In this post, we will look at the book Integral Equations In Elasticity by V. Z. Parton, P. I. Perlin.
About the book
This book presents the fundamentals of the theory of regular and singular integral equations in the case of one and two variables. The general principles of the theory of approximate methods are considered as well as their application for the efficient solution of both regular and singular integral equations. The necessary information is given on the three-dimensional and two-dimensional equations of the theory of elasticity including the formulation of boundary value problems. The book contains the derivation and analysis of various integral equations of the plane problem for both fundamental boundary value problems and mixed problems, and also for bodies with cuts. In the three-dimensional case the construction and analysis of integral equations are carried out for the first and second fundamental problems.
Emphasis is placed on efficient methods for solving integral equations for the plane and three-dimensional problems of elasticity. Examples are given illustrating the advantages of a particular approach. The book is appended with an extensive list of references giving comprehensive information of the subject of investigation.
The emphasis on numerical methods for the solution of integral equations for elastostatic problems corresponds to the author’s conviction that this approach has considerable promise, particularly with the advent of the nearest-generation computers.
The scope of the book is limited to elastostatic problems though the extension of the methods described to dynamic problems apparently involves no fundamental difficulties.
The book was translated from the Russian by ???? and was published by Mir in 1982.
Many thanks to Akbar Azimi for the scans.
Preface to the English Edition 7
Preface to the Russian Edition 8
On the Formation of Integral Equation Methods in the Theory of Elasticity by D. I. Sherman 10
Chapter 1 ELEMENTS OF THE THEORY OF ONE-DIMENSIONAL AND MULTIDIMENSIONAL INTEGRAL EQUATIONS
1. Analytic Theory of a Resolvent 21
2. Cauchy-type Integral 35
3. Riemann Boundary Value Problem 48
4. Singular Integral Equations 52
5. Riemann Boundary Value Problem in the Case of Discontinuous Coefficients and Unclosed Contours 64
6. Singular Integral Equations in the Case of Discontinuous Coefficients and Unclosed Contours 71
7. Two-dimensional Singular Integrals 75
8. Two-dimensional Singular Integral Equations 89
Chapter II APPROXIMATE METHODS FOR SOLVING INTEGRAL EQUATIONS
9. General Principles of the Theory of Approximate Methods 98
10. Method of Successive Approximations 105
11. Mechanical Quadrature Method for Regular Integral Equations 111
12. Approximate Methods for Solving Singular Integral Equations 114
13. Approximate Methods for Solving Singular Integral ^
Equations (Continued) 120
Chapter III FUNDAMENTAL PRINCIPLES OF THE MATHEMATICAL THEORY OF ELASTICITY
14. Three-dimensional Problem 137
15. Plane Problem 137
16. Bending of Thin Plates 143
17. On Singular Solutions of Elastic Equations 148
Chapter IV INTEGRAL EQUATIONS FOR TWO-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY
18. Muskhelishvili’s Integral Equations 155
19. Sherman-Lauricella Integral Equations 159
20. Sherman-Lauricella Integral Equations (Continued) 164
21. Multiply (Doubly) Connected Regions 168
22. Problems of the Theory of Elasticity for Piecewise Homogeneous Bod ies 171
Chapter V SOME SPECIAL TOPICS OF TWO-DIMENSIONAL ELASTICITY
23. Problems of the Theory of Elasticity for Bodies with Cuts 175
24. Integral Equations for Mixed (Contact) Problems 179
25. Problems of the Theory of Elasticity for Bodies Bounded by Piecewise Smooth Contours 182
26. Method of Linear Relationship 186
27. Method of Linear Relationship (Continued) 189
Chapter VI INTEGRAL EQUATIONS FOR FUNDAMENTAL THREE-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY
28. Generalized Elastic Potentials 199
29. Regular and Singular Integral-Equations for Fundamental Three-dimensional Problems 206
30. Extension of the Fredholm Alternatives to Singular Integral Equations of the Theory of Elasticity 215
31. Spectral Properties of Regular and Singular Integral Equations. Method of Successive Approximations 217
32. Differential Properties of Solutions of Integral Equations and Generalized Elastic Potentials 223
33. Approximate Methods of Solving Integral Equations for Fundamental Three-dimensional Problems 224
34. Problems of the Theory of Elasticity for Bodies Bounded by Several Surfaces 239
35. Three-dimensional Problems of the Theory of Elasticity for Bodies with Gut 244
36. Piecewise Homogeneous Bodies 253
37. Solution of Problems of the Theory of Elasticity for Bodies Bounded by Piecewise Smooth Surfaces 262
38. Mixed (Contact) Problems 269
Author Index 299
Subject Index 302