Finite element analysis with error estimators : an introduction to the FEM and adaptive error analysis for engineering students / J.E. Akin.

Format:

Book

Author/Creator:

Akin, J. E.

Language:

English

Subjects (All):

Finite element method.

Structural analysis (Engineering).

Error analysis (Mathematics).

Physical Description:

1 online resource (465 p.)

Edition:

1st ed.

Place of Publication:

Oxford : Elsevier, 2005.

Language Note:

English

Summary:

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 th

Contents:

Cover; Front matter; 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 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; 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 interpolations 3.8 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 Bibliography 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; 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 cylinder 8.3 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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-281-01611-X

9786611016111

0-08-047275-3

OCLC:

126845904