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Variational, incremental, and energy methods in solid mechanics and shell theory /
Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York :
Elsevier Scientific Pub. Co.,
1980.
|
| Colección: | Studies in applied mechanics ;
4. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory; Copyright Page; Preface; Table of Contents; Introduction; Chapter 1. Mathematical preliminaries; 1.1 Tensor formulas in three-dimensional Euclidean spaces; 1.2 Tensor fomulas for surfaces; 1.3 Basic concepts and definitions in the theory of abstract spaces and operators; 1.4 Fundamentals of the classical calculus of variations; 1.5 Differentials and derivatives of operators
- Variations; 1.6 Variational boundary value problems; 1.7 Variational methods of approximation.
- Part I: Three-dimensional theoryChapter 2. Kinematics and stress in three-dimensional solid continua; 2.1 Description of motion coordinates reference and deformed states; 2.2 Kinematics of deformation; 2.3 Kinematics of incremental deformation; 2.4 Definitions of stress
- Stress rates; 2.5 Incremental stresses; 2.6 External loadings
- Boundary conditions; 2.7 Illustrative example of physical components of displacements and stress; Chapter 3. General principles
- The First and the Second Laws of Thermodynamics; 3.1 Kinematics of rigid body motions
- Invariance requirements.
- 3.2 The First Law of Thermodynamics3.3 The Second Law of Thermodynamics; 3.4 The Principles of Virtual Displacements and Virtual Forces; 3.5 Equations of equilibrium in physical components for cylindrical and spherical coordinates; Chapter 4. Constitutive material laws; 4.1 Elastic hypoelastic and hyperelastic materials; 4.2 Elastic-plastic materials; 4.3 Visco-elastic materials; Part II: Shell theory; Chapter 5. Deformation and stress in shells; 5.1 Shell middle surface: coordinates base vectors; 5.2 Description of deformation and motion in shells.
- 5.3 Kinematics of incremental deformation in shells5.4 Stress resultants and stress couples for shells
- Three-dimensional approach; 5.5 Load vectors and incremental load vectors; Chapter 6. The First Law of Thermodynamics applied to shells
- General principles; 6.1 Formulation of the First Law
- Invariance requirements; 6.2 Reduced and local forms of the First Law; 6.3 The First Law in the reference state; 6.4 Some consequences of the First Law
- Discussion
- Boundary condition; 6.5 Incremental forms of the First Law of Thermodynamics; 6.6 Incremental theory and stability.
- 6.7 The Principles of Virtual Displacements and Virtual Forces for shellsChapter 7. Constitutive relations and material laws for shells; 7.1 Material laws for thin elastic shells; 7.2 Hyperelastic incremental material relations; 7.3 A note on the constitutive relations for inelastic shells; Part III: Variational principles finite element models and applications elastic stability; Chapter 8. Variational principles of elasticity and shell theory
- Classical approach; 8.1 Variational principles of three-dimensional elasticity; 8.2 Variational principles of elastic shell theory.
- 8.3 Special cases
- the Principles of Reciprocity Clapeyron Castigliano and Menabrea.