Front Cover CONCEPTS AND APPLICATIONS OF FINITE ELEMENT ANALYSISPrefaceContentsNotation1 Introduction 1.1 Finite Element Analysis1.2 Problem Classification, Modeling and Discretization1.3 Interpolation, Elements, Nodes and D.O.F.1.4 Example Applications. History of FEA1.5 Solving a Problem by FEA1.6 Learning and using FEAAnalytical Problems

2 One-dimensional Elements and Computational Procedures2.1 Introduction2.2 Bar element2.3 Beam element2.4 Bar and Beam element of arbitrary orientation2.5 Assembly of Elements2.6 Properties of Stiffness Matrices2.7 Boundary Conditions2.8 Exploiting Sparsity. Solving Equations2.9 Mechanical Load Stresses2.10 Thermal Load Stresses2.11 Structural Symetry2.12 Review. Remarks regarding modeling2.13 An ApplicationAnalytical ProblemsComputational Problems

3 Basic Elements 3.1 Preliminaries3.2 Interpolation and Shape Functions3.3 Formulas for Element Matrices3.4 Linear Triangle (CST)3.5 Quadratic Triangle (LST)3.6 Bilinear Rectangle (Q4)3.7 Quadratic Rectangle (Q8,Q9)3.8 Rectangular Solid Elements3.9 Choice of Interpolation Functions3.10 Improved Triangles and Quadrilaterals3.11 Nodal Loads3.12 Stress Calculation3.13 Nature of a Finite Element Solution3.14 Example: A Simple Stress Concentration Problem3.15 An Application with High Stress GradientAnalytical ProblemsComputational Problems

4 Formulation Techniques: Variational Methods 4.1 Introduction4.2 Principle of Stationary Potential Energy4.3 Problems having many D.O.F.4.4 Potential energy of an elastic body4.5 The Rayleigh-Ritz Method4.6 Comments Regarding the Rayleigh-Ritz Method4.7 Strong Form and Weak Form4.8 Finite Element of The Rayleigh-Ritz Method4.9 Convergence of Finite Element Solutions4.10 Additional Formulations. Hybrid ElementsAnalytical Problems

5 Formulation Techniques: Galerkin and other Weighted Residual Methods5.1 Galerkin Method5.2 Methods of Weighted Residuals (MWR)5.3 Galerkin Finite Element Method in One Dimension5.4 Integration by Parts5.5 Galerkin Finite Element Method in Two Dimensions5.6 A Mixed FormulationAnalytical Problems

6 Isoparametric Elements6.1 Introduction6.2 Bilinear Quadrilateral (Q4)6.3 Quadrature: [K] obtained by numerical integration6.4 Quadratic Quadrilaterals (Q8,Q9)6.5 Hexahedral Isoparametric Elements6.6 Incompatible Modes. Nodeless D.O.F.6.7 Static Condensation6.8 Choices in Numerical Integration6.9 Load Considerations6.10 Stress Calculation6.11 Effect of Element Geometry6.12 Validity of Isoparametric Elements6.13 Patch Test6.14 A 2D Application6.15 A 3D ApplicationAnalytical ProblemsComputational Problems

7 Isoparametric Triangles and Tetrahedra7.1 Reference Coordinates Shape Functions7.2 Element Characteristic Matrices7.3 Analytical Integration Area and Volume Coordinates7.4 Numerical IntegrationAnalytical Problems

8 Coordinate Transformation and Selected Analysis Options8.1 Transformation: Introduction and Vector Forms8.2 Strain, Stress, and Material Property Transformation8.3 Transformation of the Characteristic Matrix8.4 Changing the Directions of Restraints8.5 Connecting Dissimilar Elements. Rigids Elements8.6 Higher Derivatives as Nodal D.O.F.8.7 Fracture Mechanics. Singularity Elements8.8 Elastic Foundations. Infinite Media8.9 Structural Modification. Reanalysis8.10 Tests of Element QualityAnalytical ProblemsComputational Problems

9 Error, Error Estimation and Convergence9.1 Sources of Error9.2 Ill-Conditioning9.3 The Condition Number9.4 Diagonal Decay Test9.5 Residuals9.6 Discretization Error. Convergence Rate9.7 Multimesh Extrapolation9.8 Mesh Revision Methods9.9 Gradient (Stress) Recovery and Smoothing9.10 A Posteriori Error Estimate9.11 Adaptative MeshingAnalytical Problems

10 Modeling Considerations and Software Use10.1 Introduction10.2 Physical Behaviour versus Element Behaviour10.3 Element Shapes and Interconnection10.4 Test Cases and Pilot Studies10.5 Material Properties10.6 Loads and Reactions10.7 Connections in Structures10.8 Boundary Conditions10.9 Repetitive Symmetry10.10 Stress Concentrations. Submodels10.11 Substructures10.12 Planning an Analysis10.13 Common mistakes10.14 Checking the model10.15 Critique of Computed Results10.16 Design Optimization10.17 Software10.18 Concluding RemarksAnalytical ProblemsComputational Problems

11 Finite Element in Structural Dynamics and Vibrations11.1 Introduction11.2 Dynamic Equations. Mass and Damping Matrices11.3 Mass Matrices: Consistent, Diagonal and Other11.4 Natural Frequencies and Modes11.5 Damping11.6 Reduction of the number of D.O.F.11.7 Response History: Modal Methods11.8 Response History: Ritz Vectors11.9 Component Mode Synthesis (CMS)11.10 Harmonic Response11.11 Response History: Direct Integration Methods11.12 Explicit Direct Integration11.13 Implicit Direct Integration11.14 Direct Integration: Stability and Accuracy Analysis11.15 Analysis by Response Spectra11.16 Remarks. Modeling Considerations11.17 An Application: Vibration and Harmonic Response11.18 An Application: Response HistoryAnalytical ProblemsComputational Problems

12 Heat Transfer and Selected Fluid Problems12.1 Heat Transfer: Introduction12.2 Finite Element Formulation12.3 Radiation. Nonlinear Heat Transfer Problems12.4 Trasient Thermal Analysis12.5 Modeling Considerations. Remarks12.6 An Application12.7 Acoustic Frequencies and Modes12.8 Fluid-Structure Interaction12.9 Plane Incompressible. Irrotational FlowAnalytical ProblemsComputational Problems

13 Constraints: Penalty Forms, Locking and Constraint Counting13.1 Explicit Constraints. Transformation Equations13.2 Lagrange Multipliers to Enforce Constraints13.3 Penalty Functions to Enforce Constraints13.4 Implicit Penalty Constraints and Locking13.5 Constraint Counting13.6 Remarks about Techniques for Incompressible MediaAnalytical Problems

14 Solids of Revolution14.1 Introduction. Elasticity Relations for Axial Symmetry14.2 Axisymmetric Solid Elements14.3 An Application14.4 Loads without axial symmetry: Introduction14.5 Loads without axial symmetry: Some details of FEAAnalytical ProblemsComputational Problems

15 Plate Bending15.1 Introduction. Elasticity Relations for Axial Symmetry15.2 C1 (Kirchhoff) Plate Elements15.3 C0 (Mindlin) Plate Elements15.4 Mindlin Beam. More Devices for C0 Plate Elements15.5 Boundary Conditions. Test Problems15.6 An ApplicationAnalytical ProblemsComputational Problems

16 Shells16.1 Introduction16.2 Circular Arches and Arch Elements16.3 Shells of Revolution16.4 General Shells: Three and Four Node Elements16.5 General Shells: Curved Isoparametric Elements16.6 Test Cases Remarks16.7 An Axisymmetric Shell ApplicationAnalytical ProblemsComputational Problems

17 Nonlinearity: An Introduction17.1 Nonlinear Problems17.2 Some Solution Methods17.3 Plasticity: Introduction17.4 Plasticity: General Formulation for Small Strains17.5 Plasticity: Formulation for Von Mises Theory17.6 Plasticity: Some Computational Procedures17.7 Nonlinear Dynamic Problems17.8 Problems of Gaps and Contact17.9 Geometric Nonlinearity17.10 Modeling Considerations. RemarksAnalytic ProblemsComputational Problems

18 Stress Stiffness and Buckling18.1 Introduction. Energy Considerations18.2 Bar and Beam Elements18.3 Plate Elements18.4 A General Formulation18.5 Calculation of Buckling Loads18.6 Remarks on Stress Stiffness and its Uses18.7 Remarks and ExamplesAnalytical ProblemsComputational Problems

Appendix A - Selected Definitions and ManipulationsAppendix B - Simultaneous Algebraic EquationsB.1 OverviewB.2 Direct SolversB.3 Iterative Solvers

Appendix C - Eigenvalues and EigenvectorsC.1 OverviewC.2 The Standard EigenproblemC.3 The General EigenproblemC.4 Solution Algorithms

ReferencesIndex