What Every Engineer Should Know About Computational Techniques of Finite Element Analysis

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface to the Third Edition
Acknowledgments
Author
I: Numerical Model Generation
	1 Finite Element Analysis
		1.1 Solution of Boundary Value Problems
		1.2 Finite Element Shape Functions
		1.3 Finite Element Basis Functions
		1.4 Assembly of Finite Element Matrices
		1.5 Element Matrix Generation
		1.6 Local to Global Coordinate Transformation
		1.7 A Linear Quadrilateral Finite Element
		1.8 Quadratic Finite Elements
		References
	2 Finite Element Model Generation
		2.1 Bezier Spline Approximation
		2.2 Bezier Surfaces
		2.3 B-Spline Technology
		2.4 Computational Example
		2.5 NURBS Objects
		2.6 Geometric Model Discretization
		2.7 Delaunay Mesh Generation
		2.8 Model Generation Case Study
		References
	3 Modeling of Physical Phenomena
		3.1 Lagrange’s Equations of Motion
		3.2 Continuum Mechanical Systems
		3.3 Finite Element Analysis of Elastic Continuum
		3.4 A Tetrahedral Finite Element
		3.5 Equation of Motion of Mechanical System
		3.6 Transformation to Frequency Domain
		References
	4 Constraints and Boundary Conditions
		4.1 The Concept of Multi-Point Constraints
		4.2 The Elimination of Multi-Point Constraints
		4.3 An Axial Bar Element
		4.4 The Concept of Single-Point Constraints
		4.5 The Elimination of Single-Point Constraints
		4.6 Rigid Body Motion Support
		4.7 Constraint Augmentation Approach
		References
	5 Singularity Detection of Finite Element Models
		5.1 Local Singularities
		5.2 Global Singularities
		5.3 Massless Degrees of Freedom
		5.4 Massless Mechanisms
		5.5 Industrial Case Studies
		References
	6 Coupling Physical Phenomena
		6.1 Fluid-Structure Interaction
		6.2 A Hexahedral Finite Element
		6.3 Fluid Finite Elements
		6.4 Coupling Sructure with Compressible Fluid
		6.5 Coupling Structure with Incompressible Fluid
		6.6 Structural Acoustic Case Study
		References
II: Computational Reduction Techniques
	7 Matrix Factorization and Linear Systems
		7.1 Finite Element Matrix Reordering
		7.2 Sparse Matrix Factorization
		7.3 Multi-Frontal Factorization
		7.4 Linear System Solution
		7.5 Distributed Factorization and Solution
		7.6 Factorization and Solution Case Studies
		7.7 Iterative Solution of Linear Systems
		7.8 Preconditioned Iterative Solution Technique
		References
	8 Static Condensation
		8.1 Single-Level, Single-Component Condensation
		8.2 Computational Example
		8.3 Single-Level, Multiple-Component Condensation
		8.4 Multiple-Level Static Condensation
		8.5 Static Condensation Case Study
		References
	9 Real Spectral Computations
		9.1 Spectral Transformation
		9.2 Lanczos Reduction
		9.3 Generalized Eigenvalue Problem
		9.4 Eigensolution Computation
		9.5 Distributed Eigenvalue Computation
		9.6 Dense Eigenvalue Analysis
		9.7 Householder Reduction Technique
		9.8 Normal Modes Analysis Case Studies
		References
	10 Complex Spectral Computations
		10.1 Complex Spectral Transformation
		10.2 Biorthogonal Lanczos Reduction
		10.3 Implicit Operator Multiplication
		10.4 Recovery of Physical Solution
		10.5 Solution Evaluation
		10.6 Reduction to Hessenberg Form
		10.7 Rotating Component Application
		10.8 Complex Modal Analysis Case Studies
		References
	11 Dynamic Reduction
		11.1 Single-Level, Single-Component Dynamic Reduction
		11.2 Accuracy of Dynamic Reduction
		11.3 Computational Example
		11.4 Single-Level, Multiple-Component Dynamic Reduction
		11.5 Multiple-Level Dynamic Reduction
		11.6 Multi-Body Analysis Application
		References
	12 Component Mode Synthesis
		12.1 Single-Level, Single-Component Modal Synthesis
		12.2 Mixed Boundary Component Mode Reduction
		12.3 Computational Example
		12.4 Single-Level, Multiple-Component Modal Synthesis
		12.5 Multiple-Level Modal Synthesis
		12.6 Component Mode Synthesis Case Study
		References
III: Engineering Solution Computations
	13 Modal Solution Technique
		13.1 Modal Solution
		13.2 Truncation Error in Modal Solution
		13.3 The Method of Residual Flexibility
		13.4 The Method of Mode Acceleration
		13.5 Coupled Modal Solution Application
		13.6 Modal Contributions and Energies
		References
	14 Transient Response Analysis
		14.1 The Central Difference Method
		14.2 The Newmark Method
		14.3 Starting Conditions and Time Step Changes
		14.4 Stability of Time Integration Techniques
		14.5 Transient Response Case Study
		14.6 State-Space Formulation
		References
	15 Frequency Domain Analysis
		15.1 Direct and Modal Frequency Response Analysis
		15.2 Reduced-Order Frequency Response Analysis
		15.3 Accuracy of Reduced-Order Solution
		15.4 Frequency Response Case Study
		15.5 Enforced Motion Application
		References
	16 Nonlinear Analysis
		16.1 Introduction to Nonlinear Analysis
		16.2 Geometric Nonlinearity
		16.3 Newton-Raphson Methods
		16.4 Quasi-Newton Iteration Techniques
		16.5 Convergence Criteria
		16.6 Computational Example
		16.7 Nonlinear Dynamics
		References
	17 Sensitivity and Optimization
		17.1 Design Sensitivity
		17.2 Design Optimization
		17.3 Planar Bending of the Bar
		17.4 Computational example
		17.5 Eigenfunction Sensitivities
		17.6 Variational Analysis
		References
	18 Engineering Result Computations
		18.1 Displacement Recovery
		18.2 Stress Calculation
		18.3 Nodal Data Interpolation
		18.4 Level Curve Computation
		18.5 Engineering Analysis Case Study
		References
IV: Advanced Industrial Solutions
	19 Heat Transfer
		19.1 Heat Conduction Phenomenon
		19.2 Weak form of Heat Equation
		19.3 Capacity Matrix
		19.4 Conduction Matrix
		19.5 Heat Source and Boundary Condition Matrices
		19.6 Heat Conduction Analysis
		19.7 Thermo-Elastic Application
		References
	20 Wave Propagation
		20.1 The Wave Propagation Phenomenon
		20.2 Weighted Residual Form
		20.3 Finite Element Discretization
		20.4 Time Domain Interpolation
		20.5 Governing Equation
		20.6 Elastic Waves
		20.7 Architectural Application
		References
	21 Topology Optimization
		21.1 Matrix Sensitivities
		21.2 Deformation Constraint
		21.3 Natural Frequency Constraint
		21.4 The Topology Optimization Process
		21.5 Aircraft Application
		References
	22 Fluid Dynamics
		22.1 The Navier–Stokes Equation
		22.2 Fluid Finite Element Discretization
		22.3 Weighted Residual Form
		22.4 Element Matrix Generation
		22.5 The Vorticity Equation
		22.6 The Vortex Street Phenomenon
		22.7 Marine Applications
		References
Appendix: A Numerical Example
	A.1 Elastic Beam Element
	A.2 Structural Example
	A.3 Numerical Solution
	A.4 Static Condensation
Index