{"product_id":"advances-in-computational-dynamics-of-particles-materials-and-structures-hardback-9780470749807","title":"Advances in Computational Dynamics of Particles, Materials and Structures (Hardback) 9780470749807","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAdvances in Computational Dynamics of Particles, Materials and Structures\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eJason Har (Author), Kumar Tamma (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470749807, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 27 July 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e710 pages\u003cbr\u003e25.2 x 19.6 x 3.6 cm, 1.338 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eComputational 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAdvances in Computational Dynamics of Particles, Materials and Structures\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eHighlights and key features\u003c\/p\u003e \u003cul\u003e \u003cli\u003e Provides practical applications, from a unified perspective, to both particle and continuum mechanics of flexible structures and materials\u003c\/li\u003e \u003cli\u003ePresents new and traditional developments, as well as alternate perspectives, for space and time discretization \u003c\/li\u003e \u003cli\u003eDescribes a unified viewpoint under the umbrella of Algorithms by Design for the class of linear multi-step methods\u003c\/li\u003e \u003cli\u003eIncludes fundamentals underlying the theoretical aspects and numerical developments, illustrative applications and practice exercises\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe completeness and breadth and depth of coverage makes \u003ci\u003eAdvances in Computational Dynamics of Particles, Materials and Structures\u003c\/i\u003e a valuable textbook and reference for graduate students, researchers and engineers\/scientists working in the field of computational mechanics; and in the general areas of computational sciences and engineering.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePREFACE xv\u003c\/p\u003e \u003cp\u003eACKNOWLEDGMENTS xxi\u003c\/p\u003e \u003cp\u003eABOUT THE AUTHORS xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 INTRODUCTION 1\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e1.1 Overview 1\u003cbr\u003e\u003cbr\u003e1.2 Applications 13\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 MATHEMATICAL PRELIMINARIES 15\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e2.1 Sets and Functions 15\u003cbr\u003e\u003cbr\u003e2.2 Vector Spaces 18\u003cbr\u003e\u003cbr\u003e2.3 Matrix Algebra 24\u003cbr\u003e\u003cbr\u003e2.4 Vector Differential Calculus 28\u003cbr\u003e\u003cbr\u003e2.5 Vector Integral Calculus 32\u003cbr\u003e\u003cbr\u003e2.6 Mean Value Theorem 33\u003cbr\u003e\u003cbr\u003e2.7 Function Spaces 34\u003cbr\u003e\u003cbr\u003e2.8 Tensor Analysis 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I N-BODY DYNAMICAL SYSTEMS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 CLASSICAL MECHANICS 57\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e3.1 Newtonian Mechanics 57\u003cbr\u003e\u003cbr\u003e3.2 Lagrangian Mechanics 60\u003cbr\u003e\u003cbr\u003e3.3 Hamiltonian Mechanics 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 PRINCIPLE OF VIRTUAL WORK 108\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e4.1 Virtual Work in N-Body Dynamical Systems 108\u003cbr\u003e\u003cbr\u003e4.2 Vector Formalism: Newtonian Mechanics in N-Body Dynamical Systems 114\u003cbr\u003e\u003cbr\u003e4.3 Scalar Formalisms: Lagrangian and Hamiltonian Mechanics in N-Body Dynamical Systems 116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 HAMILTON’S PRINCIPLE AND HAMILTON’S LAW OF VARYING ACTION 121\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e5.1 Introduction 121\u003cbr\u003e\u003cbr\u003e5.2 Variation of the Principal Function 122\u003cbr\u003e\u003cbr\u003e5.3 Calculus of Variations 125\u003cbr\u003e\u003cbr\u003e5.4 Hamilton’s Principle 129\u003cbr\u003e\u003cbr\u003e5.5 Hamilton’s Law of Varying Action 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 PRINCIPLE OF BALANCE OF MECHANICAL ENERGY 141\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e6.1 Introduction 142\u003cbr\u003e\u003cbr\u003e6.2 Principle of Balance of Mechanical Energy 142\u003cbr\u003e\u003cbr\u003e6.3 Total Energy Representations and Framework in the Differential Calculus Setting 144\u003cbr\u003e\u003cbr\u003e6.4 Appendix: Total Energy Representations and Framework in the Variational Calculus Setting 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 EQUIVALENCE OF EQUATIONS 163\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e7.1 Equivalence in the Lagrangian Form of D’Alembert’s Principle\/Principle of Virtual Work 163\u003cbr\u003e\u003cbr\u003e7.2 Equivalence in Hamilton’s Principle or Hamilton’s Law of Varying Action 165\u003cbr\u003e\u003cbr\u003e7.3 Equivalence in the Principle of Balance of Mechanical Energy 166\u003cbr\u003e\u003cbr\u003e7.4 Equivalence Relations Between Governing Equations 167\u003cbr\u003e\u003cbr\u003e7.5 Conservation Laws 171\u003cbr\u003e\u003cbr\u003e7.6 Noether’s Theorem 171\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II CONTINUOUS-BODY DYNAMICAL SYSTEMS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 CONTINUUM MECHANICS 175\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e8.1 Displacements, Strains and Stresses 175\u003cbr\u003e\u003cbr\u003e8.2 General Principles 197\u003cbr\u003e\u003cbr\u003e8.3 Constitutive Equations in Elasticity 206\u003cbr\u003e\u003cbr\u003e8.4 Virtual Work and Variational Principles 220\u003cbr\u003e\u003cbr\u003e8.5 Direct Variational Methods for Two-Point Boundary-Value Problems 237\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 PRINCIPLE OF VIRTUAL WORK: FINITE ELEMENTS AND SOLID\/STRUCTURAL MECHANICS 267\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e9.1 Introduction 267\u003cbr\u003e\u003cbr\u003e9.2 Finite Element Library 301\u003cbr\u003e\u003cbr\u003e9.3 Nonlinear Finite Element Formulations 343\u003cbr\u003e\u003cbr\u003e9.4 Scalar Formalisms: Lagrangian and Hamiltonian Mechanics and Finite Element Formulations in Continuous-Body Dynamical Systems 350\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 HAMILTON'S PRINCIPLE AND HAMILTON'S LAW OF VARYING ACTION: FINITE ELEMENTS AND SOLID\/STRUCTURAL MECHANICS 364\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e10.1 Introduction 364\u003cbr\u003e\u003cbr\u003e10.2 Hamilton’s Principle and Hamilton’s Law of Varying Action in Elastodynamics 365\u003cbr\u003e\u003cbr\u003e10.3 Lagrangian Mechanics Framework and Finite Element Formulations 370\u003cbr\u003e\u003cbr\u003e10.4 Hamiltonian Mechanics Framework and Finite Element Formulations 400\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 PRINCIPLE OF BALANCE OF MECHANICAL ENERGY: FINITE ELEMENTS AND SOLID\/STRUCTURAL MECHANICS 426\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e11.1 Introduction 427\u003cbr\u003e\u003cbr\u003e11.2 Total Energy Representations and Framework in the Differential Calculus Setting and Finite Element \u003cbr\u003eFormulations 429\u003cbr\u003e\u003cbr\u003e11.3 Lagrangian Mechanics Framework in the Differential Calculus Setting and Finite Element Formulations 449\u003cbr\u003e\u003cbr\u003e11.4 Hamiltonian Mechanics Framework in the Differential Calculus Setting and Finite Element Formulations 454\u003cbr\u003e\u003cbr\u003e11.5 Appendix: Total Energy Representations and Framework in the Variational Calculus Setting and Finite Element Formulations 458\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 EQUIVALENCE OF EQUATIONS 475\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e12.1 Equivalence in the Principle of Virtual Work in Dynamics 475\u003cbr\u003e\u003cbr\u003e12.2 Equivalence in Hamilton’s Principle or Hamilton’s Law of Varying Action 478\u003cbr\u003e\u003cbr\u003e12.3 Equivalence in the Principle of Balance of Mechanical Energy 482\u003cbr\u003e\u003cbr\u003e12.4 Equivalence of Strong and Weak Forms for Initial Boundary-Value Problems 483\u003cbr\u003e\u003cbr\u003e12.5 Equivalence of the Semi-Discrete Finite Element Equations of Motion 487\u003cbr\u003e\u003cbr\u003e12.6 Equivalence of Finite Element Formulations 488\u003cbr\u003e\u003cbr\u003e12.7 Conservation Laws 490\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III THE TIME DIMENSION\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 TIME DISCRETIZATION OF EQUATIONS OF MOTION: OVERVIEW AND CONVENTIONAL PRACTICES 495\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e13.1 Introduction 495\u003cbr\u003e\u003cbr\u003e13.2 Single-Step Methods for First-Order Ordinary Differential Equations 500\u003cbr\u003e\u003cbr\u003e13.3 Linear Multistep Methods 505\u003cbr\u003e\u003cbr\u003e13.4 Second-Order Systems and Single Step and\/or Equivalent LMS Methods: Brief Overview of Classical \u003cbr\u003eMethods from Historical Perspectives and Chronological Developments 507\u003cbr\u003e\u003cbr\u003e13.5 Symplectic-Momentum Conservation and Variational Time Integrators 527\u003cbr\u003e\u003cbr\u003e13.6 Energy-Momentum Conservation and Time Integration Algorithms 536\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 TIME DISCRETIZATION OF EQUATIONS OF MOTION: RECENT ADVANCES 553\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e14.1 Introduction 553\u003cbr\u003e\u003cbr\u003e14.2 Time Discretization and the Total Energy Framework: Linear Dynamic Algorithms and Designs - Generalized Single Step Single Solve [GSSSS] Unified Framework Encompassing LMS Methods 555\u003cbr\u003e\u003cbr\u003e14.3 Time Discretization and the Total Energy Framework: Nonlinear Dynamics Algorithms and Designs - Generalized Single Step Single Solve [GSSSS] Framework Encompassing LMS Methods 578\u003cbr\u003e\u003cbr\u003e14.4 Time Discretization and Total Energy Framework: N-Body Systems 632\u003cbr\u003e\u003cbr\u003e14.5 Time Discretization and Total Energy Framework: Nonconservative\/Conservative Mechanical Systems with Holonomic-Scleronomic Constraints 649\u003cbr\u003e\u003cbr\u003e14.5.1 General Formulations 650\u003cbr\u003e\u003cbr\u003eExercises 662\u003c\/p\u003e \u003cp\u003eREFERENCES 669\u003c\/p\u003e \u003cp\u003eINDEX 681\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mechanical engineering \u0026amp; materials [\u003ca title=\"See our other books on Mechanical engineering \u0026amp; materials\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20\u0026amp;%20materials%20%5BTG%5D%22\"\u003eTG\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand 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