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Introduction to the variational formulation in mechanics : fundamentals and applications /
"This book was written intermittently over the period between 1980 and 2016 with an aim to provide students attending the courses organized by the authors, and particularly for the graduate students at the National Laboratory for Scientific Computing (LNCC), with the foundational material of Me...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, NJ :
John Wiley & Sons,
2020.
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| Edición: | First edition. |
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Intro; Title Page; Copyright Page; Contents; Preface; Part I Vector and Tensor Algebra and Analysis; Chapter 1 Vector and Tensor Algebra; 1.1 Points and Vectors; 1.2 Second-Order Tensors; 1.3 Third-Order Tensors; 1.4 Complementary Reading; Chapter 2 Vector and Tensor Analysis; 2.1 Differentiation; 2.2 Gradient; 2.3 Divergence; 2.4 Curl; 2.5 Laplacian; 2.6 Integration; 2.7 Coordinates; 2.8 Complementary Reading; Part II Variational Formulations in Mechanics; Chapter 3 Method of Virtual Power; 3.1 Introduction; 3.2 Kinematics; 3.2.1 Body and Deformations; 3.2.2 Motion: Deformation Rate.
- 3.2.3 Motion Actions: Kinematical Constraints3.3 Duality and Virtual Power; 3.3.1 Motion Actions and Forces; 3.3.2 Deformation Actions and Internal Stresses; 3.3.3 Mechanical Models and the Equilibrium Operator; 3.4 Bodies without Constraints; 3.4.1 Principle of Virtual Power; 3.4.2 Principle of Complementary Virtual Power; 3.5 Bodies with Bilateral Constraints; 3.5.1 Principle of Virtual Power; 3.5.2 Principle of Complementary Virtual Power; 3.6 Bodies with Unilateral Constraints; 3.6.1 Principle of Virtual Power; 3.6.2 Principle of Complementary Virtual Power.
- 3.7 Lagrangian Description of the Principle of Virtual Power3.8 Configurations with Preload and Residual Stresses; 3.9 Linearization of the Principle of Virtual Power; 3.9.1 Preliminary Results; 3.9.2 Known Spatial Configuration; 3.9.3 Known Material Configuration; 3.10 Infinitesimal Deformations and Small Displacements; 3.10.1 Bilateral Constraints; 3.10.2 Unilateral Constraints; 3.11 Final Remarks; 3.12 Complementary Reading; Chapter 4 Hyperelastic Materials at Infinitesimal Strains; 4.1 Introduction; 4.2 Uniaxial Hyperelastic Behavior; 4.3 Three-Dimensional Hyperelastic Constitutive Laws.
- 4.4 Equilibrium in Bodies without Constraints4.4.1 Principle of Virtual Work; 4.4.2 Principle of Minimum Total Potential Energy; 4.4.3 Local Equations and Boundary Conditions; 4.4.4 Principle of Complementary Virtual Work; 4.4.5 Principle of Minimum Complementary Energy; 4.4.6 Additional Remarks; 4.5 Equilibrium in Bodies with Bilateral Constraints; 4.5.1 Principle of Virtual Work; 4.5.2 Principle of Minimum Total Potential Energy; 4.5.3 Principle of Complementary Virtual Work; 4.5.4 Principle of Minimum Complementary Energy; 4.6 Equilibrium in Bodies with Unilateral Constraints.
- 4.6.1 Principle of Virtual Work4.6.2 Principle of Minimum Total Potential Energy; 4.6.3 Principle of Complementary Virtual Work; 4.6.4 Principle of Minimum Complementary Energy; 4.7 Min-Max Principle; 4.7.1 Hellinger-Reissner Functional; 4.7.2 Hellinger-Reissner Principle; 4.8 Three-Field Functional; 4.9 Castigliano Theorems; 4.9.1 First and Second Theorems; 4.9.2 Bounds for Displacements and Generalized Loads; 4.10 Elastodynamics Problem; 4.11 Approximate Solution to Variational Problems; 4.11.1 Elastostatics Problem; 4.11.2 Hellinger-Reissner Principle.