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A First Course in Finite Elements

Jacob Fish; Ted Belytschko (Northwestern

2007

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.

Focusing 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.

This authoritative text on Finite Elements: *Adopts a generic approach to the subject, and is not application specific *In conjunction with a web-based chapter, it integrates code development, theory, and application in one book *Provides an accompanying Web site that includes ABAQUS Student Edition, Matlab data and programs, and instructor resources *Contains a comprehensive set of homework problems at the end of each chapter *Produces a practical, meaningful course for both lecturers, planning a finite element module, and for students using the text in private study.

A First Course in Finite Elements 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.

WILEY

ISBN-10: 0470035803
ISBN-13: 9780470035801

PGS: 352

List: 84.95 YOUR PRICE: 80.70

A First Course in the Finite Element Method - SI Version , 4th Ed.

Daryl L. Logan

2011

Contents: Chapter 1 - Introduction Prologue. Brief History. Introduction to Matrix Notation. Role of the Computer. General Steps of the Finite Element of Method. Applications of the Finite Element Methods. Advantages of the Finite Element Method. Computer Programs for the Finite Element Method. References. Problems. Chapter 2 - Introduction to the Stiffness (Displacement) Method Introduction. Definitions of the Stiffness Matrix. Derivation of the Stiffness Matrix for a Spring Element. Example of a Spring Assemblage. Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method). Boundary Conditions. Potential Energy Approach to Derive Spring Element Equations. References. Problems. Chapter 3 - Development of Truss Equations Introduction. Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates. Selecting Approximation Functions for Displacements. Transformation of Vectors in Two Dimensions. Global Stiffness Matrix. Computation of Stress for a Bar in the x-y Plane. Solution of a Plane Truss. Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space. Use of Symmetry in Structure. Inclined, or Skewed, Supports. Potential Energy Approach to Derive Bar Element Equations. Comparison of Finite Element Solution to Exact Solution for Bar. Galerkin''s Residual Method and Its Application to a One-Dimensional Bar. References. Problems. Chapter 4 - Development of Beam Equations Introduction. Beam Stiffness. Example of Assemblage of Beam Stiffness Matrices. Examples of Beam Analysis Using the Direct Stiffness Method. Distributed Loading. Comparison of Finite Element Solution to the Exact Solution for a Beam. Beam Element with Nodal Hinge. Potential Energy Approach to Derive Beam Element Equations. Galerkin''s Method for Deriving Beam Element Equations. References. Problems. Chapter 5 - Frame and Grid Equations Introduction. Two-Dimensional Arbitrarily Oriented Beam Element. Rigid Plane Frame Examples. Inclined or Skewed Supports-Frame Element. Grid Equations. Beam Element Arbitrarily Oriented in Space. Concepts of Substructure Analysis. References. Problems. Chapter 6 - Development of the Plane Stress and Plane Strain Stiffness Equations Introduction. Basic Concepts of Plane Stress and Plane Strain. Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations. Treatment of Body and Surface Forces. Explicit Expression for the Constant-Strain Triangle Stiffness Matrix. Finite Element Solution of a Plane Stress Problem. References. Problems. Chapter 7 - Practical Considerations in Modeling; Interpreting Results and Examples of Plane Stress/Strain Analysis Introduction. Finite Element Modeling. Equilibrium and Compatibility of Finite Element Results. Convergence of Solution. Interpretation of Stresses. Static Condensation. Flowchart for the Solution of Plane Stress Problems. Computer Program Results for Some Plane Stress/Strain Problems. References. Problems. Chapter 8 - Development of the Linear-Strain Triangle Equations Introduction. Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations. Example LST Stiffness Determination. Comparison of Elements. References. Problems. Chapter 9 - Axisymmetric Elements Introduction. Derivation of the Stiffness Matrix. Solutions of an Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements. References. Problems. Chapter 10 - Isoparametric Formulation Introduction. Isoparametric Formulation of the Bar Element Stiffness Matrix. Rectangular Plane Stress Element. Isoparametric Formulation of the Plane Element Stiffness Matrix. Gaussian Quadrature (Numerical Integration). Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature. Higher-Order Shape Functions. References. Problems. Chapter 11 - Three-Dimensional Stress Analysis Introduction. Three Dimensional Stress and Strain. Tetrahedral Element. Isoparametric Formulation. References. Problems. Chapter 12 - Plate Bending Element Introduction. Basic Concepts of Plate Bending. Derivation of a Plate Bending Element Stiffness Matrix and Equations. Some Plate Element Numerical Comparisons. Computer Solutions for a Plate Bending Problem. References. Problems. Chapter 13 - Heat Transfer and Mass Transport Introduction. Derivation of the Basic Differential Equation. Heat Transfer with Convection. Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h. One-Dimensional Finite Element Formulation Using a Variational Method. Two-Dimensional Finite Element Formulation. Line or Point Sources. One-Dimensional Heat Transfer with Mass Transport. Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin''''s Method. Flowchart and Examples of Heat-Transfer Program. References. Problems. Chapter 14 - Fluid Flow Introduction. Derivation of the Basic Differential Equations. One-Dimensional Finite Element Formulation. Two-Dimensional Finite Element Formulation. Flo

CL-Engineering - CENGAGE

ISBN-10: 0495667919
ISBN-13: 9780495667919

PGS: 752

List: 176.95 YOUR PRICE: 168.10

A First Course in the Finite Element Method Using Algor, 2nd Ed.

Daryl L. Logan

2001

1. INTRODUCTION Prologue / Brief History / Introduction to Matrix Notation / Role of the Computer / General Steps of the Finite Element Method / Applications of the Finite Element Method / Advantages of the Finite Element Method / Computer Programs for the Finite Element Method / References / Problems 2. INTRODUCTION TO THE STIFFNESS (DISPLACEMENT) METHOD Introduction / Definition of the Stiffness Matrix / Derivation of the Stiffness Matrix for a Spring Element / Example of a Spring Assemblage / Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method) / Boundary Conditions / Potential Energy Approach to Derive Spring Element Equations / References / Problems 3. DEVELOPMENT OF TRUSS EQUATIONS Introduction / Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates / Selecting Approximation Functions for Displacements / Transformation of Vectors in Two Dimensions / Global Stiffness Matrix / Computation of Stress for a Bar in the x-y Plane / Solution of a Plane Truss / Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space / Use of Symmetry in Structure / Inclined, or Skewed, Supports / Potential Energy Approach to Derive Bar Element Equations / Comparison of Finite Element Solution to Exact Solution for Bar / Galerkin''s Residual Method and Its Application to a One-Dimensional Bar / References / Problems 4. ALGOR? PROGRAM FOR TRUSS ANALYSIS Introduction / Overview of the Algor system and Flowcharts for the Solution of a Truss Problem Using Algor / Algor Example Solutions for Truss Analysis / References / Problems 5. DEVELOPMENT OF BEAM EQUATIONS Introduction / Beam Stiffness / Example of Assemblage of Beam Stiffness Matrices / Examples of Beam Analysis Using the Direct Stiffness Method / Distributed Loading / Comparison of Finite Element Solution to Exact Solution for Beam / Beam Element with Nodal Hinge / Potential Energy Approach to Derive Beam Element Equations / Galerkin''s Method to Derive Beam Element Equations / Algor Example Solutions for Beam Analysis / References / Problems 6. FRAME AND GRID EQUATIONS Introduction / Two-Dimensional Arbitrarily Oriented Beam Element / Rigid Plane Frame Examples / Inclined or Skewed Supports---Frame Element / Grid Equations / Beam Element Arbitrarily Oriented in Space / Concept of Substructure Analysis / Algor Example Solutions for Plane Frame, Grid, and Space Frame Analysis / References / Problems 7. DEVELOPMENT OF THE PLANE STRESS AND PLANE STRAIN STIFFNESS EQUATIONS Introduction / Basic Concepts of Plane Stress and Plane Strain / Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations / Treatment of Body and Surface Forces / Explicit Expression for the Constant-Strain Triangle Stiffness Matrix / Finite Element Solution of a Plane Stress Problem / References / Problems 8. PRACTICAL CONSIDERATIONS IN MODELING; INTERPRETING RESULTS; AND USE OF THE ALGOR? PROGRAM FOR PLANE STRESS/STRAIN ANALYSIS Introduction / Finite Element Modeling / Equilibrium and Compatibility of Finite Element Results / Convergence of Solution / Interpretation of Stresses / Static Condensation / Flowchart for the Solution of Plane Stress/Strain / Problems and Typical Steps Using Algor / Algor Example Solutions for Plane Stress/Strain Analysis / References / Problems 9. DEVELOPMENT OF THE LINEAR-STRAIN TRIANGLE EQUATIONS Introduction / Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations / Example LST Stiffness Determination / Comparison of Elements / References / Problems 10. AXISYMMETRIC ELEMENTS Introduction / Derivation of the Stiffness Matrix / Solution of an Axisymmetric Pressure Vessel / Applications of Axisymmetric Elements / Algor Example Solutions for Axisymmetric Problems / References / Problems 11. ISOPARAMETRIC FORMULATION Introduction / Isoparametric Formulation of the Bar Element Stiffness Matrix / Rectangular Plane Stress Element / Isoparametric Formulation of the Plane Element Stiffness Matrix / Gaussian Quadrature (Numerical Integration) / Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature / Higher-Order Shape Functions / References / Problems 12. THREE-DIMENSIONAL STRESS ANALYSIS Introduction / Three-Dimensional Stress and Strain / Tetrahedral Element / Isoparametric Formulation / Algor Example Solutions of Three-Dimensional Stress Analysis / References / Problems 13. HEAT TRANSFER AND MASS TRANSPORT Introduction / Derivation of the Basic Differential Equation / Heat Transfer with Convection / Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h / One-Dimensional Finite Element Formulation Using a Variational Method / Two-Dimensional Finite Element Formulation / Line or Point Sources / One-Dimensional Heat Transfer with Mass Transport / Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin''s Method / Flowchart of a Heat-Transfer Program / Algor Example Solutions for Heat-Transfer Problems

Thomson-Engineering - CENGAGE

ISBN-10: 0534380689
ISBN-13: 9780534380687

PGS: 864

List: 191.95 YOUR PRICE: 182.35

A First Course in the Finite Element Method, 3rd Ed.

Daryl L. Logan

2002

Contents: 1. Introduction. Prologue. Brief History. Introduction to Matrix Notation. Role of the Computer. General Steps of the Finite Element of Method. Applications of the Finite Element Methods. Advantages of the Finite Element Method. Computer Programs for the Finite Element Method. References. Problems. 2. Introduction to the Stiffness (Displacement) Method. Introduction. Definitions of the Stiffness Matrix. Derivation of the Stiffness Matrix for a Spring Element. Example of a Spring Assemblage. Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method). Boundary Conditions. Potential Energy Approach to Derive Spring Element Equations. References. Problems. 3. Development of Truss Equations. Introduction. Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates. Selecting Approximation Functions for Displacements. Transformation of Vectors in Two Dimensions. Global Stiffness Matrix. Computation of Stress for a Bar in the x-y Plane. Solution of a Plane Truss. Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space. Use of Symmetry in Structure. Inclined, or Skewed, Supports. Potential Energy Approach to Derive Bar Element Equations. Comparison of Finite Element Solution to Exact Solution for Bar. Galerkin''''s Residual Method and Its Application to a One-Dimensional Bar. References. Problems. 4. Development of Beam Equations. Introduction. Beam Stiffness. Example of Assemblage of Beam Stiffness Matrices. Examples of Beam Analysis Using the Direct Stiffness Method. Distributed Loading. Comparison of Finite Element Solution to the Exact Solution for a Beam. Beam Element with Nodal Hinge. Potential Energy Approach to Derive Beam Element Equations. Galerkin''''s Method for Deriving Beam Element Equations. References. Problems. 5. Frame and Grid Equations. Introduction. Two-Dimensional Arbitrarily Oriented Beam Element. Rigid Plane Frame Examples. Inclined or Skewed Supports-Frame Element. Grid Equations. Beam Element Arbitrarily Oriented in Space. Concepts of Substructure Analysis. References. Problems. 6. Development of the Plane Stress and Plane Strain Stiffness Equations. Introduction. Basic Concepts of Plane Stress and Plane Strain. Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations. Treatment of Body and Surface Forces. Explicit Expression for the Constant-Strain Triangle Stiffness Matrix. Finite Element Solution of a Plane Stress Problem. References. Problems. 7. Practical Considerations in Modeling; Interpreting Results and Examples of Plane Stress/Strain Analysis. Introduction. Finite Element Modeling. Equilibrium and Compatibility of Finite Element Results. Convergence of Solution. Interpretation of Stresses. Static Condensation. Flowchart for the Solution of Plane Stress Problems. Computer Program Results for Some Plane Stress/Strain Problems. References. Problems. 8. Development of the Linear-Strain Triangle Equations. Introduction. Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations. Example LST Stiffness Determination. Comparison of Elements. References. Problems. 9. Axisymmetric Elements. Introduction. Derivation of the Stiffness Matrix. Solutions of an Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements. References. Problems. 10. Isoparametric Formulation. Introduction. Isoparametric Formulation of the Bar Element Stiffness Matrix. Rectangular Plane Stress Element. Isoparametric Formulation of the Plane Element Stiffness Matrix. Gaussian Quadrature (Numerical Integration). Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature. Higher-Order Shape Functions. References. Problems. 11. Three-Dimensional Stress Analysis. Introduction. Three Dimensional Stress and Strain. Tetrahedral Element. Isoparametric Formulation. References. Problems. 12. Plate Bending Element. Introduction. Basic Concepts of Plate Bending. Derivation of a Plate Bending Element Stiffness Matrix and Equations. Some Plate Element Numerical Comparisons. Computer Solutions for a Plate Bending Problem. References. Problems. 13. Heat Transfer and Mass Transport. Introduction. Derivation of the Basic Differential Equation. Heat Transfer with Convection. Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h. One-Dimensional Finite Element Formulation Using a Variational Method. Two-Dimensional Finite Element Formulation. Line or Point Sources. One-Dimensional Heat Transfer with Mass Transport. Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin''''s Method. Flowchart and Examples of Heat-Transfer Program. References. Problems. 14. Fluid Flow. Introduction. Derivation of the Basic Differential Equations. One-Dimensional Finite Element Formulation. Two-Dimensional Finite Element Formulation. Flowchart and Example of a Fluid-Flow Program. References. Problems. 15. Thermal Stress. Introduction. Formulat

CL-Engineering - CENGAGE

ISBN-10: 0534385176
ISBN-13: 9780534385170

PGS: 724

List: 190.95 YOUR PRICE: 181.40

A First Course in the Finite Element Method, 4th Ed.

Daryl L. Logan

2007

Chapter 1 - Introduction Prologue. Brief History. Introduction to Matrix Notation. Role of the Computer. General Steps of the Finite Element of Method. Applications of the Finite Element Methods. Advantages of the Finite Element Method. Computer Programs for the Finite Element Method. References. Problems. Chapter 2 - Introduction to the Stiffness (Displacement) Method Introduction. Definitions of the Stiffness Matrix. Derivation of the Stiffness Matrix for a Spring Element. Example of a Spring Assemblage. Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method). Boundary Conditions. Potential Energy Approach to Derive Spring Element Equations. References. Problems. Chapter 3 - Development of Truss Equations Introduction. Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates. Selecting Approximation Functions for Displacements. Transformation of Vectors in Two Dimensions. Global Stiffness Matrix. Computation of Stress for a Bar in the x-y Plane. Solution of a Plane Truss. Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space. Use of Symmetry in Structure. Inclined, or Skewed, Supports. Potential Energy Approach to Derive Bar Element Equations. Comparison of Finite Element Solution to Exact Solution for Bar. Galerkin's Residual Method and Its Application to a One-Dimensional Bar. References. Problems. Chapter 4 - Development of Beam Equations Introduction. Beam Stiffness. Example of Assemblage of Beam Stiffness Matrices. Examples of Beam Analysis Using the Direct Stiffness Method. Distributed Loading. Comparison of Finite Element Solution to the Exact Solution for a Beam. Beam Element with Nodal Hinge. Potential Energy Approach to Derive Beam Element Equations. Galerkin's Method for Deriving Beam Element Equations. References. Problems. Chapter 5 - Frame and Grid Equations Introduction. Two-Dimensional Arbitrarily Oriented Beam Element. Rigid Plane Frame Examples. Inclined or Skewed Supports-Frame Element. Grid Equations. Beam Element Arbitrarily Oriented in Space. Concepts of Substructure Analysis. References. Problems. Chapter 6 - Development of the Plane Stress and Plane Strain Stiffness Equations Introduction. Basic Concepts of Plane Stress and Plane Strain. Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations. Treatment of Body and Surface Forces. Explicit Expression for the Constant-Strain Triangle Stiffness Matrix. Finite Element Solution of a Plane Stress Problem. References. Problems. Chapter 7 - Practical Considerations in Modeling; Interpreting Results and Examples of Plane Stress/Strain Analysis Introduction. Finite Element Modeling. Equilibrium and Compatibility of Finite Element Results. Convergence of Solution. Interpretation of Stresses. Static Condensation. Flowchart for the Solution of Plane Stress Problems. Computer Program Results for Some Plane Stress/Strain Problems. References. Problems. Chapter 8 - Development of the Linear-Strain Triangle Equations Introduction. Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations. Example LST Stiffness Determination. Comparison of Elements. References. Problems. Chapter 9 - Axisymmetric Elements Introduction. Derivation of the Stiffness Matrix. Solutions of an Axisymmetric Pressure Vessel. Applications of Axisymmetric Elements. References. Problems. Chapter 10 - Isoparametric Formulation Introduction. Isoparametric Formulation of the Bar Element Stiffness Matrix. Rectangular Plane Stress Element. Isoparametric Formulation of the Plane Element Stiffness Matrix. Gaussian Quadrature (Numerical Integration). Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature. Higher-Order Shape Functions. References. Problems. Chapter 11 - Three-Dimensional Stress Analysis Introduction. Three Dimensional Stress and Strain. Tetrahedral Element. Isoparametric Formulation. References. Problems. Chapter 12 - Plate Bending Element Introduction. Basic Concepts of Plate Bending. Derivation of a Plate Bending Element Stiffness Matrix and Equations. Some Plate Element Numerical Comparisons. Computer Solutions for a Plate Bending Problem. References. Problems. Chapter 13 - Heat Transfer and Mass Transport Introduction. Derivation of the Basic Differential Equation. Heat Transfer with Convection. Typical Units; Thermal Conductivities, K; and Heat-Transfer Coefficients, h. One-Dimensional Finite Element Formulation Using a Variational Method. Two-Dimensional Finite Element Formulation. Line or Point Sources. One-Dimensional Heat Transfer with Mass Transport. Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin''s Method. Flowchart and Examples of Heat-Transfer Program. References. Problems. Chapter 14 - Fluid Flow Introduction. Derivation of the Basic Differential Equations. One-Dimensional Finite Element Formulation. Two-Dimensional Finite Element Formulation. Flowchart and Exa

Thomson-Engineering - CENGAGE

ISBN-10: 0534552986
ISBN-13: 9780534552985

PGS: 752

List: 190.95 YOUR PRICE: 181.40

A Practical Guide to Reliable Finite Element Modelling

Alan Morris (Cranfield University)

2008

Many books have been written about the finite element method; little however has been written about procedures that assist a practicing engineer in undertaking an analysis in such a way that errors and uncertainties can be controlled. In A Practical Guide CONTENTS: Preface.@pChapter 1. Introduction.@p1.1 Aim of the book.@p1.2 Finite Element Types - a Brief Overview.@p1.3 Finite Element Analysis and Finite Element Representations.@p1.4 Multi-Model Analyses.@p1.5 Consistency, Logic and Error Control.@p1.6 Chapter Cont

Wiley

ISBN-10: 0470018321
ISBN-13: 9780470018323

PGS: N/A

List: 142.00 YOUR PRICE: 134.90

A Unified Approach to the Finite Element Method and Error Analysis Procedures

Not Listed

1998

This book provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results.
Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers.

* New, simpler element formulation techniques, model-independent results, and error measures
* New polynomial-based methods for identifying critical points
* New procedures for evaluating sheer/strain accuracy
* Accessible to undergraduates, insightful to researchers, and useful to practitioners
* Taylor series (polynomial) based
* Intuitive elemental and point-wise error measures
* Essential background information provided in 12 appendices

Academic Press - ELSEVIER

ISBN-10: 0122214404
ISBN-13: 9780122214400

PGS: 533

List: 135.00 YOUR PRICE: 128.25

Adaptive Finite Element Methods for Differential Equations

Bangerth, Wolfgang; Rannacher, Rolf;

2003

The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented er

Birkhauser - SV

ISBN-10: 3764370092
ISBN-13: 9783764370091

PGS: 207

List: 29.95 YOUR PRICE: 28.45

Advanced Topics in Finite Element Analysis of Structures: with Mathematica and Matlab Computations

M. Asghar Bhatti

2005

Essential Background.@p1.1 Steps in a Finite Element Solution.@p1.1.1 Two Node Uniform Bar Element.@p1.2 Interpolation Functions.@p1.2.1 Lagrange interpolation.@p1.2.2 Hermite interpolation for fourth-order problems.@p1.2.3 Lagrange interpolation for rectangular elements.@p1.2.4 Triangular elements.@p1.3 Integration by Parts.@p1.4 Numerical Integration Using Gauss Quadrature.@p1.5 Mapped Elements.@pProblems.@pAnalysis of Elastic Solids.@p2.1 Governing Equations.@p2.1.1 Stresses.@p2.1.2 Strains.@p2.1.3 Constitutive equations.@p2.1.4 Temperature effects and initial strains.@p2.1.5 Stress equilibrium equations.@p2.2 General Form of Finite Element Equations.@p2.2.1 Weak form.@p2.2.2 Finite Element Equations.@p2.3 Tetrahedral Element.@p2.3.1 Interpolation Functions for a Tetrahedral Element.@p2.3.2 Tetrahedral Element for Three Dimensional Elasticity.@p2.4 Mapped Solid Elements.@p2.4.1 Interpolation functions for an Eight node solid element.@p2.4.2 Interpolation functions for a Twenty node solid element.@p2.4.3 Evaluation of derivatives.@p2.4.4 Integration over volume.@p2.4.5 Evaluation of surface integrals.@p2.4.6 Evaluation of line integrals.@p2.4.7 Complete Mathematica/Matlab Implementations.@p2.5 Stress Calculations.@p2.5.1 Optimal Locations for Calculating Element Stresses.@p2.5.2 Interpolation-Extrapolation of Stresses.@p2.5.3 Average Nodal Stresses.@p2.5.4 Iterative Improvement in Stresses.@p2.6 Static Condensation.@p2.7 Substructuring.@p2.8 The Patch Test and Incompatible Elements.@p2.8.1 Convergence Requirements.@p2.8.2 Extra Zero Energy Modes.@p2.8.3 Patch Test For Plane Elasticity Problems.@p2.8.4 Quadrilateral Element with Additional Bending Shape Functions.@p2.9 Computer Implementation - fe2Quad.@pProblems.@pSolids of Revolution.@p3.1 Equations of Elasticity in Cylindrical Coordinates.@p3.2 Axisymmetric Analysis.@p3.2.1 Potential energy.@p3.2.2 Finite element equations.@p3.2.3 Three node triangular element.@p3.2.4 Mapped quadrilateral elements.@p3.3 Unsymmetrical Loading.@pProblems.@pMulti-Field Formulations for.@pBeam Elements.@p4.1 Euler-Bernoulli Beam Theory (EBT).@p4.2 Mixed Beam Element Based on EBT.@p4.3 Timoshenko Beam Theory (TBT).@p4.4 Displacement Based Element for Timoshenko Beam6.@p4.5 Shear Locking in Displacement Based Elements for Timoshenko Beam.@p4.6 Mixed Beam Element Based on Timoshenko Beam Theory.@p4.7 A Four Field Timoshenko Beam Element.@p4.8 Timoshenko Beam Element Using Linked Interpolation.@p4.9 Problems.@pMultifield Formulations for.@pAnalysis of Elastic Solids.@p5.1 Governing Equations.@p5.2. Displacement Formulation.@p5.3. Stress Formulation.@p5.4. Mixed Formulation.@p5.5 Assumed Stress Field For Mixed Formulation.@p5.6 Analysis of Nearly Incompressible Solids.@p5.6.1 Deviatoric and Volumetric Stresses and Strains.@p5.6.2 Poisson Ratio Locking in the Displacement Based Finite Elements.@p5.6.3 Mixed Formulation for Nearly Incompressible Solids.@p5.6.4 Finite Element Equations.@p5.6.5 Assumed Pressure Solution.@p5.6.6 Quadrilateral Elements for Planar Problems.@pProblems.@pPlates and Shells.@p6.1 Kirchhoff Plate Theory.@pStress resultants (shear and moment intensities).@pStress resultants on an arbitrarily oriented plane.@p6.1.1 Equilibrium equations.@p6.1.2 Stress Computations.@p6.1.3 Weak Form for Displacement Based Formulation.@p6.1.4 General Form of Kirchhoff Plate Element Equations.@p6.2 Rectangular Kirchhoff Plate Elements.@p6.2.1 MZC Rectangular Plate Element (Melosh, Zienkiewicz, and Cheung).@p6.2.2 The Patch Test for Plate Elements.@p6.2.3 BFS Rectangular Plate Element (Bogner, Fox, and Schmit).@p6.3 Triangular Kirchhoff Plate Elements.@p6.3.1 BCIZ Triangular Plate Element (Bazeley, Cheung, Irons, and Zienkiewicz).@p6.3.2 Conforming Triangular Plate Elements.@p6.4 Mixed Formulation for Kirchhoff Plates.@p6.5 Mindlin Plate Theory.@p6.6 Displacement Based Finite Elements for Mindlin Plates.@p6.6.1 Weak Form.@p6.6.2 General Form of Mindlin Plate Element Equations.@p6.6.3 Heterosis Element.@p6.7 Multifield Elements for Mindlin Plates.@p6.8 Analysis of Shell Structures.@pProblems.@pIntroduction to Nonlinear Problems.@p7.1 Nonlinear differential equation.@p7.1.1 Approximate solutions using the classical form of the Galerkin method.@p7.1.2 Finite element solution.@p7.2 Solution Procedures for Nonlinear Problems.@p7.2.1 Constant Stiffness Iteration.@p7.2.2 Load Increments.@p7.2.3 Arc-Length Method.@p7.3 Linearization and Directional Derivative.@pProblems.@pMaterial Nonlinearity.@p8.1 Analysis of Axially Loaded Bars.@p8.1.1 Weak form.@p8.1.2 Two Node Finite Element.@p8.1.3 One Dimensional Plasticity.@p8.1.4 Ramberg-Osgood Model.@p8.2 Nonlinear Analysis of Trusses.@p8.3 Material Nonlinearity in General Solids.@p8.3.1 General Form of Finite Element Equations.@p8.3.2 General Formulation for Incremental Stress-Strain Equations.@p8.3.3 State Determination Procedure.@p8.3.4 von Mises Yield Criterion and Associated Hardening Models.@pProblems.@pGeometric Nonlinearity.@p9.1 Basic

Wiley

ISBN-10: 0471648078
ISBN-13: 9780471648079

PGS: N/A

List: 145.00 YOUR PRICE: 137.75

An Introduction to Linear and Nonlinear Finite Element Analysis

KYTHE

2003

Although finite element courses have become more popular in the undergraduate and graduate engineering, science, and applied mathematics curricula, there are very few introductory textbooks geared toward students accustomed to using computers for everyday, Preface Notation Introduction One-Dimensional Shape Functions One-Dimensional Second-Order Equation One-Dimensional Fourth-Order Equation Two-Dimensional Elements Two-Dimensional Problems More Two-Dimensional Problems Axisymmetric Heat T

SPRINGER VERLAG

ISBN-10: 0817643089
ISBN-13: 9780817643089

PGS: N/A

List: 79.95 YOUR PRICE: 75.95

An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach

Kythe, Prem K.; Wei, Dongming

2004

Preface Notation Introduction One-Dimensional Shape Functions One-Dimensional Second-Order Equation One-Dimensional Fourth-Order Equation Two-Dimensional Elements Two-Dimensional Problems More Two-Dimensional Problems Axisymmetric Heat T

Birkhauser - SV

ISBN-10: 0817643087
ISBN-13: 9780817643089

PGS: 445

List: 79.95 YOUR PRICE: 75.95

An Introduction to the Finite Element Method, 3rd Ed.

Reddy , J. N.

2006

McGraw-Hill Science/Engineering/Math

ISBN-10: 0072466855
ISBN-13: 9780072466850

PGS: 912

List: 148.25 YOUR PRICE: 140.84

Application of the Finite Element Method in Implant Dentistry

GENG

2008

Part of the new series, Advanced Topics in Science and Technology in China, this book is designed to give the necessary theoretical foundation to new users of the finite element method in implant dentistry, and show how both the implant dentist and des,

Part I. Finite Element Method.- Introduction.- General Considerations of Finite Element Formulation.- Critical Factors in Computer Analysis.- Part II. Introduction to Implant Dentistry.- History of Dental Implants.- Phenomenon of Osseointegration.- The

SPRINGER VERLAG

ISBN-10: 3540737636
ISBN-13: 9783540737636

PGS: N/A

List: 319.00 YOUR PRICE: 303.05

Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods, 2nd Edition

Rainald Lohner (George Mason University

2008

Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics. CFD techniques are commonly used in the many areas of engineering where fluid behavior is an importan CONTENTS: FOREWORD TO THE SECOND EDITION.@pACKNOWLEDGEMENTS.@p@p1 INTRODUCTION AND GENERAL CONSIDERATIONS.@p1.1 The CFD code.@p1.2 Porting research codes to an industrial context.@p1.3 Scope of the book.@p@p2 DATA STRUCTURES AND ALGORITHMS.@p2.1 Representation of a

Wiley

ISBN-10: 047051907X
ISBN-13: 9780470519073

PGS: N/A

List: 130.00 YOUR PRICE: 123.50

Applied Finite Element Analysis, 2nd Edition

Larry J. Segerlind (Michigan State Univ.

1984

BASIC CONCEPTS. One-Dimensional Linear Element. A Finite Element Example. Element Matrices: Galerkin Formulation. Two-Dimensional Elements. Coordinate Systems. FIELD PROBLEMS. Two-Dimensional Field Equation. Torsion of Noncircular Sections. Derivative Boundary Conditions: Point Sources and Sinks. Irrotational Flow. Heat Transfer by Conduction and Convection. Acoustical Vibrations. Axisymmetric Field Problems. Time-Dependent Field Problems: Theoretical Considerations. Time-Dependent Field Problems: Practical Considerations. Computer Program for Two-Dimensional Field Problems. STRUCTURAL AND SOLID MECHANICS. The Axial Force Member. Element Matrices: Potential Energy Formulations. The Truss Element. A Beam Element. A Plane Frame Element. Theory of Elasticity. Two-Dimensional Elasticity. Axisymmetric Elasticity. Computer Programs for Structural and Solid Mechanics. LINEAR AND QUADRATIC ELEMENTS. Element Shape Functions. Element Matrices. Isoparametric Computer Programs. References. Appendices.

Wiley

ISBN-10: 0471806625
ISBN-13: 9780471806622

PGS: N/A

List: 152.95 YOUR PRICE: 145.30

Characteristics Finite Element Methods in Computational Fluid Dynamics

IANNELLI

2006

The book details multi-dimensional upstream-bias algorithms for the numerical solution of the Euler and Navier-Stokes equations. Several sections derive the Fluid Dynamics equations from fundamental thermo-mechanics principles and systematically develo,

SPRINGER VERLAG

ISBN-10: 3540251811
ISBN-13: 9783540251811

PGS: N/A

List: 229.00 YOUR PRICE: 217.55

Computing with hp-ADAPTIVE FINITE ELEMENTS

Demkowicz, Leszek

2006

One-Dimensional Problems. Two-Dimensional Elliptic Problems. Two-Dimensional Maxwell Problems.

Chapman & Hall/CRC - TAYLOR & FRANCIS

ISBN-10: 1584886714
ISBN-13: 9781584886716

PGS: 368

List: 97.95 YOUR PRICE: 93.05

Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with A

Demkowicz, Leszek

2007

Chapman & Hall/CRC - TAYLOR & FRANCIS &

ISBN-10: 1584886722
ISBN-13: 9781584886723

PGS: N/A

List: 97.95 YOUR PRICE: 93.05

Concepts and Applications of Finite Element Analysis, 4th Edition

Robert D. Cook; David S. Malkus; Michael

2001

Notation. Introduction. One-Dimensional Elements, Computational Procedures. Basic Elements. Formulation Techniques: Variational Methods. Formulation Techniques: Galerkin and Other Weighted Residual Methods. Isoparametric Elements. Isoparametric Triangles and Tetrahedra. Coordinate Transformation and Selected Analysis Options. Error, Error Estimation, and Convergence. Modeling Considerations and Software Use. Finite Elements in Structural Dynamics and Vibrations. Heat Transfer and Selected Fluid Problems. Constaints: Penalty Forms, Locking, and Constraint Counting. Solid of Revolution. Plate Bending. Shells. Nonlinearity: An Introduction. Stress Stiffness and Buckling. Appendix A: Matrices: Selected Definition and Manipulations. Appendix B: Simultaneous Algebraic Equations. Appendix C: Eigenvalues and Eigenvectors. References. Index.

Wiley

ISBN-10: 0471356050
ISBN-13: 9780471356059

PGS: N/A

List: 170.95 YOUR PRICE: 162.40

Conjugate Gradient Algorithms and Finite Element Methods

KRIEK

2004

The position taken in this collection of pedagocically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. The aim of this book is to present both methods in the context of complic,

On the Application of Preconditioning Operators for Nonlinear Elliptic Problems.- Conjugate Gradients & Finite Elements - A Golden Jubilee.- The Convergence of Krylov Methods and Ritz Values.- On a Conjugate Gradient/Newton/Penalty Method for the S

SPRINGER VERLAG

ISBN-10: 3540213192
ISBN-13: 9783540213192

PGS: N/A

List: 139.00 YOUR PRICE: 132.05

Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer

2006

This text offers a systematic and practical introduction to the discontinuous finite element method. It moves from a brief review of the fundamental laws and equations governing thermal and fluid systems, through a discussion of different approaches to,

SPRINGER VERLAG

ISBN-10: 1852339883
ISBN-13: 9781852339883

PGS: N/A

List: 145.00 YOUR PRICE: 137.75

Electrical Machine Analysis Using Finite Elements

Bianchi, Nicola

2005

Brief Recall of Electromagnetic Fields, Basic Principle of the Finite Element Method. Application of the Finite Element Method to Two-Dimensional Field Problems. Application of the Finite Element Method to the Analysis of Electrical Devices. Cylindric Electromagnetic Device. Low-Power Transformer. Controlled Single-Phase Reactance. Synchronous Alternator. Surface-Mounted PM Motor. Interior PM Motor. Single-Phase PM Motor. Switched Resistance Motor. Three-Phase Induction Motor.

CRC - TAYLOR & FRANCIS

ISBN-10: 0849333997
ISBN-13: 9780849333996

PGS: N/A

List: 104.95 YOUR PRICE: 99.70

Electromagnetic Modeling by Finite Element Methods

Joao Pedro Bastos; Nelson Sadowski

2003

Unlike any other source in the field, Electromagnetic Modeling by Finite Element Methods examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. This reference examines phenomena such as nonlinearity, mechanical force, electrical circuit coupling, vibration, heat, and movement for applications in the electrical, mechanical, nuclear, aeronautics, and transportation industries. It offers a wide range of examples, including torque, vibration, and iron loss calculation; coupling of the FEM with mechanical equations, circuits, converters, and thermal effects; and proven methods for hysteresis implementation into FEM codes. TOC:

MARCEL DEKKER - TAYLOR & FRANCIS & FRANC

ISBN-10: 0824742699
ISBN-13: 9780824742690

PGS: 510

List: 104.95 YOUR PRICE: 99.70

Elements of Finite Model Theory

LIBKIN

2004

This book is an introduction to finite model theory which stresses the computer science origins of the area. In addition to presenting the main techniques for analyzing logics over finite models, the book deals extensively with applications in database,

SPRINGER VERLAG

ISBN-10: 3540212027
ISBN-13: 9783540212027

PGS: N/A

List: 54.95 YOUR PRICE: 52.20

Energy And Finite Element Methods

Not Listed

1985

Taylor & Francis

ISBN-10: 0891165053
ISBN-13: 9780891165057

PGS: N/A

List: 134.95 YOUR PRICE: 128.20

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