Finite Element Analysis for Engineering Design

Inhaltsangabe1. A Review of the Equations of Mechanics.- Classification of Equations.- Descriptions of Motion.- Strains and Strain-Displacement Relations.- Compatibility Equations.- Stress and Equations of Motion and Equilibrium.- Constitutive Relations.- Equations of Linear Elasticity.- Biographical Sketch.- 2. Variational Formulations and Methods.- The Variational Operator.- Principle of Virtual Displacements.- The Principle of Virtual Forces.- Incremental Variational Formulations of Nonlinear Problems.- Variational Methods of Approximation.- 3. An Introduction to the Finite Element Method.- One-Dimensional Problems.- Two-Dimensional Problems.- Closure.- 4. Interpolation, Simple Elements, Convergence, Stress Calculation.- A Piecewise Polynomial field.- Finite Element Form of the Rayleigh-Ritz Method.- Interpolation.- Shape Functions for C0 Elements.- Shape Functions for C1 Elements.- Formulas for Element Matrices [k] and {re}.- Overivew of Element Stiffness Matrices.- Consistent Element Nodal Loads {re}.- Equilibrium and Compatibility in the Solution.- Convergence Requirements.,.- The Patch Test.- Stress Calculation.- References.- Symbols.- Biographical Sketch.- 5. The Isoparametric Formulation.- An Isoparametric Bar Element.- Plane Bilinear Isoparametric Element.- Summary of Gauss Quadrature.- Computer Subroutines for the Bilinear Element.- Quadratic Plane Elements.- Hexahedral (Solid) Isoparametric Elements.- The Validity of Isoparametric Elements.- Appropriate Order of Quadrature.- Element and Mesh Instabilities.- Remarks on Stress Computation.- Examples. Effect of Element Geometry.- References l58.- 6. Constraints.- Constraints. Transformations.- Lagrange Multipliers.- Penalty Functions.- Naturally Arising Penalty Formulations. Numerical Integration and Constraints.- Constraint Counting.- References.- 7. Remarks About Modeling.- References.- 8. Three-Dimensional Finite Element Models.- 3-D Solid Elements.- Eight-Noded Isoparametric Element.- Twenty-Noded Isoparametric Element.- Element Load Vector.- Computation of Stresses.- 30 Solid Elements for Concrete Structures Analysis.- Applications.- References.- 9. Geometric Nonlinear Analysis of Framed Structures.- Strain-Displacement Relationship.- Types of Formulation/Coordinate Systems.- Generalized Approach - Total Lagrangian Formulation.- Case Studies and Discussion.- Discussion.- References.- 10. Two-Dimensional Theories of Plates.- A Review of Literature.- Classical and First-Order Plate Theories.- Mixed Formulation of the Third-Order Theory.- Moderate Rotation Plate Theories.- References.- 11. Solution of Nonlinear Equations.- Governing Equations.- Solution Procedures.- Newton-Like Methods.- Accelerators and Line Search.- References.- 12. Dynamics of Structures: Fundamentals.- Finite Element Formulation.- Modal Analysis.- Structural Damping.- Consistent and Lumped Mass Models.- References.- 13. Dynamics of Structures: Solution Techniques.- Solution of First-Order Parabolic Systems.- Solution of the Structural Dynamics Equations.- Recent Developments in Time Integration 33l.- References.- 14. Mechanics of Composite Structures.- Definitions and Terminology.- Stress-Strain Relations for Laminates.- Classical and First-Order Laminate Theories.- Special Cases of Lamination Schemes.- A General Laminate Plate Theory.- References.- 15. Analysis Of Laminated Composite Structures.- Analytical Solutions of Classical and First-Order Theories.- Analytical Solutions of the Third-Order Theory.- Analytical Solutions of the Generalized Laminate Theory.- Finite-Element Models of 2-D Plate Theories.- Degenerate 3-D Composite Shell Element Based on the Total Lagrangian Formulation.- References.- 16. Applications of the Finite Element Method in Geotechnical Engineering.- Soil-Structure Interaction Problems.- Earth and Rock-Fill Dam.- Foundation of a Concrete Dam.- Power House Cavern.- References.- Biographical Sketch.- 17. Vibration Problems: Theory.- Typical Problem Formulations.- Simultaneous Iteratio

Inhaltsangabe1. A Review of the Equations of Mechanics.- Classification of Equations.- Descriptions of Motion.- Strains and Strain-Displacement Relations.- Compatibility Equations.- Stress and Equations of Motion and Equilibrium.- Constitutive Relations.- Equations of Linear Elasticity.- Biographical Sketch.- 2. Variational Formulations and Methods.- The Variational Operator.- Principle of Virtual Displacements.- The Principle of Virtual Forces.- Incremental Variational Formulations of Nonlinear Problems.- Variational Methods of Approximation.- 3. An Introduction to the Finite Element Method.- One-Dimensional Problems.- Two-Dimensional Problems.- Closure.- 4. Interpolation, Simple Elements, Convergence, Stress Calculation.- A Piecewise Polynomial field.- Finite Element Form of the Rayleigh-Ritz Method.- Interpolation.- Shape Functions for C0 Elements.- Shape Functions for C1 Elements.- Formulas for Element Matrices [k] and {re}.- Overivew of Element Stiffness Matrices.- Consistent Element Nodal Loads {re}.- Equilibrium and Compatibility in the Solution.- Convergence Requirements.,.- The Patch Test.- Stress Calculation.- References.- Symbols.- Biographical Sketch.- 5. The Isoparametric Formulation.- An Isoparametric Bar Element.- Plane Bilinear Isoparametric Element.- Summary of Gauss Quadrature.- Computer Subroutines for the Bilinear Element.- Quadratic Plane Elements.- Hexahedral (Solid) Isoparametric Elements.- The Validity of Isoparametric Elements.- Appropriate Order of Quadrature.- Element and Mesh Instabilities.- Remarks on Stress Computation.- Examples. Effect of Element Geometry.- References l58.- 6. Constraints.- Constraints. Transformations.- Lagrange Multipliers.- Penalty Functions.- Naturally Arising Penalty Formulations. Numerical Integration and Constraints.- Constraint Counting.- References.- 7. Remarks About Modeling.- References.- 8. Three-Dimensional Finite Element Models.- 3-D Solid Elements.- Eight-Noded Isoparametric Element.- Twenty-Noded Isoparametric Element.- Element Load Vector.- Computation of Stresses.- 30 Solid Elements for Concrete Structures Analysis.- Applications.- References.- 9. Geometric Nonlinear Analysis of Framed Structures.- Strain-Displacement Relationship.- Types of Formulation/Coordinate Systems.- Generalized Approach - Total Lagrangian Formulation.- Case Studies and Discussion.- Discussion.- References.- 10. Two-Dimensional Theories of Plates.- A Review of Literature.- Classical and First-Order Plate Theories.- Mixed Formulation of the Third-Order Theory.- Moderate Rotation Plate Theories.- References.- 11. Solution of Nonlinear Equations.- Governing Equations.- Solution Procedures.- Newton-Like Methods.- Accelerators and Line Search.- References.- 12. Dynamics of Structures: Fundamentals.- Finite Element Formulation.- Modal Analysis.- Structural Damping.- Consistent and Lumped Mass Models.- References.- 13. Dynamics of Structures: Solution Techniques.- Solution of First-Order Parabolic Systems.- Solution of the Structural Dynamics Equations.- Recent Developments in Time Integration 33l.- References.- 14. Mechanics of Composite Structures.- Definitions and Terminology.- Stress-Strain Relations for Laminates.- Classical and First-Order Laminate Theories.- Special Cases of Lamination Schemes.- A General Laminate Plate Theory.- References.- 15. Analysis Of Laminated Composite Structures.- Analytical Solutions of Classical and First-Order Theories.- Analytical Solutions of the Third-Order Theory.- Analytical Solutions of the Generalized Laminate Theory.- Finite-Element Models of 2-D Plate Theories.- Degenerate 3-D Composite Shell Element Based on the Total Lagrangian Formulation.- References.- 16. Applications of the Finite Element Method in Geotechnical Engineering.- Soil-Structure Interaction Problems.- Earth and Rock-Fill Dam.- Foundation of a Concrete Dam.- Power House Cavern.- References.- Biographical Sketch.- 17. Vibration Problems: Theory.- Typical Problem Formulations.- Simultaneous Iteratio