Finite Element Analysis

Method, Verification and Validation
2. Auflage 2021
ISBN: 978-1-119-42642-4
Verlag: Wiley

Buch, Englisch, 384 Seiten, Format (B × H): 184 mm x 254 mm, Gewicht: 897 g

Finite Element Analysis

An updated and comprehensive review of the theoretical foundation of the finite element method

The revised and updated second edition of Finite Element Analysis: Method, Verification, and Validation offers a comprehensive review of the theoretical foundations of the finite element method and highlights the fundamentals of solution verification, validation, and uncertainty quantification. Written by noted experts on the topic, the book covers the theoretical fundamentals as well as the algorithmic structure of the finite element method. The text contains numerous examples and helpful exercises that clearly illustrate the techniques and procedures needed for accurate estimation of the quantities of interest. In addition, the authors describe the technical requirements for the formulation and application of design rules.

Designed as an accessible resource, the book has a companion website that contains a solutions manual, PowerPoint slides for instructors, and a link to finite element software. This important text:

- Offers a comprehensive review of the theoretical foundations of the finite element method
- Puts the focus on the fundamentals of solution verification, validation, and uncertainty quantification
- Presents the techniques and procedures of quality assurance in numerical solutions of mathematical problems
- Contains numerous examples and exercises

Written for students in mechanical and civil engineering, analysts seeking professional certification, and applied mathematicians, Finite Element Analysis: Method, Verification, and Validation, Second Edition includes the tools, concepts, techniques, and procedures that help with an understanding of finite element analysis.

Autoren/Hrsg.

Szabó, Barna

Babuska, Ivo

Babuška, Ivo

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau Konstruktionslehre, Bauelemente, CAD
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

1 Introduction to FEM 3

1.1 An introductory problem 6

1.2 Generalized formulation 9

1.2.1 The exact solution 9

1.2.2 The principle of minimum potential energy 14

1.3 Approximate solutions 16

1.3.1 The standard polynomial space 17

1.3.2 Finite element spaces in one dimension 20

1.3.3 Computation of the coefficient matrices 22

1.3.4 Computation of the right hand side vector 26

1.3.5 Assembly 27

1.3.6 Condensation 30

1.3.7 Enforcement of Dirichlet boundary conditions 30

1.4 Post-solution operations 33

1.4.1 Computation of the quantities of interest 33

1.5 Estimation of error in energy norm 37

1.5.1 Regularity 38

1.5.2 A priori estimation of the rate of convergence 38

1.5.3 A posteriori estimation of error 40

1.5.4 Error in the extracted QoI 46

1.6 The choice of discretization in 1D 47

1.6.1 The exact solution lies in Hk(I), k - 1 > p 47

1.6.2 The exact solution lies in Hk(I), k - 1 = p 49

1.7 Eigenvalue problems 52

1.8 Other finite element methods 57

1.8.1 The mixed method 59

1.8.2 Nitsche’s method 60

2 Boundary value problems 63

2.1 Notation 63

2.2 The scalar elliptic boundary value problem 65

2.2.1 Generalized formulation 66

2.2.2 Continuity 68

2.3 Heat conduction 68

2.3.1 The differential equation 70

2.3.2 Boundary and initial conditions 71

2.3.3 Boundary conditions of convenience 73

2.3.4 Dimensional reduction 75

2.4 Linear elasticity - strong form 82

2.4.1 The Navier equations 86

2.4.2 Boundary and initial conditions 86

2.4.3 Symmetry, antisymmetry and periodicity 88

2.4.4 Dimensional reduction in linear elasticity 89

2.4.5 Incompressible elastic materials 93

2.5 Stokes flow 95

2.6 Elasticity - generalized formulation 96

2.6.1 The principle of minimum potential energy 98

2.6.2

Über Autor(innen)

Barna Szabo is Senior Professor in the Department of Mechanical Engineering and Materials Science at Washington University in St. Louis, USA. He is also co-founder and chairman of Engineering Software Research and Development, Inc.

Ivo Babu?ka is Professor Emeritus of The University of Texas at Austin, USA, Professor of Aerospace Engineering and Engineering Mechanics, Professor of Mathematics, and Senior Research Scientist of the Oden Institute of Computational Engineering and Sciences.