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Nonlinear theory of elasticity /
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A co...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Amsterdam ; New York : New York, N.Y., U.S.A. :
North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1990.
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| Colección: | North-Holland series in applied mathematics and mechanics ;
v. 36. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Nonlinear Theory of Elasticity; Copyright Page; PUBLISHERS' NOTE; FOREWORD; Table of Contents; CHAPTER 1. DEFORMATION OF A CONTINUOUS MEDIUM; 1. MATERIAL COORDINATES. SPATIAL COORDINATES; 2. VECTOR BASES; 3. DEFORMATION GRADIENTS; 4. CAUCHY-GREEN AND ALMANSI STRAIN MEASURES; 5. THE INVERSE TENSORS OF THE CAUCHY-GREEN AND ALMANSI STRAIN MEASURES; 6. ORTHOGONAL TENSORS ACCOMPANYING DEFORMATION. THE LEFT AND RIGHT STRETCH TENSORS. THE HENCKY STRAIN MEASURE; 7. STRAIN TENSORS; 8. DILATATION. THE ORIENTED ELEMENTARY AREA; 9. DIFFERENTIATION OF THE CAUCHY-GREEN AND FINGER MEASURES.
- 10. variation of the state of strain11. the variation of an orthogonal tensor accompanying deformation; 12. the second derivative of a scalar function of a tensor argument; 13. kinematic relations; 14. the material derivative of an integral and the law of conservation of mass; 15. rigid motions. frame-indifferent tensors; 16. the objective derivative of a tensor; 17. reference with respect to the present configuration. the rivlin-ericksen tensors; 18. determination of an absolute position by prescribed strain measure; 19. tensors of affine deformation; chapter 2. stress in a continuous medium.
- 1. body and surface forces2. the cauchy stress tensor; 3. the equations of motion of a continuous medium; 4. the tensor of stress functions; 5. on polar media; 6. alternative definitions of the stress tensor; 7. the incremental work; chapter 3. the state equations; 1. the simple body; 2. the principle of material frame-indifference; 3. elastic materials; 4. the symmetry group of a material; 5. orthogonal transformation. isotropic material; 6. the solid body; 7. an isotropic solid material; 8. an elastic fluid.
- Chapter 4. the equations of nonlinear theory of elasticity and the statement of problems1. the specific stored energy of deformation; 2. the state equations of orthotropic and transversally isotropic materials; 3. the state equation of an elastic isotropic material; 4. the similarity transformation of a reference configuration; 5. variation of the stress state; 6. the equilibrium equations for a varied stress state; 7. the relaxation tensor of an isotropic medium; 8. the representation of the relaxation tensor with reference to the proper basis of a stress tensor; 9. the relaxation tensor.
- 10. equations of motion and equilibrium for an isotropic elastic body11. ellipticity of the equations of equilibrium; 12. the acoustical tensor of an elastic medium; 13. on the posing of equilibrium boundary-value problems; 14. methods of analysis of equilibrium boundary-value problems for a nonlinearly elastic body; 15. general solutions of equations of the nonlinear theory of elasticity. the theorem of ericksen; 16. the stationary value principle for the stored energy of a system; 17. the principle of stationary complementary energy.