A First Course in the Finite Element Method Using Algor - Tapa dura

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 / References / Problems 14. FLUID FLOW Introduction / Derivation of the Basic Differential Equations / One-Dimensional Finite Element Formulation / Two-Dimensional Finite Element Formulation / Flowchart of a Fluid-Flow Program / Algor Example Solutions for Two-Dimensional Steady-State Fluid Flow / References / Problems 15. THERMAL STRESS Introduction / Formulation of the Thermal Stress Problem and Examples / Algor Example Solutions for Thermal Stress Problems / References / Problems 16. STRUCTURAL DYNAMICS AND TIME-DEPENDENT HEAT TRANSFER Introduction / Dynamics of a Spring-Mass System / Direct Derivation of the Bar Element Equations / Numerical Integration in Time / Natural Frequencies of a One-Dimensional Bar / Time-Dependent One-Dimensional Bar Analysis / Beam Element Mass Matrices and Natural Frequencies / Truss, Plane Frame, Plane Stress/Strain, Axisymmetric, and Solid Element Mass Matrices / Time-Dependent Heat Transfer / Algor Example Solutions for Structural Dynamics and Transient Heat Transfer / References / Problems 17. PLATE BENDING ELEMENT Introduction / Basic Concepts of Plate Bending / Derivation of a Plate Bending Element Stiffness Matrix and Equations / Some Plate Element Numerical Comparisons / Algor Example Solutions for Plate Bending Problems / References / Problems / APPENDIX A: MATRIX ALGEBRA / Introduction / Definition of a Matrix / Matrix Operations / Cofactor or Adjoint Method to Determine the Inverse of a Matrix / Inverse of a Matrix by Row Reduction / References / Problems / APPENDIX B: METHODS FOR SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS / Introduction / General Form of the Equations / Uniqueness, Nonuniqueness, and Nonexistence of Solution / Methods for Solving Linear Algebraic Equations / Banded-Symmetric Matrices, Bandwidth, Skyline, and Wavefront Methods / References / Problems / APPENDIX C: EQUATIONS FROM ELASTICITY THEORY / Introduction / Differential Equations of Equilibrium / Strain/Displacement and Compatibility Equations / Stress/Strain Relationships / Reference / APPENDIX D: EQUIVALENT NODAL FORCES / Problems / APPENDIX E: PRINCIPLE OF VIRTUAL WORK / References / APPENDIX F: BASICS OF ALGOR? / Introduction / Hardware Requirements for Windows Installation / Conventions / Getting Around the Menu System / Function Keys / Algor Processor Names / File Extensions Generated by the Algor System / Checking Model for Defects by Using Superview / ANSWERS TO SELECTED PROBLEMS / INDEX

Daryl Logan's clear and easy to understand text provides a thorough treatment of the finite element method and how to apply it to solve practical physical problems in engineering. Concepts are presented simply, making it understandable for students of all levels of experience. The first edition of this book enjoyed considerable success and this new edition includes a chapter on plates and plate bending, along with additional homework exercise. All examples in this edition have been updated to Algor (TM) Release 12.