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 Be.