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Introduction to Finite Element Analysis: Formulation, Verification and Validation (Wiley Series in Computational Mechanics)

by

Introduction to Finite Element Analysis: Formulation, Verification and Validation (Wiley Series in Computational Mechanics) Cover

 

Synopses & Reviews

Publisher Comments:

When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided?

Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort.

Giving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout.

  • Delivers the tools needed to have a working knowledge of the finite element method
  • Illustrates the concepts and procedures of verification and validation
  • Explains the process of conceptualization supported by virtual experimentation
  • Describes the convergence characteristics of the h-, p- and hp-methods
  • Covers the hierarchic view of mathematical models and finite element spaces
  • Uses examples and exercises which illustrate the techniques and procedures of quality assurance
  • Ideal for mechanical and structural engineering students, practicing engineers and applied mathematicians
  • Includes parameter-controlled examples of solved problems in a companion website (www.wiley.com/go/szabo)

Book News Annotation:

Szab, who retired from Washington University to run his own engineering software company; and Babuska, a specialist in the reliability of computational analysis of mathematical problems, present a systematic approach to determining whether a mathematical model meets necessary criteria for acceptance; and whether the approximate solution, as well as the data computed from it, meet necessary conditions for acceptance given the goals of computation. They provide users of finite element analysis software products a basic understanding of how mathematical models are constructed; what essential assumptions are incorporated into a mathematical model; the algorithmic structure of the finite element method; how the discretization parameters affect the accuracy of the finite element solution; how to assess the accuracy of the computed data; and how to avoid common pitfalls and mistakes. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Various plant metabolites are useful for human life, and the induction and reduction of these metabolites using modern biotechnical technique is of enormous potential important especially in the fields of agriculture and health. Plant Metabolism and Biotechnology describes the biosynthetic pathways of plant metabolites, their function in plants, and some applications for biotechnology. Topics covered include:
  • biosynthesis and metabolism of starch and sugars
  • lipid biosynthesis
  • symbiotic nitrogen fixation
  • sulfur metabolism
  • nucleotide metabolism
  • purine alkaloid metabolism
  • nicotine biosynthesis
  • terpenoid biosynthesis
  • benzylisoquinoline alkaloid biosynthesis
  • monoterpenoid indole alkaloid biosynthesis
  • flavonoid biosynthesis
  • pigment biosynthesis: anthocyanins, betacyanins and carotenoids
  • metabolomics in biotechnology

Plant Metabolism and Biotechnology is an essential guide to this important field for researchers and students of biochemistry, plant biology, metabolic engineering, biotechnology, food science, agriculture, and medicine.

Synopsis:

The authors believe that users of finite element analysis (FEA) software products must have a basic understanding of how mathematical models are constructed; what are the essential assumptions incorporated in a mathematical model; what is the algorithmic structure of the finite element solution; how the accuracy of the computed data can be assessed, and how to avoid common pitfalls and mistakes. The primary objective in assembling the material presented in the book is to provide a basic working knowledge of the finite element method. A professional quality software product will also be made available to the reader providing over 400 parameter-controlled examples of solved problems.

About the Author

Barna Szabó is co-founder and president of Engineering Software Research and Development, Inc. (ESRD), the company that produces the professional finite element analysis software StressCheck®. Prior to his retirement from the School of Engineering and Applied Science of Washington University in 2006 he served as the Albert P. and Blanche Y. Greensfelder Professor of Mechanics. His primary research interest is assurance of quality and reliability in the numerical stimulation of structural and mechanical systems by the finite element method. He has published over 150 papers in refereed technical journals. Several of them in collaboration with Professor Ivo Babuška, with whom he also published a book on finite element analysis (John Wiley & Sons, Inc., 1991). He is a founding member and Fellow of the US Association for Computational Mechanics. Among his honors are election to the Hungarian Academy of Sciences as External Member and an honorary doctorate.

Ivo Babuška’s research has been concerned mainly with the reliability of computational analysis of mathematical problems and their applications, especially by the finite element method. He was the first to address a posteriori error estimation and adaptivity in finite element analysis. His research papers on these subjects published in the 1970s have been widely cited. His joint work with Barna Szabó on the p-version of the finite element method established the theoretical foundations and the algorithmic structure for this method. His recent work has been concerned with the mathematical formulation and treatment of uncertainties which are present in every mathematical model. In recognition of his numerous important contributions, Professor Babuška received may honors, which include honorary doctorates, medals and prizes and election to prestigious academies.

Table of Contents

About the Authors.

Series Preface.

Preface.

1 Introduction.

1.1 Numerical simulation.

1.2 Why is numerical accuracy important?

1.3 Chapter summary.

2 An outline of the finite element method.

2.1 Mathematical models in one dimension.

2.2 Approximate solution.

2.3 Generalized formulation in one dimension.

2.4 Finite element approximations.

2.5 FEM in one dimension.

2.6 Properties of the generalized formulation.

2.7 Error estimation based on extrapolation.

2.8 Extraction methods.

2.9 Laboratory exercises.

2.10 Chapter summary.

3 Formulation of mathematical models.

3.1 Notation.

3.2 Heat conduction.

3.3 The scalar elliptic boundary value problem.

3.4 Linear elasticity.

3.5 Incompressible elastic materials.

3.6 Stokes' flow.

3.7 The hierarchic view of mathematical models.

3.8 Chapter summary.

4 Generalized formulations.

4.1 The scalar elliptic problem.

4.2 The principle of virtual work.

4.3 Elastostatic problems.

4.4 Elastodynamic models.

4.5 Incompressible materials.

4.6 Chapter summary.

5 Finite element spaces.

5.1 Standard elements in two dimensions.

5.2 Standard polynomial spaces.

5.3 Shape functions.

5.4 Mapping functions in two dimensions.

5.5 Elements in three dimensions.

5.6 Integration and differentiation.

5.7 Stiffness matrices and load vectors.

5.8 Chapter summary.

6 Regularity and rates of convergence.

6.1 Regularity.

6.2 Classification.

6.3 The neighborhood of singular points.

6.4 Rates of convergence.

6.5 Chapter summary.

7 Computation and verification of data.

7.1 Computation of the solution and its first derivatives.

7.2 Nodal forces.

7.3 Verification of computed data.

7.4 Flux and stress intensity factors.

7.5 Chapter summary.

8 What should be computed and why?

8.1 Basic assumptions.

8.2 Conceptualization: drivers of damage accumulation.

8.3 Classical models of metal fatigue.

8.4 Linear elastic fracture mechanics.

8.5 On the existence of a critical distance.

8.6 Driving forces for damage accumulation.

8.7 Cycle counting.

8.8 Validation.

8.9 Chapter summary.

9 Beams, plates and shells.

9.1 Beams.

9.2 Plates.

9.3 Shells.

9.4 The Oak Ridge experiments.

9.5 Chapter summary.

10 Nonlinear models.

10.1 Heat conduction.

10.2 Solid mechanics.

10.3 Chapter summary.

A Definitions.

A.1 Norms and seminorms.

A.2 Normed linear spaces.

A.3 Linear functionals.

A.4 Bilinear forms.

A.5 Convergence.

A.6 Legendre polynomials.

A.7 Analytic functions.

A.8 The Schwarz inequality for integrals.

B Numerical quadrature.

B.1 Gaussian quadrature.

B.2 Gauss–Lobatto quadrature.

C Properties of the stress tensor.

C.1 The traction vector.

C.2 Principal stresses.

C.3 Transformation of vectors.

C.4 Transformation of stresses.

D Computation of stress intensity factors.

D.1 The contour integral method.

D.2 The energy release rate.

E Saint-Venant's principle.

E.1 Green's function for the Laplace equation.

E.2 Model problem.

F Solutions for selected exercises.

Bibliography.

Index.

Product Details

ISBN:
9780470977286
Author:
Szabo, Barna
Publisher:
John Wiley & Sons
Author:
Barna Szab
Author:
oacute
Author:
Babu?ka, Ivo
Author:
Ivo Babu
Author:
Komamine, Atsushi
Author:
Babu
Author:
Ka
Author:
Szab?, Barna
Author:
Szab
Author:
Scaron
Author:
Crozier, Alan
Author:
&
Author:
ka, Ivo
Author:
Barna
Author:
Ashihara, Hiroshi
Subject:
Drafting & Mechanical Drawing
Subject:
Biochemistry
Subject:
Mechanical Engineering - Design
Subject:
Biochemistry (Chemical Biology)
Subject:
Architecture-Drafting
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Wiley Series in Computational Mechanics
Series Volume:
34
Publication Date:
20110308
Binding:
HARDCOVER
Language:
English
Pages:
382
Dimensions:
244 x 168 mm

Related Subjects

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Introduction to Finite Element Analysis: Formulation, Verification and Validation (Wiley Series in Computational Mechanics) New Hardcover
0 stars - 0 reviews
$119.50 In Stock
Product details 382 pages John Wiley & Sons - English 9780470977286 Reviews:
"Synopsis" by , Various plant metabolites are useful for human life, and the induction and reduction of these metabolites using modern biotechnical technique is of enormous potential important especially in the fields of agriculture and health. Plant Metabolism and Biotechnology describes the biosynthetic pathways of plant metabolites, their function in plants, and some applications for biotechnology. Topics covered include:
  • biosynthesis and metabolism of starch and sugars
  • lipid biosynthesis
  • symbiotic nitrogen fixation
  • sulfur metabolism
  • nucleotide metabolism
  • purine alkaloid metabolism
  • nicotine biosynthesis
  • terpenoid biosynthesis
  • benzylisoquinoline alkaloid biosynthesis
  • monoterpenoid indole alkaloid biosynthesis
  • flavonoid biosynthesis
  • pigment biosynthesis: anthocyanins, betacyanins and carotenoids
  • metabolomics in biotechnology

Plant Metabolism and Biotechnology is an essential guide to this important field for researchers and students of biochemistry, plant biology, metabolic engineering, biotechnology, food science, agriculture, and medicine.

"Synopsis" by , The authors believe that users of finite element analysis (FEA) software products must have a basic understanding of how mathematical models are constructed; what are the essential assumptions incorporated in a mathematical model; what is the algorithmic structure of the finite element solution; how the accuracy of the computed data can be assessed, and how to avoid common pitfalls and mistakes. The primary objective in assembling the material presented in the book is to provide a basic working knowledge of the finite element method. A professional quality software product will also be made available to the reader providing over 400 parameter-controlled examples of solved problems.
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