Problems 18.P.1-18.P.4 | p. 151 |
| Answers to Problems 18.P.1-18.P.4 | p. 152 |
| 18.L Green's Matrices for Lame's Equations | p. 153 |
| Problems of First Type | p. 153 |
| Problems 18.L.1-18.L.4 | p. 153 |
| Answers to Problems 18.L.1-18.L.4 | p. 153 |
| 19. Half-Layer (0 [less than or equal] x[subscript 1] [less than or equal] [infinity], -[infinity] [less than or equal] x[subscript 2] [less than or equal] [infinity],0 [less than or equal] x[subscript 3] [less than or equal] a[subscript 3]) | p. 155 |
| 19.P Green's Functions for Poisson's Equation | p. 155 |
| Problems 19.P.1-19.P.8 | p. 134 |
| Answers to Problems 19.P.1-19.P.8 | p. 156 |
| 19.L Green's Matrices for Lame's Equations | p. 159 |
| Problems of First Type | p. 159 |
| Problems 19.L.1-19.L.8 | p. 159 |
| Answers to Problems 19.L.1-19.L.8 | p. 160 |
| Problem of Second Type | p. 161 |
| Problems 19.L.9-19.L.12 | p. 161 |
| Answers to Problems 19.L.9-19.L.12 | p. 162 |
| 20. Quarter-Layer (0 [less than or equal] x[subscript 1],x[subscript 2] [less than or equal] [infinity], 0 [less than or equal] x[subscript 3] [less than or equal] a[subscript 3]) | p. 164 |
| 20.P Green's Functions for Poisson's Equation | p. 164 |
| Problems 20.P.1-20.P.16 | p. 164 |
| Answers to Problems 20.P.1-20.P.16 | p. 166 |
| 20.L Green's Matrices for Lame's Equations | p. 173 |
| Problems of First Type | p. 173 |
| Problems 20.L.1-20.L.16 | p. 173 |
| Answers to Problems 20.L.1-20.L.16 | p. 175 |
| Problems of Second Type | p. 178 |
| Problems 20.L.17-20.L.24 | p. 178 |
| Answers to Problems 20.L.17-20.L.24 | p. 179 |
| 21. Unbounded Parallelepiped (- [infinity] [less than or equal] x[subscript 1] [less than or equal] [infinity];0 [less than or equal] x[subscript 2] [less than or equal] a[subscript 2];0 [less than or equal] x[subscript 3] [less than or equal] a[subscript 3]) | p. 183 |
| 21.P Green's Functions for Poisson's Equation | p. 184 |
| Problems 21.P.1-21.P.16 | p. 184 |
| Answers to Problems 21.P.1-21.P.16 | p. 186 |
| 21.L Green's Matrices for Lame's Equations | p. 189 |
| Problems of First Type | p. 189 |
| Problems 21.L.1-21.L.16 | p. 189 |
| Answers to Problems 21.L.1-21.L.16 | p. 191 |
| 22. Semi-bounded Parallelpiped (0 [less than or equal] x[subscript 1] [less than or equal] [infinity];0 [less than or equal] x[subscript 2] [less than or equal] a[subscript 2];0 [less than or equal] x[subscript 3] [less than or equal] a[subscript 3]) | p. 193 |
| 22.P Green's Functions for Poisson's Equation | p. 193 |
| Problems 22.P.1-22.P.32 | p. 193 |
| Answers to Problems 22.P.1-22.P.32 | p. 198 |
| 22.L Green's Matrices for Lame's Equations | p. 205 |
| Problems of First Type | p. 205 |
| Problems 22.L.1-22.L.32 | p. 205 |
| Answers to Problems 22.L.1-22.L.32 | p. 209 |
| Problems of Second Type | p. 211 |
| Problems 22.L.33-22.L.48 | p. 211 |
| Answers to Problems 22.L.33-22.L.48 | p. 213 |
| Problem of Third Type | p. 217 |
| Problems 22.L.49-22.L.64 | p. 217 |
| Answers to Problems 22.L.49-22.L.64 | p. 219 |
| 23. Bounded Parallelepiped (0 [less than or equal] x[subscript 1] [less than or equal] a[subscript 1];0 [less than or equal] x[subscript 2] [less than or equal] a[subscript 2];0 [less than or equal] x[subscript 3] [less than or equal] a[subscript 3]) | p. 223 |
| 23.P Green's Functions for Poisson's Equation | p. 223 |
| Problems 23.P.1-23.P.64 | p. 223 |
| Answers to Problems 23.P.1-23.P.64 | p. 232 |
| 23.L Green's Matrices for Lame's Equations | p. 246 |
| Problems of First Type | p. 246 |
| Problems 23.L.1-23.L.61 | p. 246 |
| Answers to Problems 23.L.1-23.L.61 | p. 255 |
| Notations | p. 267 |
| References | p. 271 |
| Index | p. 277 |
