(Ebook PDF) Introduction to the Variational Formulation in Mechanics 1st edition by Edgardo Taroco, Pablo Blanco, Raúl Feijóo 1119600952 9781119600954 full chapters

Introduction to the Variational Formulation in Mechanics 1st edition by Edgardo O. Taroco, Pablo J. Blanco, Raúl A. Feijóo – Ebook PDF Instant Download/DeliveryISBN:  1119600952, 9781119600954 

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ISBN-10 :  1119600952 

ISBN-13 :  9781119600954

Author :  Edgardo Taroco, Pablo Blanco, Raúl Feijóo 

Introduces readers to the fundamentals and applications of variational formulations in mechanics Nearly 40 years in the making, this book provides students with the foundation material of mechanics using a variational tapestry. It is centered around the variational structure underlying the Method of Virtual Power (MVP). The variational approach to the modeling of physical systems is the preferred approach to address complex mathematical modeling of both continuum and discrete media. This book provides a unified theoretical framework for the construction of a wide range of multiscale models.

Introduction to the Variational Formulation in Mechanics 1st Table of contents:

Part I: Vector and Tensor Algebra and Analysis
1 Vector and Tensor Algebra
1.1 Points and Vectors
1.2 Second‐Order Tensors
1.3 Third‐Order Tensors
1.4 Complementary Reading
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
3 Method of Virtual Power
3.1 Introduction
3.2 Kinematics
3.3 Duality and Virtual Power
3.4 Bodies without Constraints
3.5 Bodies with Bilateral Constraints
3.6 Bodies with Unilateral Constraints
3.7 Lagrangian Description of the Principle of Virtual Power
3.8 Configurations with Preload and Residual Stresses
3.9 Linearization of the Principle of Virtual Power
3.10 Infinitesimal Deformations and Small Displacements
3.11 Final Remarks
3.12 Complementary Reading
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 Constraints
4.5 Equilibrium in Bodies with Bilateral Constraints
4.6 Equilibrium in Bodies with Unilateral Constraints
4.7 Min–Max Principle
4.8 Three‐Field Functional
4.9 Castigliano Theorems
4.10 Elastodynamics Problem
4.11 Approximate Solution to Variational Problems
4.12 Complementary Reading
5 Materials Exhibiting Creep
5.1 Introduction
5.2 Phenomenological Aspects of Creep in Metals
5.3 Influence of Temperature
5.4 Recovery, Relaxation, Cyclic Loading, and Fatigue
5.5 Uniaxial Constitutive Equations
5.6 Three‐Dimensional Constitutive Equations
5.7 Generalization of the Constitutive Law
5.8 Constitutive Equations for Structural Components
5.9 Equilibrium Problem for Steady‐State Creep
5.10 Castigliano Theorems
5.11 Examples of Application
5.12 Approximate Solution to Steady‐State Creep Problems
5.13 Unsteady Creep Problem
5.14 Approximate Solutions to Unsteady Creep Formulations
5.15 Complementary Reading
6 Materials Exhibiting Plasticity
6.1 Introduction
6.2 Elasto‐Plastic Materials
6.3 Uniaxial Elasto‐Plastic Model
6.4 Three‐Dimensional Elasto‐Plastic Model
6.5 Drucker and Hill Postulates
6.6 Convexity, Normality, and Plastic Potential
6.7 Plastic Flow Rule
6.8 Internal Dissipation
6.9 Common Yield Functions
6.10 Common Hardening Laws
6.11 Incremental Variational Principles
6.12 Incremental Constitutive Equations
6.13 Complementary Reading
Part III: Modeling of Structural Components
7 Bending of Beams
7.1 Introduction
7.2 Kinematics
7.3 Generalized Forces
7.4 Mechanical Equilibrium
7.5 Timoshenko Beam Model
7.6 Final Remarks
8 Torsion of Bars
8.1 Introduction
8.2 Kinematics
8.3 Generalized Forces
8.4 Mechanical Equilibrium
8.5 Dual Formulation
9 Plates and Shells
9.1 Introduction
9.2 Geometric Description
9.3 Differentiation and Integration
9.4 Principle of Virtual Power
9.5 Unified Framework for Shell Models
9.6 Classical Shell Models
9.7 Constitutive Equations and Internal Constraints
9.8 Characteristics of Shell Models
9.9 Basics Notions of Surfaces
Part IV: Other Problems in Physics
10 Heat Transfer
10.1 Introduction
10.2 Kinematics
10.3 Principle of Thermal Virtual Power
10.4 Principle of Complementary Thermal Virtual Power
10.5 Constitutive Equations
10.6 Principle of Minimum Total Thermal Energy
10.7 Poisson and Laplace Equations
11 Incompressible Fluid Flow
11.1 Introduction
11.2 Kinematics
11.3 Principle of Virtual Power
11.4 Navier–Stokes Equations
11.5 Stokes Flow
11.6 Irrotational Flow
12 High‐Order Continua
12.1 Introduction
12.2 Kinematics
12.3 Principle of Virtual Power
12.4 Dynamics
12.5 Micropolar Media
12.6 Second Gradient Theory
Part V: Multiscale Modeling
13 Method of Multiscale Virtual Power
13.1 Introduction
13.2 Method of Virtual Power
13.3 Fundamentals of the Multiscale Theory
13.4 Kinematical Admissibility between Scales
13.5 Duality in Multiscale Modeling
13.6 Principle of Multiscale Virtual Power
13.7 Dual Operators
13.8 Final Remarks
14 Applications of Multiscale Modeling
14.1 Introduction
14.2 Solid Mechanics with External Forces
14.3 Mechanics of Incompressible Solid Media
14.4 Final Remarks

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