Front Cover
Title Page
Contents
Preface to the English Edition
On the Formation of Integral Equation Methods in the Theory of Elasticity
Notation
Chapter 1 ELEMENTS OF THE THEORY OF ONE-DIMENSIONALAND MULTIDIMENSIONAL INTEGRAL EQUATIONS
1. Analytic Theory of a Resolvent
2. Cauchy-type Integral
3. Riemann Boundary Value Problem
4. Singular Integral Equations
5. Riemann Boundary Value Problem in the Case of Discontinuous Coefficients and Unclosed Contours
6. Singular Integral Equations in the Case of Discontinuous Coefficients and Unclosed Contours
7. Two-dimensional Singular Integrals
8. Two-dimensional Singular Integral Equations
Chapter 2 APPROXIMATE METHODS FOR SOLVING INTEGRAL EQUATIONS
9. General Principles of the Theory of Approximate Methods
10. Method of Successive Approximations
11. Mechanical Quadrature Method for Regular Integral Equations
12. Approximate Methods for Solving Singular Integral Equations
13. Approximate Methods for Solving Singular Integral Equations (Continued)
Chapter 3 FUNDAMENTAL PRINCIPLES OF THE MATHEMATICAL THEORY OF ELASTICITY
14. Three-dimensional Problem
15. Plane Problem
16. Bending of Thin Plates
17. On Singular Solutions of Elastic Equations
Chapter 4 INTEGRAL EQUATIONS FOR TWO-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY
18. Muskhelishvili's Integral Equations
19. Sherman-Lauricella Integral Equations
20. Sherman-Lauricella Integral Equations (Continued)
21. Multiply (Doubly) Connected Regions
22. Problems of the Theory of Elasticity for Piecewise Homogeneous Bodies
Chapter 5 SOME SPECIAL TOPICS OF TWO-DIMENSIONAL ELASTICITY
23. Problems of the Theory of Elasticity for Bodies with Cuts
24. Integral Equations for Mixed (Contact) Problems
25. Problems of the Theory of Elasticity for Bodies Bounded by Piecewise Smooth Contours
26. Method of Linear Relationship
27. Method of Linear Relationship (Continued)
Chapter 6 INTEGRAL EQUATIONS FOR FUNDAMENTALTHREE-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY
28. Generalized Elastic Potentials
29, Regular and Singular Integral Equations for Fundamental Three-dimensional Problems
30. Extension of the Fredholm Alternatives to Singular Integral Equations of the Theory of Elasticity
31. Spectral Properties of Regular and Singular Integral Equations. Method of Successive Approximations
32. Differential Properties of Solutions of Integral Equations and Generalized Elastic Potentials
33. Approximate Methods of Solving Integral Equations for Fundamental Three-dimensional Problems
34. Problems of the Theory of Elasticity for Bodies Bounded by Several Surfaces
35. Three-dimensional Problems of the Theory of Elasticity for Bodies with Cuts
36. Piecewise Homogeneous Bodies
37. Solution of Problems of the Theory of Elasticity for Bodies Bounded by Piecewise Smooth Surfaces
38. Mixed (Contact) Problems
Conclusion
References
Author Index
Subject Index
Back Cover
