Finite Element Analysis with Error Estimators
An Introduction to the FEM and Adaptive Error Analysis for Engineering Students
- 1st Edition - August 4, 2005
- Latest edition
- Author: J. E. Akin
- Language: English
This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation… Read more
This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic.
- The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics
- Includes source code for creating and proving FEA error estimators
Senior undergraduate and masters level courses in engineering, computational science, and some applied mathematics programs. Most aerospace, chemical, civil & mechanical engineering programs, & senior level electrical engineering courses
Preface
Features of the text and accompanying resources
Notation
Chapter 1: Introduction
1.1 Finite element methods
1.2 Capabilities of FEA
1.3 Outline of finite element procedures
1.4 Assembly into the system equations
1.5 Error section-titles
1.6 Exercises
Chapter 2: Mathematical preliminaries
2.1 Introduction
2.2 Linear spaces and norms
2.3 Sobolev norms *
2.4 Dual problem, self-adjointness
2.5 Weighted residuals
2.6 Boundary condition terms
2.7 Adding more unknowns
2.8 Numerical integration
2.9 Integration by parts
2.10 Finite element model problem
2.11 Continuous nodal flux recovery
2.12 A one-dimensional example error analysis
2.13 General boundary condition choices
2.14 General matrix partitions
2.15 Elliptic boundary value problems
2.16 Initial value problems
2.17 Eigen-problems
2.18 Equivalent forms *
2.19 Exercises
Chapter 3: Element interpolation and local coordinates
3.1 Introduction
3.2 Linear interpolation
3.3 Quadratic interpolation
3.4 Lagrange interpolation
3.5 Hermitian interpolation
3.6 Hierarchical interpolation
3.7 Space-time interpolations*
3.8 Nodally exact interpolations *
3.9 Interpolation error *
3.10 Gradient estimates *
3.11 Exercises
Chapter 4: One-dimensional integration
4.1 Introduction
4.2 Local coordinate Jacobian
4.3 Exact polynomial integration *
4.4 Numerical integration
4.5 Variable Jacobians
4.6 Exercises
Chapter 5: Error estimates for elliptic problems
5.1 Introduction
5.2 Error estimates
5.3 Hierarchical error indicator
5.4 Flux balancing error estimates
5.5 Element adaptivity
5.6 H-adaptivity
5.7 P-adaptivity
5.8 HP-adaptivity
5.9 Exercises
Chapter 6: Super-convergent patch recovery
6.1 Patch implementation database
6.2 SCP nodal flux averaging
6.3 Computing the SCP element error estimates
6.4 Hessian matrix *
6.5 Exercises
Chapter 7: Variational methods
7.1 Introduction
7.2 Structural mechanics
7.3 Finite element analysis
7.4 Continuous elastic bar
7.5 Thermal loads on a bar *
7.6 Reaction flux recovery for an element
7.7 Heat transfer in a rod
7.8 Element validation *
7.9 Euler’s equations of variational calculus *
7.10 Exercises
Chapter 8: Cylindrical analysis problems
8.1 Introduction
8.2 Heat conduction in a cylinder
8.3 Cylindrical stress analysis
8.4 Exercises
Chapter 9: General interpolation
9.1 Introduction
9.2 Unit coordinate interpolation
9.3 Natural coordinates
9.4 Isoparametric and subparametric elements
9.5 Hierarchical interpolation
9.6 Differential geometry *
9.7 Mass properties *
9.8 Interpolation error *
9.9 Element distortion*
9.10 Space-time interpolation *
9.11 Exercises
Chapter 10: Integration methods
10.1 Introduction
10.2 Unit coordinate integration
10.3 Simplex coordinate integration
10.4 Numerical integration
10.4.1 Unit coordinate quadrature
10.4.2 Natural coordinate quadrature
10.5 Typical source distribution integrals *
10.6 Minimal, optimal, reduced and selected integration
10.7 Exercises
Chapter 11: Scalar fields
11.1 Introduction
11.2 Variational formulation
11.3 Element and boundary matrices
11.4 Linear triangular element
11.5 Linear triangle applications
11.5.1 Internal source
11.6 Bilinear rectangles *
11.7 General 2-d elements
11.8 Numerically integrated arrays
11.9 Strong diagonal gradient SCP test case
11.10 Orthotropic conduction
11.11 Axisymmetric conductions
11.12 Torsion
11.13 Introduction to linear flows
11.14 Potential flow
11.15 Axisymmetric plasma equilibria
11.16 Slider bearing lubrication
11.17 Transient scalar fields
11.18 Exercises
Chapter 12: Vector fields
12.1 Introduction
12.2 Displacement based stress analysis summary
12.3 Planar models
12.4 Matrices for the constant strain triangle (CST)
12.5 Stress and strain transformations *
12.6 Axisymmetric solid stress *
12.7 General solid stress *
12.8 Anisotropic materials *
12.9 Circular hole in an infinite plate
12.10 Dynamics of solids
12.11 Exercises
Index
- Edition: 1
- Latest edition
- Published: August 4, 2005
- Language: English
JA
J. E. Akin
Affiliations and expertise
Professor of Mechanical Engineering, Rice University, Houston, TXRead Finite Element Analysis with Error Estimators on ScienceDirect