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Mathematical elasticity. Volume I, Three-dimensional elasticity /
This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two comp...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| 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.,
1988.
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| Colección: | Studies in mathematics and its applications ;
v. 20. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Studies in Mathematics and Its Applications; Copyright Page; Contents; General plan; Preface; Main Notation, Definitions, and Formulas; PART A: DESCRIPTION OF THREE-DIMENSIONAL ELASTICITY; Chapter 1. Geometrical, and other preliminaries; Introduction; 1.1. The cofactor matrix; 1.2. The Fr�echet derivative; 1.3. Higher-order derivatives; 1.4. Deformations in R3; 1.5. Volume element in the deformed configuration; 1.6. Surface integrals; Green's formulas; 1.7. The Piola transform; area element in the deformed configuration; 1.8. Length element in the deformed configuration
- Strain tensorsExercises; Chapter 2. The equations of equilibrium and the principle of virtual work; Introduction; 2.1. Applied forces; 2.2. The stress principle of Euler and Cauchy; 2.3. Cauchy's theorem; the Cauchy stress tensor; 2.4. The equations of equilibrium and the principle of virtual work in the deformed configuration; 2.5. The Piola-Kirchhoff stress tensors; 2.6. The equations of equilibrium and the principle of virtual work in the reference configuration; 2.7. Examples of applied forces; conservative forces; Exercises
- Chapter 3. Elastic materials and their constitutive equationsIntroduction; 3.1. Elastic materials; 3.2. The polar factorization and the singular values of a matrix; 3.3. Material frame-indifference; 3.4. Isotropic elastic materials; 3.5. Principal invariants of a matrix of order three; 3.6. The response function of an isotropic elastic material; 3.7. The constitutive equation near the reference configuration; 3.8. The Lam�e constants of a homogeneous isotropic elastic material whose reference configuration is a natural state; 3.9. St Venant-Kirchhoff materials; Exercises
- Chapter 4. HyperelasticityIntroduction; 4.1. Hyperelastic materials; 4.2. Material frame-indifference for hyperelastic materials; 4.3. Isotropic hyperelastic materials; 4.4. The stored energy function of an isotropic hyperelastic material; 4.5. The stored energy function near a natural state; 4.6. Behavior of the stored energy function for large strains; 4.7. Convex sets and convex functions; 4.8. Nonconvexity of the stored energy function; 4.9. John Ball's polyconvex stored energy functions; 4.10. Examples of Ogden's and other hyperelastic materials; Exercises
- Chapter 5. The boundary value problems of three-dimensional elasticityIntroduction; 5.1. Displacement-traction problems; 5.2. Other examples of boundary conditions; 5.3. Unilateral boundary conditions of place in hyperelasticity; 5.4. The topological degree in Rn; 5.5. Orientation-preserving character and injectivity of mappings; 5.6. Interior injectivity, self-contact, and noninterpenetration in hyperelasticity; 5.7. Internal and external geometrical constraints on the admissible deformations; 5.8. Physical examples of nonuniqueness; 5.9. The nonlinearities in three-dimensional elasticity