Finite element analysis with error estimators: an introduction to the FEM and adaptive error analysis for engineering students

Medientyp: E-Book

Titel: Finite element analysis with error estimators : an introduction to the FEM and adaptive error analysis for engineering students

Enthält: Cover; Frontmatter; Half Title Page; Title Page; Copyright; Contents; Preface; Features of the text and accompanying resources; Notation; 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 concepts; 1.6 Exercises; 1.7 Bibliography; 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 parts2.10 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; 2.20 Bibliography; 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 interpolations3.8 Nodally exact interpolations; 3.9 Interpolation error; 3.10 Gradient estimates; 3.11 Exercises; 3.12 Bibliography; 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; 4.7 Bibliography; 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
5.10 Bibliography6. 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; 6.6 Bibliography; 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; 7.11 Bibliography; 8. Cylindrical analysis problems; 8.1 Introduction
8.2 Heat conduction in a cylinder8.3 Cylindrical stress analysis; 8.4 Exercises; 8.5 Bibliography; 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; 9.12 Bibliography; 10. Integration methods; 10.1 Introduction; 10.2 Unit coordinate integration; 10.3 Simplex coordinate integration; 10.4 Numerical integration
10.5 Typical source distribution integrals

Beteiligte: Akin, J. E. [Sonstige Person, Familie und Körperschaft]

Erschienen: Oxford [u.a.]: Elsevier/Butterworth-Heinemann, 2005
Online-Ausg.

Umfang: XVIII, 447 S.; graph. Darst

Sprache: Englisch

ISBN: 9780750667227; 0080472753; 9780080472751

Schlagwörter: Finite-Elemente-Methode
Finite-Elemente-Methode

Art der Reproduktion: Online-Ausg.

Entstehung:

Anmerkungen: Includes bibliographical references and index

Beschreibung: Introduction, Mathematical Premliminaries, Element Interpolation and Local Coordinates, One-Dimensional Integration, Error Estimation for Elliptic Problems, Super-convergent Patch Recovery, Variational Methods, Cylindrical Analysis Problems, General Interpolation, Integration Methods, Scalar Fields, Vector Fields, Index, Solutions Manual

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 *Complete with homework exercises and supporting website with instructor's solutions manual

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