{"product_id":"a-first-course-in-finite-elements-isbn-9780470035801","title":"A First Course in Finite Elements","description":"The text material evolved from over 50 years of combined teaching experience it deals with a formulation and application of the finite element method. A meaningful course can be constructed from a subset of the chapters in this book for a quarter course; instructions for such use are given in the preface. The course material is organized in three chronological units of one month each: 1) the finite element formulation for one-dimensional problems, 2) the finite element formulation for scalar field problems in two dimensions and 3) finite element programming and application to scalar field problems; and finite element formulation for vector field problems in two dimensions and beams. In conjunction with the book there will be the access and use of ABAQUS software and MATLAB exercises. \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Background 1\u003c\/p\u003e \u003cp\u003e1.2 Applications of Finite elements 7\u003c\/p\u003e \u003cp\u003eReferences 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Direct Approach for Discrete Systems 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Describing the Behavior of a Single Bar Element 11\u003c\/p\u003e \u003cp\u003e2.2 Equations for a System 15\u003c\/p\u003e \u003cp\u003e2.2.1 Equations for Assembly 18\u003c\/p\u003e \u003cp\u003e2.2.2 Boundary Conditions and System Solution 20\u003c\/p\u003e \u003cp\u003e2.3 Applications to Other Linear Systems 24\u003c\/p\u003e \u003cp\u003e2.4 Two-Dimensional Truss Systems 27\u003c\/p\u003e \u003cp\u003e2.5 Transformation Law 30\u003c\/p\u003e \u003cp\u003e2.6 Three-Dimensional Truss Systems 35\u003c\/p\u003e \u003cp\u003eReferences 36\u003c\/p\u003e \u003cp\u003eProblems 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Strong and Weak Forms for One-Dimensional Problems 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Strong Form in One-Dimensional Problems 42\u003c\/p\u003e \u003cp\u003e3.1.1 The Strong Form for an Axially Loaded Elastic Bar 42\u003c\/p\u003e \u003cp\u003e3.1.2 The Strong Form for Heat Conduction in One Dimension 44\u003c\/p\u003e \u003cp\u003e3.1.3 Diffusion in One Dimension 46\u003c\/p\u003e \u003cp\u003e3.2 The Weak Form in One Dimension 47\u003c\/p\u003e \u003cp\u003e3.3 Continuity 50\u003c\/p\u003e \u003cp\u003e3.4 The Equivalence Between the Weak and Strong Forms 51\u003c\/p\u003e \u003cp\u003e3.5 One-Dimensional Stress Analysis with Arbitrary Boundary Conditions 58\u003c\/p\u003e \u003cp\u003e3.5.1 Strong Form for One-Dimensional Stress Analysis 58\u003c\/p\u003e \u003cp\u003e3.5.2 Weak Form for One-Dimensional Stress Analysis 59\u003c\/p\u003e \u003cp\u003e3.6 One-Dimensional Heat Conduction with Arbitrary Boundary Conditions 60\u003c\/p\u003e \u003cp\u003e3.6.1 Strong Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 60\u003c\/p\u003e \u003cp\u003e3.6.2 Weak Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 61\u003c\/p\u003e \u003cp\u003e3.7 Two-Point Boundary Value Problem with Generalized Boundary Conditions 62\u003c\/p\u003e \u003cp\u003e3.7.1 Strong Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 62\u003c\/p\u003e \u003cp\u003e3.7.2 Weak Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 63\u003c\/p\u003e \u003cp\u003e3.8 Advection–Diffusion 64\u003c\/p\u003e \u003cp\u003e3.8.1 Strong Form of Advection–Diffusion Equation 65\u003c\/p\u003e \u003cp\u003e3.8.2 Weak Form of Advection–Diffusion Equation 66\u003c\/p\u003e \u003cp\u003e3.9 Minimum Potential Energy 67\u003c\/p\u003e \u003cp\u003e3.10 Integrability 71\u003c\/p\u003e \u003cp\u003eReferences 72\u003c\/p\u003e \u003cp\u003eProblems 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Approximation of Trial Solutions, Weight Functions and Gauss Quadrature for One-Dimensional Problems 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Two-Node Linear Element 79\u003c\/p\u003e \u003cp\u003e4.2 Quadratic One-Dimensional Element 81\u003c\/p\u003e \u003cp\u003e4.3 Direct Construction of Shape Functions in One Dimension 82\u003c\/p\u003e \u003cp\u003e4.4 Approximation of the Weight Functions 84\u003c\/p\u003e \u003cp\u003e4.5 Global Approximation and Continuity 84\u003c\/p\u003e \u003cp\u003e4.6 Gauss Quadrature 85\u003c\/p\u003e \u003cp\u003eReference 90\u003c\/p\u003e \u003cp\u003eProblems 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Finite Element Formulation for One-Dimensional Problems 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Development of Discrete Equation: Simple Case 93\u003c\/p\u003e \u003cp\u003e5.2 Element Matrices for Two-Node Element 97\u003c\/p\u003e \u003cp\u003e5.3 Application to Heat Conduction and Diffusion Problems 99\u003c\/p\u003e \u003cp\u003e5.4 Development of Discrete Equations for Arbitrary Boundary Conditions 105\u003c\/p\u003e \u003cp\u003e5.5 Two-Point Boundary Value Problem with Generalized Boundary Conditions 111\u003c\/p\u003e \u003cp\u003e5.6 Convergence of the FEM 113\u003c\/p\u003e \u003cp\u003e5.6.1 Convergence by Numerical Experiments 115\u003c\/p\u003e \u003cp\u003e5.6.2 Convergence by Analysis 118\u003c\/p\u003e \u003cp\u003e5.7 FEM for Advection–Diffusion Equation 120\u003c\/p\u003e \u003cp\u003eReferences 122\u003c\/p\u003e \u003cp\u003eProblems 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Strong and Weak Forms for Multidimensional Scalar Field Problems 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Divergence Theorem and Green’s Formula 133\u003c\/p\u003e \u003cp\u003e6.2 Strong Form 139\u003c\/p\u003e \u003cp\u003e6.3 Weak Form 142\u003c\/p\u003e \u003cp\u003e6.4 The Equivalence Between Weak and Strong Forms 144\u003c\/p\u003e \u003cp\u003e6.5 Generalization to Three-Dimensional Problems 145\u003c\/p\u003e \u003cp\u003e6.6 Strong and Weak Forms of Scalar Steady-State Advection–Diffusion in Two Dimensions 146\u003c\/p\u003e \u003cp\u003eReferences 148\u003c\/p\u003e \u003cp\u003eProblems 148\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Approximations of Trial Solutions, Weight Functions and Gauss Quadrature for Multidimensional Problems 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Completeness and Continuity 152\u003c\/p\u003e \u003cp\u003e7.2 Three-Node Triangular Element 154\u003c\/p\u003e \u003cp\u003e7.2.1 Global Approximation and Continuity 157\u003c\/p\u003e \u003cp\u003e7.2.2 Higher Order Triangular Elements 159\u003c\/p\u003e \u003cp\u003e7.2.3 Derivatives of Shape Functions for the Three-Node Triangular Element 160\u003c\/p\u003e \u003cp\u003e7.3 Four-Node Rectangular Elements 161\u003c\/p\u003e \u003cp\u003e7.4 Four-Node Quadrilateral Element 164\u003c\/p\u003e \u003cp\u003e7.4.1 Continuity of Isoparametric Elements 166\u003c\/p\u003e \u003cp\u003e7.4.2 Derivatives of Isoparametric Shape Functions 166\u003c\/p\u003e \u003cp\u003e7.5 Higher Order Quadrilateral Elements 168\u003c\/p\u003e \u003cp\u003e7.6 Triangular Coordinates 172\u003c\/p\u003e \u003cp\u003e7.6.1 Linear Triangular Element 172\u003c\/p\u003e \u003cp\u003e7.6.2 Isoparametric Triangular Elements 174\u003c\/p\u003e \u003cp\u003e7.6.3 Cubic Element 175\u003c\/p\u003e \u003cp\u003e7.6.4 Triangular Elements by Collapsing Quadrilateral Elements 176\u003c\/p\u003e \u003cp\u003e7.7 Completeness of Isoparametric Elements 177\u003c\/p\u003e \u003cp\u003e7.8 Gauss Quadrature in Two Dimensions 178\u003c\/p\u003e \u003cp\u003e7.8.1 Integration Over Quadrilateral Elements 179\u003c\/p\u003e \u003cp\u003e7.8.2 Integration Over Triangular Elements 180\u003c\/p\u003e \u003cp\u003e7.9 Three-Dimensional Elements 181\u003c\/p\u003e \u003cp\u003e7.9.1 Hexahedral Elements 181\u003c\/p\u003e \u003cp\u003e7.9.2 Tetrahedral Elements 183\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003eProblems 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Finite Element Formulation for Multidimensional Scalar Field Problems 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Finite Element Formulation for Two-Dimensional Heat Conduction Problems 189\u003c\/p\u003e \u003cp\u003e8.2 Verification and Validation 201\u003c\/p\u003e \u003cp\u003e8.3 Advection–Diffusion Equation 207\u003c\/p\u003e \u003cp\u003eReferences 209\u003c\/p\u003e \u003cp\u003eProblems 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Finite Element Formulation for Vector Field Problems – Linear Elasticity 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Linear Elasticity 215\u003c\/p\u003e \u003cp\u003e9.1.1 Kinematics 217\u003c\/p\u003e \u003cp\u003e9.1.2 Stress and Traction 219\u003c\/p\u003e \u003cp\u003e9.1.3 Equilibrium 220\u003c\/p\u003e \u003cp\u003e9.1.4 Constitutive Equation 222\u003c\/p\u003e \u003cp\u003e9.2 Strong and Weak Forms 223\u003c\/p\u003e \u003cp\u003e9.3 Finite Element Discretization 225\u003c\/p\u003e \u003cp\u003e9.4 Three-Node Triangular Element 228\u003c\/p\u003e \u003cp\u003e9.4.1 Element Body Force Matrix 229\u003c\/p\u003e \u003cp\u003e9.4.2 Boundary Force Matrix 230\u003c\/p\u003e \u003cp\u003e9.5 Generalization of Boundary Conditions 231\u003c\/p\u003e \u003cp\u003e9.6 Discussion 239\u003c\/p\u003e \u003cp\u003e9.7 Linear Elasticity Equations in Three Dimensions 240\u003c\/p\u003e \u003cp\u003eProblems 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Finite Element Formulation for Beams 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Governing Equations of the Beam 249\u003c\/p\u003e \u003cp\u003e10.1.1 Kinematics of Beam 249\u003c\/p\u003e \u003cp\u003e10.1.2 Stress–Strain Law 252\u003c\/p\u003e \u003cp\u003e10.1.3 Equilibrium 253\u003c\/p\u003e \u003cp\u003e10.1.4 Boundary Conditions 254\u003c\/p\u003e \u003cp\u003e10.2 Strong Form to Weak Form 255\u003c\/p\u003e \u003cp\u003e10.2.1 Weak Form to Strong Form 257\u003c\/p\u003e \u003cp\u003e10.3 Finite Element Discretization 258\u003c\/p\u003e \u003cp\u003e10.3.1 Trial Solution and Weight Function Approximations 258\u003c\/p\u003e \u003cp\u003e10.3.2 Discrete Equations 260\u003c\/p\u003e \u003cp\u003e10.4 Theorem of Minimum Potential Energy 261\u003c\/p\u003e \u003cp\u003e10.5 Remarks on Shell Elements 265\u003c\/p\u003e \u003cp\u003eReference 269\u003c\/p\u003e \u003cp\u003eProblems 269\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Commercial Finite Element Program ABAQUS Tutorials 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 275\u003c\/p\u003e \u003cp\u003e11.1.1 Steady-State Heat Flow Example 275\u003c\/p\u003e \u003cp\u003e11.2 Preliminaries 275\u003c\/p\u003e \u003cp\u003e11.3 Creating a Part 276\u003c\/p\u003e \u003cp\u003e11.4 Creating a Material Definition 278\u003c\/p\u003e \u003cp\u003e11.5 Defining and Assigning Section Properties 279\u003c\/p\u003e \u003cp\u003e11.6 Assembling the Model 280\u003c\/p\u003e \u003cp\u003e11.7 Configuring the Analysis 280\u003c\/p\u003e \u003cp\u003e11.8 Applying a Boundary Condition and a Load to the Model 280\u003c\/p\u003e \u003cp\u003e11.9 Meshing the Model 282\u003c\/p\u003e \u003cp\u003e11.10 Creating and Submitting an Analysis Job 284\u003c\/p\u003e \u003cp\u003e11.11 Viewing the Analysis Results 284\u003c\/p\u003e \u003cp\u003e11.12 Solving the Problem Using Quadrilaterals 284\u003c\/p\u003e \u003cp\u003e11.13 Refining the Mesh 285\u003c\/p\u003e \u003cp\u003e11.13.1 Bending of a Short Cantilever Beam 287\u003c\/p\u003e \u003cp\u003e11.14 Copying the Model 287\u003c\/p\u003e \u003cp\u003e11.15 Modifying the Material Definition 287\u003c\/p\u003e \u003cp\u003e11.16 Configuring the Analysis 287\u003c\/p\u003e \u003cp\u003e11.17 Applying a Boundary Condition and a Load to the Model 288\u003c\/p\u003e \u003cp\u003e11.18 Meshing the Model 289\u003c\/p\u003e \u003cp\u003e11.19 Creating and Submitting an Analysis Job 290\u003c\/p\u003e \u003cp\u003e11.20 Viewing the Analysis Results 290\u003c\/p\u003e \u003cp\u003e11.20.1 Plate with a Hole in Tension 290\u003c\/p\u003e \u003cp\u003e11.21 Creating a New Model 292\u003c\/p\u003e \u003cp\u003e11.22 Creating a Part 292\u003c\/p\u003e \u003cp\u003e11.23 Creating a Material Definition 293\u003c\/p\u003e \u003cp\u003e11.24 Defining and Assigning Section Properties 294\u003c\/p\u003e \u003cp\u003e11.25 Assembling the Model 295\u003c\/p\u003e \u003cp\u003e11.26 Configuring the Analysis 295\u003c\/p\u003e \u003cp\u003e11.27 Applying a Boundary Condition and a Load to the Model 295\u003c\/p\u003e \u003cp\u003e11.28 Meshing the Model 297\u003c\/p\u003e \u003cp\u003e11.29 Creating and Submitting an Analysis Job 298\u003c\/p\u003e \u003cp\u003e11.30 Viewing the Analysis Results 299\u003c\/p\u003e \u003cp\u003e11.31 Refining the Mesh 299\u003c\/p\u003e \u003cp\u003eAppendix 303\u003c\/p\u003e \u003cp\u003eA. 1 Rotation of Coordinate System in Three Dimensions 303\u003c\/p\u003e \u003cp\u003eA. 2 Scalar Product Theorem 304\u003c\/p\u003e \u003cp\u003eA. 3 Taylor’s Formula with Remainder and the Mean Value Theorem 304\u003c\/p\u003e \u003cp\u003eA. 4 Green’s Theorem 305\u003c\/p\u003e \u003cp\u003eA. 5 Point Force (Source) 307\u003c\/p\u003e \u003cp\u003eA. 6 Static Condensation 308\u003c\/p\u003e \u003cp\u003eA. 7 Solution Methods 309\u003c\/p\u003e \u003cp\u003eDirect Solvers 310\u003c\/p\u003e \u003cp\u003eIterative Solvers 310\u003c\/p\u003e \u003cp\u003eConditioning 311\u003c\/p\u003e \u003cp\u003eReferences 312\u003c\/p\u003e \u003cp\u003eProblem 312\u003c\/p\u003e \u003cp\u003eIndex 313\u003c\/p\u003e \"Recommended for upper division undergraduates and above.\" (\u003ci\u003eCHOICE\u003c\/i\u003e, February 2008) \u003cp\u003erong\u0026gt;Jacob Fish The Rosalind and John J. Redfern, Jr. '33 Chaired Professor in Engineering Rensselaer Polytechnic Institute, Troy, NY\u003cbr\u003eDr. Fish has 20 years of experience (both industry and academia) in the field of multi-scale computational engineering, which bridges the gap between modeling, simulation and design of products based on multi-scale principles. Dr. Fish has published over one hundred journal articles and book chapters. Two of his papers, one on development of multilevel solution techniques for large scale systems presented at the 1995 ASME International Computers in Engineering Conference and the second one, on fatigue crack growth in aging aircraft presented at the 1993 Structures, Structural Dynamics, and Materials Conference have won the Best Paper Awards. Dr. Fish is a recipient of 2005 USACM Computational Structural Mechanics Award given \"in recognition of outstanding and sustained contributions to the broad field of Computational Structural Mechanics\". He is editor of the International Journal for Multiscale Computational Engineering.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTed Belytschko\u003c\/b\u003e, Department of Mechanical Engineering, Northwestern University, Evanston, IL\u003cbr\u003eTed Belytschko's main interests lie in the development of computational methods for engineering problems. He has developed explicit finite element methods that are widely used in crashworthiness analysis and virtual prototyping. He is also interested in engineering education, and he chaired the committee that developed the \"Engineering First Program\" at Northwestern.  He obtained his B.S. and Ph.D. at Illinois Institute of Technology in 1965 and 1968, respectively.  He has been at Northwestern since 1977 where he is currently Walter P. Murphy Professor and McCormick Distinguished Professor of Computational Mechanics. He is co-author of the book NONLINEAR FINITE ELEMENTS FOR CONTINUA AND STRUCTURES with W.K.Liu and B. Moran (published by Wiley and in the third printing) and he has edited more than 10 other books. n January 2004, he was listed as the 4th most cited researcher in engineering. He is past Chairman of the Engineering Mechanics Division of the ASCE, the Applied Mechanics Division of ASME, past President of USACM, and a member of the National Academy of Engineering (elected in 1992) and the American Academy of Arts and Sciences (elected in 2002). He is the editor of Numerical Methods in Engineering.\u003c\/p\u003e  Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations.   \u003cp\u003eFocusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student.\u003c\/p\u003e \u003cp\u003eThis authoritative text on Finite Elements:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eAdopts a generic approach to the subject, and is not application specific\u003c\/li\u003e \u003cli\u003eIn conjunction with a web-based chapter, it integrates code development, theory, and application in one book\u003c\/li\u003e \u003cli\u003eProvides an accompanying Web site that includes ABAQUS Student Edition, Matlab data and programs, and instructor resources\u003c\/li\u003e \u003cli\u003eContains a comprehensive set of homework problems at the end of each chapter\u003c\/li\u003e \u003cli\u003eProduces a practical, meaningful course for both lecturers, planning a finite element module, and for students using the text in private study.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eA First Course in Finite Elements\u003c\/i\u003e is the ideal practical introductory course for junior and senior undergraduate students from a variety of science and engineering disciplines.  The accompanying advanced topics at the end of each chapter also make it suitable for courses at graduate level, as well as for practitioners who need to attain or refresh their knowledge of finite elements through private study.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988627505381,"sku":"NP9780470035801","price":73.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470035801.jpg?v=1761781030","url":"https:\/\/k12savings.com\/es\/products\/a-first-course-in-finite-elements-isbn-9780470035801","provider":"K12savings","version":"1.0","type":"link"}