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Handbook of Green's Functions and Matrices Book

Handbook of Green's Functions and Matrices
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Handbook of Green's Functions and Matrices, The book presents two decades of the author's scientific work.The presented results have been reported, partially published in Russian, discussed and approved at the prestigious scientific centres of the former USSR. The book contains Green's matrices for, Handbook of Green's Functions and Matrices
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  • Handbook of Green's Functions and Matrices
  • Written by author V.D. Sheremet
  • Published by WIT Press, 9/28/2002
  • The book presents two decades of the author's scientific work.The presented results have been reported, partially published in Russian, discussed and approved at the prestigious scientific centres of the former USSR. The book contains Green's matrices for
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Preface 9
Introduction 15
Pt. I The Basis of Incompressible Influence Elements Method (Theoretical Basis of the Handbook) 26
Ch. I Integral Representations of Solutions in the Theory of Elasticity 27
1 Boundary-value-Problem for the General Incompressible Element 27
2 Integral Representations of Solutions in Terms of Green's Functions 38
Ch. II Constructive Solutions for Green's Matrices in the Form of Integrals 57
3 First Theorem for Locally Mixed Problems 57
4 Second Theorem on Green's Matrix for the Partially Restrained Influence Element 64
5 Third Theorem on Green's Matrix for Partially Free Influence Element 69
6 Main Corollaries of Theorems Used to Construct Green's Matrices 75
7 Generalized Green's Functions and Formulae in Uncoupled Thermoelastostatics 91
Pt. II Handbook on Green's Functions and Matrices: (List of Green's Functions and Matrices) 99
Ch. III Green's Functions and Matrices for Two-Dimensional Domains 101
8 Plane (-[infinity][is equal to or less than][chi][subscript 1],[chi][subscript 2][is equal to or less than][infinity]) 101
9 Half - Plane (0 [is equal to or less than][chi][subscript 1] [is equal to or less than][infinity],-[infinity][is equal to or less than] [chi][subscript 2] [is equal to or less than][infinity]) 103
10 Quadrant (0 [is equal to or less than] [chi][subscript 1],[chi][subscript 2] [is equal to or less than][infinity]) 106
11 Strip (-[infinity][is equal to or less than][chi][subscript 1][is equal to or less than][infinity],0 [is equal to or less than] [chi][subscript 2] [is equal to or less than]a[subscript 2]) 111
12 Half-Strip (0 [is equal to or less than][chi][subscript 1][is equal to or less than][infinity],0[is equal to or less than][chi][subscript 2][is equal to or less than]a[subscript 2]) 114
13 Rectangular (0 [is equal to or less than][chi][subscript 1][is equal to or less than]a[subscript 1],0[is equal to or less than][chi][subscript 2][is equal to or less than]a[subscript 2]) 121
Ch. IV Green's Functions and Matrices for Three-Dimensional Domains 131
14 Space (-[infinity][is equal to or less than][chi][subscript 1],[chi][subscript 2],[chi][subscript 3][is equal to or less than][infinity]) 131
15 Half-space (0[is equal to or less than][chi][subscript 1][is equal to or less than][infinity],-[infinity][is equal to or less than][chi][subscript 2],[chi][subscript 3][is equal to or less than][infinity]) 133
16 Quarter-space (0[is equal to or less than][chi][subscript 1],[chi][subscript 2][is equal to or less than][infinity],-[infinity][is equal to or less than][chi][subscript 3][is equal to or less than][infinity]) 137
17 Octant (0[is equal to or less than][chi][subscript 1],[chi][subscript 2],[chi][subscript 3][is equal to or less than][infinity]) 142
18 Layer (-[infinity][is equal to or less than][chi][subscript 1],[chi][subscript 2][is equal to or less than][infinity],0[is equal to or less than][chi][subscript 3][is equal to or less than]a[subscript 3]) 151
19 Half-Layer (0[is equal to or less than][chi][subscript 1][is equal to or less than][infinity],-[infinity][is equal to or less than][chi][subscript 2][is equal to or less than][infinity],0[is equal to or less than][chi][subscript 3][is equal to or less than] a[subscript 3]) 155
20 Quarter-Layer (0[is equal to or less than][chi][subscript 1],[chi][subscript 2][is equal to or less than][infinity],0[is equal to or less than][chi][subscript 3][is equal to or less than]a[subscript 3]) 164
21 Unbounded Parallelepiped (-[infinity][is equal to or less than][chi][subscript 1][is equal to or less than][infinity];0[is equal to or less than][chi][subscript 2][is equal to or less than]a[subscript 2];0[is equal to or less than][chi][subscript 3][is equal to or less than]a[subscript 3]) 183
22 Semi-bounded Parallelepiped (0[is equal to or less than][chi][subscript 1][is equal to or less than][infinity];0[is equal to or less than][chi][subscript 2][is equal to or less than]a[subscript 2];0[is equal to or less than][chi][subscript 3][is equal to or less than]a[subscript 3]) 193
23 Bounded Parallelepiped (0[is equal to or less than][chi][subscript 1][is equal to or less than]a[subscript 1];0[is equal to or less than][chi][subscript 2][is equal to or less than]a[subscript 2];0[is equal to or less than][chi][subscript 3][is equal to or less than]a[subscript 3]) 223
Notations 267
References 271
Index 277


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Handbook of Green's Functions and Matrices, The book presents two decades of the author's scientific work.The presented results have been reported, partially published in Russian, discussed and approved at the prestigious scientific centres of the former USSR. The book contains Green's matrices for, Handbook of Green's Functions and Matrices

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Handbook of Green's Functions and Matrices, The book presents two decades of the author's scientific work.The presented results have been reported, partially published in Russian, discussed and approved at the prestigious scientific centres of the former USSR. The book contains Green's matrices for, Handbook of Green's Functions and Matrices

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Handbook of Green's Functions and Matrices, The book presents two decades of the author's scientific work.The presented results have been reported, partially published in Russian, discussed and approved at the prestigious scientific centres of the former USSR. The book contains Green's matrices for, Handbook of Green's Functions and Matrices

Handbook of Green's Functions and Matrices

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