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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 | |