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| Introduction Prologue | |
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| Brief History | |
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| Introduction to Matrix Notation | |
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| Role of the Computer | |
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| General Steps of the Finite Element of Method | |
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| Applications of the Finite Element Methods | |
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| Advantages of the Finite Element Method | |
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| Computer Programs for the Finite Element Method | |
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| References | |
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| Problems | |
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| Introduction to the Stiffness (Displacement) Method Introduction | |
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| Definitions of the Stiffness Matrix | |
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| Derivation of the Stiffness Matrix for a Spring Element | |
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| Example of a Spring Assemblage | |
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| Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method) | |
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| Boundary Conditions | |
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| Potential Energy Approach to Derive Spring Element Equations | |
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| References | |
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| Problems | |
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| Development of Truss Equations Introduction | |
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| Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates | |
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| Selecting Approximation Functions for Displacements | |
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| Transformation of Vectors in Two Dimensions | |
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| Global Stiffness Matrix | |
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| Computation of Stress for a Bar in the x-y Plane | |
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| Solution of a Plane Truss | |
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| Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space | |
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| Use of Symmetry in Structure | |
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| Inclined, or Skewed, Supports | |
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| Potential Energy Approach to Derive Bar Element Equations | |
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| Comparison of Finite Element Solution to Exact Solution for Bar | |
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| Galerkin's Residual Method and Its Application to a One-Dimensional Bar | |
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| References | |
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| Problems | |
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| Development of Beam Equations Introduction | |
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| Beam Stiffness | |
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| Example of Assemblage of Beam Stiffness Matrices | |
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| Examples of Beam Analysis Using the Direct Stiffness Method | |
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| Distributed Loading | |
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| Comparison of Finite Element Solution to the Exact Solution for a Beam | |
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| Beam Element with Nodal Hinge | |
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| Potential Energy Approach to Derive Beam Element Equations | |
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| Galerkin's Method for Deriving Beam Element Equations | |
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| References | |
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| Problems | |
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| Frame and Grid Equations Introduction | |
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| Two-Dimensional Arbitrarily Oriented Beam Element | |
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| Rigid Plane Frame Examples | |
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| Inclined or Skewed Supports-Frame Element | |
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| Grid Equations | |
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| Beam Element Arbitrarily Oriented in Space | |
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| Concepts of Substructure Analysis | |
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| References | |
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| Problems | |
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| Development of the Plane Stress and Plane Strain Stiffness Equations Introduction | |
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| Basic Concepts of Plane Stress and Plane Strain | |
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| Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations | |
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| Treatment of Body and Surface Forces | |
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| Explicit Expression for the Constant-Strain Triangle Stiffness Matrix | |
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| Finite Element Solution of a Plane Stress Problem | |
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| References | |
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| Problems | |
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| Practical Considerations in Modeling; Interpreting Results and Examples of Plane Stress/Strain Analysis | |
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| Introduction | |
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| Finite Element Modeling | |
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| Equilibrium and Compatibility of Finite Element Results | |
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| Convergence of Solution | |
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| Interpretation of Stresses | |
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| Static Condensation | |
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| Flowchart for the Solution of Plane Stress Problems | |
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| Computer Program Results for Some Plane Stress/Strain Problems | |
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| References | |
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| Problems | |
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| Development of the Linear-Strain Triangle Equations Introduction | |
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| Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations | |
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| Example LST Stiffness Determination | |
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| Comparison of Elements | |
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| References | |
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| Problems | |
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| Axisymmetric Elements Introduction | |
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| Derivation of the Stiffness Matrix | |
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| Solutions of an Axisymmetric Pressure Vessel | |
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| Applications of Axisymmetric Elements | |
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| References | |
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| Problems | |
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| Isoparametric Formulation | |
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| Introduction | |
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| Isoparametric Formulation of the Bar Element Stiffness Matrix | |
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| Rectangular Plane Stress Element | |
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| Isoparametric Formulation of the Plane Element Stiffness Matrix | |
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| Gaussian Quadrature (Numerical Integration) | |
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| Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature | |
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| Higher-Order Shape Functions | |
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| References | |
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| Problems | |
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| Three-Dimensional Stress Analysis | |
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| Introduction | |
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| Three Dimensional Stress and Strain | |
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| Tetrahedral Element | |
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| Isoparametric Formulation | |
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| References | |
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| Problems | |
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| Plate Be | |