Table of Contents1. 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 Stiff