| Description |
1 online resource : text file, PDF |
| Series |
Asian mathematics series ; v. 4 |
|
Asian mathematics series ; v. 4.
|
| Contents |
Cover; Half Title; Title Page; Copyright Page; Table of Contents; Introduction to the Series; Preface; CHAPTER I: PERIODIC BOUNDARY VALUE PROBLEMS FOR ANALYTIC FUNCTIONS; 1 Periodic Riemann Boundary Value Problems: Case of Closed Contours; 1 Formulation of the problems; 2 Transfer to classical Riemann boundary value problems; 3 Discussion on homogeneous problem P01; 4 Discussion on non-homogeneous problem P1; 5 A particular case; 2 Periodic Riemann Boundary Value Problems: Case of Open Arcs or Discontinuous Coefficients; 1 Case of open arcs; 2 An important special case |
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3 Case of discontinuous coefficients 3 Periodic Riemann-Hilbert Boundary Value Problems of the Half-plane; 1 Formulation of the problem; 2 Sketch of the method of solution; 3 An important particular case; 4 Some Integral Formulas for Hilbert Kernel in the Half-plane; CHAPTER II: PERIODIC PROBLEMS FOR ISOTROPIC MATERIAL IN PLANE ELASTIC THEORY; 1 Stress Functions; 1 General expression of stress functions; 2 The converse of Theorem 2.1; 3 Formulation of the fundamental problem; 4 Stress functions for elastic half-plane; 2 Periodic Welding Problems; 1 The case of uniform material welded |
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2 The case of welded material with the same shearing modulus 3 Periodic Fundamental Problems of Elastic Half-plane; 1 The first fundamental problem; 2 The second fundamental problem; 3 The mixed fundamental problem; 4 Periodic Contact Problems; 1 The case without friction; 2 The case with friction; CHAPTER III: PERIODIC PROBLEMS FOR ANISOTROPIC MEDIUM; 1 The Stress Functions; 1 Basic assumptions; 2 Periodicity of the stress functions for anisotropic medium; 2 Periodic Fundamental Problems of Anisotropic Half-plane; 1 The first fundamental problem; 2 The second fundamental problem |
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3 Periodic Contact Problem for Anisotropic Medium1 Stress functions expressed in terms of boundary values of the stress components; 2 Formulation of the problem; 3 Solution of the problem; 4 Periodic condition for displacements and equilibrium condition at z = -- ∞ i; 5 The pressure beneath the stamp; CHAPTER IV: PROBLEMS WITH PERIODIC MOVING LOADS ON ISOTROPIC ELASTIC HALF-PLANE; 1 Stress Functions and Fundamental Problems; 1 Periodicity of the stress functions for isotropic medium with moving loads; 2 Formulation and solution of the problems |
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3 Periodic condition for displacements and equilibrium condition at z = -- ∞ i4 A special case; 2 Periodic Contact Problems with Moving Stamps; 1 Periodic boundary condition and solution of the problems; 2 Periodic condition for displacements and equilibrium condition at z = -- ∞ i; 3 The pressure beneath the stamps; CHAPTER V: PERIODIC CRACK PROBLEMS IN PLANE ELASTICITY; 1 Fundamental Problems of Isotropic Plane with Periodic Collinear Cracks; 1 General comments; 2 The first fundamental problem; 3 The second fundamental problem |
| Summary |
"Presenting the mathematical theory of period problems in plane elasticity by methods of complex variables. The most general formulations of such problems are proposed under the assumption that the stresses are periodic and the displacements are quasi-periodic. The general expression of complex displacements are illustrated. Periodic welding problems are studied by reducing them to periodic Riemann boundary value problems. Various periodic problems of the elastic half-plane (fundamental problems, contact problems) are treated and solved by reduction to Riemann-Hilbert boundary value problems with discontinuous coefficient. Periodic crack problems are investigated which are transferred to singular integral equations whose unique solvability is guaranteed."--Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Mathematical physics.
|
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Mechanics, Applied.
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Mathematical physics
|
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Mechanics, Applied
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| Form |
Electronic book
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| Author |
Lu, Jian-Ke, author
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| ISBN |
9781482287530 |
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1482287536 |
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