Integral Equations in Elasticity

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
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