Download Product Flyer is to download PDF in new tab. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. We work hard to protect your security and privacy. You're listening to a sample of the Audible audio edition. … The first volume focuses on the use of the method for linear problems. I highly recommend the textbook to anyone who is interested in deepening their understanding of the topic. Description An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). Your recently viewed items and featured recommendations, Select the department you want to search in. Reviewed in the United States on May 18, 2018, Reviewed in the United States on November 3, 2019. Please try again. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). This shopping feature will continue to load items when the Enter key is pressed. Copyright © 2000-document.write(new Date().getFullYear()) by John Wiley & Sons, Inc., or related companies. in One-Dimensional Elasticity Problems 23, 2.3 Weak Form for One-Dimensional Elasticity Problems 24, 2.4 Equivalence of Weak Form and Strong Form 28, 2.5 Strong Form for One-Dimensional Heat Conduction 32, 2.6 Weak Form for One-Dimensional Heat Conduction 37, 3 Finite Element Formulation for One-Dimensional Problems 47, 3.1 Introduction—Piecewise Approximation 47, 3.3 Discrete Equations for Piecewise Finite Element Approximation 59, 3.4 Finite Element Equations for Heat Conduction 66, 3.5 Accounting for Nodes with Prescribed Solution Value (“Fixed” Nodes) 67, 3.6 Examples on One-Dimensional Finite Element Analysis 68, 3.7 Numerical Integration—Gauss Quadrature 91, 3.8 Convergence of One-Dimensional Finite Element Method 100, 3.9 Effect of Concentrated Forces in One-Dimensional Finite Element Analysis 106, 4 Multidimensional Problems: Mathematical Preliminaries 112, 4.3 Green’s Theorem—Divergence Theorem and Green’s Formula 118, 4.4 Procedure for Multidimensional Problems 121, 5 Two-Dimensional Heat Conduction and Other Scalar Field Problems 123, 5.1 Strong Form for Two-Dimensional Heat Conduction 123, 5.2 Weak Form for Two-Dimensional Heat Conduction 129, 5.3 Equivalence of Strong Form and Weak Form 131, 6 Finite Element Formulation for Two-Dimensional Scalar Field Problems 141, 6.1 Finite Element Discretization and Piecewise Approximation 141, 6.2 Three-Node Triangular Finite Element 148, 6.4 Isoparametric Finite Elements and the Four-Node Quadrilateral (4Q) Element 158, 6.5 Numerical Integration for Isoparametric Quadrilateral Elements 165, 6.6 Higher-Order Isoparametric Quadrilateral Elements 176, 6.7 Isoparametric Triangular Elements 178, 6.8 Continuity and Completeness of Isoparametric Elements 181, 6.9 Concluding Remarks: Finite Element Analysis for Other Scalar Field Problems 183, 7.4 Representing Stress and Strain as Column Vectors—The Voigt Notation 193, 7.5 Constitutive Law (Stress-Strain Relation) for Multidimensional Linear Elasticity 194, 7.6 Coordinate Transformation Rules for Stress, Strain, and Material Stiffness Matrix 199, 7.7 Stress, Strain, and Constitutive Models for Two-Dimensional (Planar) Elasticity 202, 7.8 Strong Form for Two-Dimensional Elasticity 208, 7.9 Weak Form for Two-Dimensional Elasticity 212, 7.10 Equivalence between the Strong Form and the Weak Form 215, 7.11 Strong Form for Three-Dimensional Elasticity 218, 7.12 Using Polar (Cylindrical) Coordinates 220, 8 Finite Element Formulation for Two-Dimensional Elasticity 226, 8.1 Piecewise Finite Element Approximation—Assembly Equations 226, 8.2 Accounting for Restrained (Fixed) Displacements 231, 8.4 Continuity—Completeness Requirements 232, 8.5 Finite Elements for Two-Dimensional Elasticity 232, 9 Finite Element Formulation for Three-Dimensional Elasticity 257, 9.1 Weak Form for Three-Dimensional Elasticity 257, 9.2 Piecewise Finite Element Approximation—Assembly Equations 258, 9.3 Isoparametric Finite Elements for Three-Dimensional Elasticity 264, 10 Topics in Applied Finite Element Analysis 289, 10.1 Concentrated Loads in Multidimensional Analysis 289, 10.2 Effect of Autogenous (Self-Induced) Strains—The Special Case of Thermal Strains 291, 10.3 The Patch Test for Verification of Finite Element Analysis Software 294, 10.4 Subparametric and Superparametric Elements 295, 10.5 Field-Dependent Natural Boundary Conditions: Emission Conditions and Compliant Supports 296, 10.7 Treatment of Compliant (Spring) Connections Between Nodal Points 309, 10.9 Axisymmetric Problems and Finite Element Analysis 316, 10.10 A Brief Discussion on Efficient Mesh Refinement 319, 11 Convergence of Multidimensional Finite Element Analysis, Locking Phenomena in Multidimensional Solids and Reduced Integration 324, 11.1 Convergence of Multidimensional Finite Elements 324, 11.2 Effect of Element Shape in Multidimensional Analysis 327, 11.3 Incompatible Modes for Quadrilateral Finite Elements 328, 11.4 Volumetric Locking in Continuum Elements 333, 11.5 Uniform Reduced Integration and Spurious Zero-Energy (Hourglass) Modes 337, 11.6 Resolving the Problem of Hourglass Modes: Hourglass Stiffness 339, 11.8 The B-bar Method for Resolving Locking 348, 12 Multifield (Mixed) Finite Elements 353, 12.1 Multifield Weak Forms for Elasticity 354, 12.2 Mixed (Multifield) Finite Element Formulations 359, 12.3 Two-Field (Stress-Displacement) Formulations and the Pian-Sumihara Quadrilateral Element 367, 12.4 Displacement-Pressure (u-p) Formulations and Finite Element Approximations 370, 12.5 Stability of Mixed u-p Formulations—the inf-sup Condition 374, 12.6 Assumed (Enhanced)-Strain Methods and the B-bar Method as a Special Case 377, 12.7 A Concluding Remark for Multifield Elements 381, 13.2 Differential Equations and Boundary Conditions for 2D Beams 385, 13.4 Strong Form for Two-Dimensional Euler-Bernoulli Beams 392, 13.5 Weak Form for Two-Dimensional Euler-Bernoulli Beams 394, 13.6 Finite Element Formulation: Two-Node Euler-Bernoulli Beam Element 397, 13.7 Coordinate Transformation Rules for Two-Dimensional Beam Elements 404, 13.9 Strong Form for Two-Dimensional Timoshenko Beam Theory 411, 13.10 Weak Form for Two-Dimensional Timoshenko Beam Theory 411, 13.11 Two-Node Timoshenko Beam Finite Element 415, 13.13 Extension of Continuum-Based Beam Elements to General Curved Beams 424, 13.14 Shear Locking and Selective-Reduced Integration for Thin Timoshenko Beam Elements 440, 14.3 Differential Equations of Equilibrium and Boundary Conditions for Flat Shells 452, 14.4 Constitutive Law for Linear Elasticity in Terms of Stress Resultants and Generalized Strains 456, 14.6 Finite Element Formulation for Shell Structures 472, 14.7 Four-Node Planar (Flat) Shell Finite Element 480, 14.8 Coordinate Transformations for Shell Elements 485, 14.9 A “Clever” Way to Approximately Satisfy C1 Continuity Requirements for Thin Shells—The Discrete Kirchhoff Formulation 500, 14.10 Continuum-Based Formulation for Nonplanar (Curved) Shells 510, 15 Finite Elements for Elastodynamics, Structural Dynamics, and Time-Dependent Scalar Field Problems 523, 15.2 Strong Form for One-Dimensional Elastodynamics 525, 15.3 Strong Form in the Presence of Material Damping 527, 15.4 Weak Form for One-Dimensional Elastodynamics 529, 15.5 Finite Element Approximation and Semi-Discrete Equations of Motion 530, 15.6 Three-Dimensional Elastodynamics 536, 15.7 Semi-Discrete Equations of Motion for Three-Dimensional Elastodynamics 539, 15.9 Diagonal (Lumped) Mass Matrices and Mass Lumping Techniques 546, 15.10 Strong and Weak Form for Time-Dependent Scalar Field (Parabolic) Problems 549, 15.11 Semi-Discrete Finite Element Equations for Scalar Field (Parabolic) Problems 555, 15.12 Solid and Structural Dynamics as a “Parabolic” Problem: The State-Space Formulation 557, 16 Analysis of Time-Dependent Scalar Field (Parabolic) Problems 560, 16.4 Predictor-Corrector Algorithms—Runge-Kutta (RK) Methods 569, 16.5 Convergence of a Time-Stepping Algorithm 572, 16.6 Modal Analysis and Its Use for Determining the Stability for Systems with Many Degrees of Freedom 583, 17 Solution Procedures for Elastodynamics and Structural Dynamics 588, 17.2 Modal Analysis: What Will NOT Be Presented in Detail 589, 17.3 Step-by-Step Algorithms for Direct Integration of Equations of Motion 594, 17.4 Application of Step-By-Step Algorithms for Discrete Systems with More than One Degrees of Freedom 608, 18 Verification and Validation for the Finite Element Method 615, 18.5 Sources and Types of Uncertainty 629, 18.8 Extrapolation of Model Prediction Uncertainty 633, 19 Numerical Solution of Linear Systems of Equations 637, 19.4 Parallel Computing and the Finite Element Method 644, 19.5 Parallel Conjugate Gradient Method 649, Appendix A: Concise Review of Vector and Matrix Algebra 654, A.3 Eigenvalues and Eigenvectors of a Matrix 660, Appendix B: Review of Matrix Analysis for Discrete Systems 664, B.3 Solving the Global Stiffness Equations of a Discrete System and Postprocessing 671, B.4 The ID Array Concept (for Equation Assembly) 673, B.5 Fully Automated Assembly: The Connectivity (LM) Array Concept 680, B.6 Advanced Interlude—Programming of Assembly When the Restrained Degrees of Freedom Have Nonzero Values 682, B.7 Advanced Interlude 2: Algorithms for Postprocessing 683, B.8 Two-Dimensional Truss Analysis—Coordinate Transformation Equations 684, B.9 Extension to Three-Dimensional Truss Analysis 693, Appendix C: Minimum Potential Energy for Elasticity—Variational Principles 695, Appendix D: Calculation of Displacement and Force Transformations for Rigid-Body Connections 700.

fundamentals of finite element analysis: linear finite element analysis

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