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Preface | |
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About The Author | |
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Fundamental Concepts | |
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Introduction | |
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Historical Background | |
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Outline of Presentation | |
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Stresses and Equilibrium | |
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Boundary Conditions | |
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Strain-Displacement Relations | |
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Stress-Strain Relations | |
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Special Cases | |
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Temperature Effects | |
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Potential Energy and Equilibrium: The Rayleigh-Ritz Method | |
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Potential Energy � | |
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Rayleigh-Ritz Method | |
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Galerkin's Method | |
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Saint Venant's Principle | |
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Von Mises Stress | |
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Principle of Superposition | |
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Computer Programs | |
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Conclusion | |
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Historical References | |
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Problems | |
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Matrix Algebra And Gaussian Elimination | |
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Matrix Algebra | |
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Row and Column Vectors | |
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Addition and Subtraction | |
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Multiplication by a Scalar | |
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Matrix Multiplication | |
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Transposition | |
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Differentiation and Integration | |
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Square Matrix | |
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Diagonal Matrix | |
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Identity Matrix | |
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Symmetric Matrix | |
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Upper Triangular Matrix | |
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Determinant of a Matrix | |
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Matrix Inversion | |
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Eigenvalues and Eigenvectors | |
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Positive Definite Matrix | |
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Cholesky Decomposition | |
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Gaussian Elimination | |
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General Algorithm for Gaussian Elimination | |
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Symmetric Matrix | |
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Symmetric Banded Matrices | |
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Solution with Multiple Right Sides | |
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Gaussian Elimination with Column Reduction | |
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Skyline Solution | |
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Frontal Solution | |
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Conjugate Gradient Method for Equation Solving | |
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Conjugate Gradient Algorithm | |
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Input Data/Output | |
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Problems | |
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Program Listings | |
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One-Dimensional Problems | |
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Introduction | |
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Finite Element Modeling | |
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Element Division | |
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Numbering Scheme | |
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Shape Functions and Local Coordinates | |
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The Potential-Energy Approach | |
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Element Stiffness Matrix | |
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Force Terms | |
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The Galerkin Approach | |
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Element Stiffness | |
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Force Terms | |
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Assembly of the Global Stiffness Matrix and Load Vector | |
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Properties of K | |
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The Finite Element Equations: Treatment of Boundary Conditions | |
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Types of Boundary Conditions | |
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Elimination Approach | |
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Penalty Approach | |
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Multipoint Constraints | |
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Quadratic Shape Functions | |
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Temperature Effects | |
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Problem Modeling and Boundary Conditions | |
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Problem in Equilibrium | |
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Symmetry | |
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Two Elements with Same End Displacements | |
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Problem with a Closing Gap | |
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Input Data/Output | |
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Problems | |
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Program Listing | |
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Trusses | |
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Introduction | |
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Plane Trusses | |
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Local and Global Coordinate Systems | |
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Formulas for Calculating / and m | |
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Element Stiffness Matrix | |
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Stress Calculations | |
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Temperature Effects | |
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Three-Dimensional Trusses | |
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Assembly of Global Stiffness Matrix for the Banded and Skyline | |
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Solutions | |
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Assembly for Banded Solution | |
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Skyline Assembly | |
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Problem Modeling and Boundary Conditions | |
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Inclined Support in Two Dimensions | |
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Inclined Support in Three Dimensions-Line Constraint | |
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Inclined Support in Three Dimensions-Plane Constraint | |
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Symmetry and Antisymmetry | |
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Input Data/Output | |
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Problems | |
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Program Listing | |
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Beams And Frames | |
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Introduction | |
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Potential-Energy Approach | |
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Galerkin Approach | |
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Finite Element Formulation | |
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Element Stiffness-Direct Approach | |
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Load Vector | |
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Boundary Considerations | |
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Shear Force and Bending Moment | |
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Beams on Elastic Supports | |
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Plane Frames | |
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Three-Dimensional Frames | |
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Problem Modeling and Boundary Conditions | |
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Some Comments | |
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Input Data/Output | |
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Problems | |
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Program Listings | |
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Two-Dimensional Problems Using Constant Strain Triangles | |
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Introduction | |
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Finite Element Modeling | |
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Constant Strain Triangle (CST) | |
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Isoparametric Representation | |
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Potential-Energy Approach | |
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Element Stiffness | |
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Force Terms | |
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Integration Formula on a Triangle | |
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Galerkin Approach | |
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Stress Calculations | |
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Temperature Effects | |
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Problem Modeling and Boundary Conditions | |
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Some General Comments on Dividing into Elements | |
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Patch Test and Convergence | |
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Patch Test | |
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Orthotropic Materials | |
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Temperature Effects | |
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Input Data/Output | |
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Problems | |
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Program Listing | |
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Axisymmetric Solids Subjected To Axisymmetric Loading | |
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Introduction | |
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Axisymmetric Formulation | |
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Finite Element Modeling: Triangular Element | |
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Potential-Energy Approach | |
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Body Force Term | |
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Rotating Flywheel | |
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Surface Traction | |
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Galerkin Approach | |
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Stress Calculations | |
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Temperature Effects | |
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Problem Modeling and Boundary Conditions | |
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Cylinder Subjected to Internal Pressure | |
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Infinite Cylinder | |
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Press Fit on a Rigid Shaft | |
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Press Fit on an Elastic Shaft | |
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Belleville Spring | |
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Thermal Stress Problem | |
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Input Data/Output | |
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Problems | |
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Program Listing | |
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Two-Dimensional Isoparametric Elements And Numerical Integration | |
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Introduction | |
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The Four-Node Quadrilateral | |
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Shape Functions | |
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Element Stiffness Matrix | |
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Element Force Vectors | |
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Numerical Integration | |
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Two-Dimensional Integrals | |
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Stiffness Integration | |
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Stress Calculations | |
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Higher Order Elements | |
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Nine-Node Quadrilateral | |
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Eight-Node Quadrilateral | |
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Six-Node Triangle | |
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Integration on a Triangle-Symmetric Points | |
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Integration on a Triangle-Degenerate Quadrilateral | |
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Four-Node Quadrilateral for Axisymmetric Problems | |
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Conjugate Gradient Implementation of the Quadrilateral Element | |
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Concluding Remarks and Convergence | |
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References for Convergence | |
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Input Data/Output | |
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Problems | |
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Program Listings | |
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Three-Dimensional Problems In Stress Analysis | |
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Introduction | |
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Finite Element Formulation | |
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Element Stiffness | |
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Force Terms | |
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Stress Calculations | |
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Mesh Preparation | |
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Hexahedral Elements and Higher Order Elements | |
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Problem Modeling | |
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Frontal Method for Finite Element Matrices | |
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Connectivity and Prefront Routine | |
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Element Assembly and Consideration of Specified dof | |
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Elimination of Completed dof | |
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Backsubstitution | |
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Consideration of Multipoint Constraints | |
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Input Data/Output | |
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Problems | |
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Program Listings | |
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Scalar Field Problems | |
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Introduction | |
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Steady State Heat Transfer | |
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One-Dimensional Heat Conduction | |
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One-Dimensional Heat Transfer in Thin Fins | |
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Two-Dimensional Steady-State Heat Conduction | |
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Two-Dimensional Fins | |
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Preprocessing for Program Heat2D | |
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Torsion | |
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Triangular Element | |
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Galerkin Approach | |
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Potential Flow, Seepage, Electric and Magnetic Fields, and Fluid Flow in Ducts | |
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Potential Flow | |
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Seepage | |
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Electrical and Magnetic Field Problems | |
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Fluid Flow in Ducts | |
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Acoustics | |
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Boundary Conditions | |
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One-Dimensional Acoustics | |
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One-Dimensional Axial Vibrations | |
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Two-Dimensional Acoustics | |
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Conclusion | |
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Input Data/Output | |
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Problems | |
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Program Listings | |
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Dynamic Considerations | |
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Introduction | |
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Formulation | |
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Solid Body with Distributed Mass | |
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Element Mass Matrices | |
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Evaluation of Eigenvalues and Eigenvectors | |
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Properties of Eigenvectors | |
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Eigenvalue-Eigenvector Evaluation | |
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Inverse Iteration Method | |
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Generalized Jacobi Method | |
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Tridiagonalization and Implicit Shift Approach | |
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Bringing Generalized Problem to Standard Form | |
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Tridiagonalization | |
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Implicit Symmetric QR Step with Wilkinson Shift for Diagonalization | |
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Interfacing with Previous Finite Element Programs and a Program for Determining Critical Speeds of Shafts | |
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Guyan Reduction | |
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Rigid Body Modes | |
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Conclusion | |
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Input Data/Output | |
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Problems | |
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Program Listings | |
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Preprocessing And Postprocessing | |
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Introduction | |