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Advances in computational dynamics of particles, materials, and structures / Jason Har and Kumar K. Tamma
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: Hoboken : John Wiley & Sons, 2012Auflage: Online-AusgBeschreibung: Online-Ressource (1 online resource (1 v.))ISBN:- 9781280778469
- 1280778466
- 9781119965909
- 9780470749807
- 531/.163 23
- 531.163
- TA352
- QA851 .H384 2012
Inhalte:
Zusammenfassung: Computational methods for the modeling and simulation of the dynamic response and behavior of particles, materials and structural systems have had a profound influence on science, engineering and technology. Complex science and engineering applications dealing with complicated structural geometries and materials that would be very difficult to treat using analytical methods have been successfully simulated using computational tools. With the incorporation of quantum, molecular and biological mechanics into new models, these methods are poised to play an even bigger role in the future. Advances in Computational Dynamics of Particles, Materials and Structures not only presents emerging trends and cutting edge state-of-the-art tools in a contemporary setting, but also provides a unique blend of classical and new and innovative theoretical and computational aspects covering both particle dynamics, and flexible continuum structural dynamics applications. It provides a unified viewpoint and encompasses the classical Newtonian, Lagrangian, and Hamiltonian mechanics frameworks as well as new and alternative contemporary approaches and their equivalences in [start italics]vector and scalar formalisms[end italics] to address the various problems in engineering sciences and physics. Highlights and key features Provides practical applications, from a unified perspective, to both particle and continuum mechanics of flexible structures and materials Presents new and traditional developments, as well as alternate perspectives, for space and time discretization Describes a unified viewpoint under the umbrella of Algorithms by Design for the class of linear multi-step methods Includes fundamentals underlying the theoretical aspects and numerical developments, illustrative applications and practice exercises The completeness and breadth and depth ofZusammenfassung: Intro -- Advances in Computational Dynamics of Particles, Materials and Structures -- Contents -- Preface -- Acknowledgments -- About the Authors -- Chapter 1 Introduction -- 1.1 Overview -- 1.1.1 The Mechanics Underlying Computational Dynamics -- 1.1.2 The Numerics Underlying Computational Dynamics in Space and Time -- 1.2 Applications -- Chapter 2 Mathematical Preliminaries -- 2.1 Sets and Functions -- 2.1.1 Sets -- 2.1.2 Functions -- 2.2 Vector Spaces -- 2.2.1 Real Vector Spaces -- 2.2.2 Linear Dependence and Independence of Vectors -- 2.2.3 Euclidean n-Space -- 2.2.4 Inner Product Space -- 2.2.5 Metric Spaces -- 2.2.6 Normed Space -- 2.3 Matrix Algebra -- 2.3.1 Determinant of a Coefficient Matrix -- 2.3.2 Matrix Multiplication -- 2.4 Vector Differential Calculus -- 2.4.1 Scalar-Valued Functions of Multivariables -- 2.4.2 Vector-Valued Functions of Multivariables -- 2.5 Vector Integral Calculus -- 2.5.1 Green's Theorem in the Plane -- 2.5.2 Gauss's Theorem -- 2.6 Mean Value Theorem -- 2.6.1 Scalar Function of a Real Variable -- 2.6.2 Scalar Function of Multivariables -- 2.6.3 Vector Function of Multivariables -- 2.7 Function Spaces -- 2.7.1 Inner Product Space -- 2.7.2 Normed Space -- 2.7.3 Metric Space -- 2.7.4 Lebesgue Space -- 2.7.5 Banach Space -- 2.7.6 Sobolev Space -- 2.7.7 Hilbert Space -- 2.8 Tensor Analysis -- 2.8.1 Tensor Algebra -- 2.8.2 Tensor Differential Calculus -- 2.8.3 Tensor Integral Calculus -- Exercises -- Part 1 N-Body Dynamical Systems -- Chapter 3 Classical Mechanics -- 3.1 Newtonian Mechanics -- 3.1.1 Newton's Laws of Motion -- 3.1.2 Newton's Equations of Motion -- 3.2 Lagrangian Mechanics -- 3.2.1 Constraints -- 3.2.2 Lagrangian Form of D'Alembert's Principle -- 3.2.3 Configuration Space -- 3.2.4 Generalized Coordinates -- 3.2.5 Tangent Bundle -- 3.2.6 Lagrange's Equations of Motion.PPN: PPN: 809709252Package identifier: Produktsigel: ZDB-26-MYL | ZDB-30-PAD | ZDB-30-PQE
Advances in Computational Dynamics of Particles, Materials and Structures; Contents; Preface; Acknowledgments; About the Authors; Chapter 1 Introduction; 1.1 Overview; 1.1.1 The Mechanics Underlying Computational Dynamics; 1.1.2 The Numerics Underlying Computational Dynamics in Space and Time; 1.2 Applications; Chapter 2 Mathematical Preliminaries; 2.1 Sets and Functions; 2.1.1 Sets; 2.1.2 Functions; 2.2 Vector Spaces; 2.2.1 Real Vector Spaces; 2.2.2 Linear Dependence and Independence of Vectors; 2.2.3 Euclidean n-Space; 2.2.4 Inner Product Space; 2.2.5 Metric Spaces; 2.2.6 Normed Space
2.3 Matrix Algebra2.3.1 Determinant of a Coefficient Matrix; 2.3.2 Matrix Multiplication; 2.4 Vector Differential Calculus; 2.4.1 Scalar-Valued Functions of Multivariables; 2.4.2 Vector-Valued Functions of Multivariables; 2.5 Vector Integral Calculus; 2.5.1 Green's Theorem in the Plane; 2.5.2 Gauss's Theorem; 2.6 Mean Value Theorem; 2.6.1 Scalar Function of a Real Variable; 2.6.2 Scalar Function of Multivariables; 2.6.3 Vector Function of Multivariables; 2.7 Function Spaces; 2.7.1 Inner Product Space; 2.7.2 Normed Space; 2.7.3 Metric Space; 2.7.4 Lebesgue Space; 2.7.5 Banach Space
2.7.6 Sobolev Space2.7.7 Hilbert Space; 2.8 Tensor Analysis; 2.8.1 Tensor Algebra; 2.8.2 Tensor Differential Calculus; 2.8.3 Tensor Integral Calculus; Exercises; Part 1 N-Body Dynamical Systems; Chapter 3 Classical Mechanics; 3.1 Newtonian Mechanics; 3.1.1 Newton's Laws of Motion; 3.1.2 Newton's Equations of Motion; 3.2 Lagrangian Mechanics; 3.2.1 Constraints; 3.2.2 Lagrangian Form of D'Alembert's Principle; 3.2.3 Configuration Space; 3.2.4 Generalized Coordinates; 3.2.5 Tangent Bundle; 3.2.6 Lagrange's Equations of Motion; 3.2.7 Kinetic Energy in Generalized Coordinates
3.2.8 Lagrange Multiplier Method3.2.9 Autonomous Lagrangian Systems; 3.3 Hamiltonian Mechanics; 3.3.1 Phase Space; 3.3.2 Canonical Coordinates; 3.3.3 Cotangent Bundle; 3.3.4 Legendre Transformation; 3.3.5 Hamilton's Equations of Motion; 3.3.6 Autonomous Hamiltonian Systems; 3.3.7 Symplectic Manifold; Exercises; Chapter 4 Principle of Virtual Work; 4.1 Virtual Work in N-Body Dynamical Systems; 4.2 Vector Formalism: Newtonian Mechanics in N-Body Dynamical Systems; 4.3 Scalar Formalisms: Lagrangian and Hamiltonian Mechanics in N-Body Dynamical Systems; Exercises
Chapter 5 Hamilton's Principle and Hamilton's Law of Varying Action5.1 Introduction; 5.2 Variation of the Principal Function; 5.3 Calculus of Variations; 5.4 Hamilton's Principle; 5.5 Hamilton's Law of Varying Action; 5.5.1 Newtonian Mechanics; 5.5.2 Lagrangian Mechanics; 5.5.3 Hamiltonian Mechanics; Exercises; Chapter 6 Principle of Balance of Mechanical Energy; 6.1 Introduction; 6.2 Principle of Balance of Mechanical Energy; 6.3 Total Energy Representations and Framework in the Differential Calculus Setting; 6.3.1 Principle of Balance of Mechanical Energy: Conservative System
6.3.2 Principle of Balance of Mechanical Energy: Nonconservative System
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