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Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity /
Three-Dimensional Problems of Elasticity and Thermoelasticity.
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Amsterdam ; New York : New York :
North-Holland Pub. Co. ; Sole distributors for the U.S.A. and Canada Elsevier/North-Holland,
1979.
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| Colección: | North-Holland series in applied mathematics and mechanics ;
v. 25. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity; Copyright Page; Table of Contents; Preface; CHAPTER I. BASIC CONCEPTS AND AXIOMATIZATION; 1. Stresses; 2. Components of stress; 3. Displacements and rotations; 4. Basic equations in terms of stress components; 5. Hooke's law in classical elasticity; 6. Strain energy in classical elasticity; 7. Strain energy and Hooke's law in the couple-stress theory; 8. Thermoelasticity. Duhamel-Neumann's law; 9. Heat conduction equation; 10. Stationary elastic oscillations.
- 11. Axiomatization of the theory12. Matrix representation of the basic equations; 13. Stress operator; 14. Formulation of the basic problems; 15. Some additional remarks and bibliographic references; CHAPTER II. BASIC SINGULAR SOLUTIONS; 1. Fundamental solutions of classical elasticity; 2. Fundamental solutions of the couple-stress theory; 3. Fundamental solutions of thermoelasticity; 4. Singular solutions of classical elasticity; 5. Singular solutions of the couple-stress theory; 6. Singular solutions of thermoelasticity; 7. Various remarks and bibliographic references; Problems.
- CHAPTER III. UNIQUENESS THEOREMS1. Static problems in classical elasticity; 2. Problems of steady elastic oscillations; 3. Problems of steady thermoelastic oscillations; 4. Static problems in the couple-stress theory; 5. Problems of steady couple-stress oscillations; 6. Uniqueness theorems in dynamic problems; 7. Some remarks and bibliographic references; Problems; CHAPTER IV. SINGULAR INTEGRALS AND INTEGRAL EQUATIONS; 1. Introductory notes. Special classes of functions and their properties; 2. Integral with the kernel having a weak singularity; 3. Singular integrals.
- 4. Formula of inversion of integration order in iterated singular integrals. Composition of singular kernels5. Regularization of singular operators; 6. Basic theorems; 7. Singular resolvent. Properties and applications; 8. Concluding remarks; Problems; CHAPTER V. THE POTENTIAL THEORY; 1. Some auxiliary operators, formulas and theorems; 2. Boundary properties of some potential-type integrals; 3. Single- and double-layer potentials. Angular boundary values; 4. Double-layer potential with density of Class C0.�(S).
- 5. Boundary properties of the first derivatives of the single-layer potential6. Derivatives of single- and double-layer potentials with differentiable density; 7. On differential properties of elastic potentials; 8. Liapunov-Tauber theorems in elasticity; 9. Boundary properties of potentials of the third and the fourth problems; 10. Volume potentials; 11. Bibliographic references; Problems; CHAPTER VI. BOUNDARY VALUE PROBLEMS OF ELASTIC EQUILIBRIUM (STATICS); 1. Boundary value problems for inhomogeneous equations; 2. Integral equations of the boundary value problems.