Kattan MATLAB Guide to Finite Elements

An Interactive Approach
2. Auflage 2007
ISBN: 978-3-540-70698-4
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 430 Seiten

later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me (pkattan@tedata. net. jo and pkattan@lsu. edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.

Autoren/Hrsg.

Kattan, Peter I.

Inhaltsverzeichnis

1;Preface to the Second Edition;6
2;Preface to the First Edition;8
3;Table of Contents;10
4;1 Introduction;12
4.1;1.1 Steps of the Finite Element Method;12
4.2;1.2 MATLAB Functions for Finite Element Analysis;13
4.3;1.3 MATLAB Tutorial;15
5;2 The Spring Element;22
5.1;2.1 Basic Equations;22
5.2;2.2 MATLAB Functions Used;23
6;3 The Linear Bar Element;38
6.1;3.1 Basic Equations;38
6.2;3.2 MATLAB Functions Used;39
7;4 The Quadratic Bar Element;55
7.1;4.1 Basic Equations;55
7.2;4.2 MATLAB Functions Used;56
8;5 The Plane Truss Element;71
8.1;5.1 Basic Equations;71
8.2;5.2 MATLAB Functions Used;72
9;6 The Space Truss Element;100
9.1;6.1 Basic Equations;100
9.2;6.2 MATLAB Functions Used;101
10;7 The Beam Element;117
10.1;7.1 Basic Equations;117
10.2;7.2 MATLAB Functions Used;118
11;8 The Plane Frame Element;144
11.1;8.1 Basic Equations;144
11.2;8.2 MATLAB Functions Used;146
12;9 The Grid Element;182
12.1;9.1 Basic Equations;182
12.2;9.2 MATLAB Functions Used;183
13;10 The Space Frame Element;199
13.1;10.1 Basic Equations;199
13.2;10.2 MATLAB Functions Used;201
14;11 The Linear Triangular Element;223
14.1;11.1 Basic Equations;223
14.2;11.2 MATLAB Functions Used;225
15;12 The Quadratic Triangular Element;254
15.1;12.1 Basic Equations;254
15.2;12.2 MATLAB Functions Used;256
16;13 The Bilinear Quadrilateral Element;279
16.1;13.1 Basic Equations;279
16.2;13.2 MATLAB Functions Used;282
17;14 The Quadratic Quadrilateral Element;315
17.1;14.1 Basic Equations;315
17.2;14.2 MATLAB Functions Used;318
18;15 The Linear Tetrahedral (Solid) Element;341
18.1;15.1 Basic Equations;341
18.2;15.2 MATLAB Functions Used;344
19;16 The Linear Brick (Solid) Element;370
19.1;16.1 Basic Equations;370
19.2;16.2 MATLAB Functions Used;374
20;17 Other Elements;400
20.1;17.1 Applications of Finite Elements in Other Areas;400
20.2;17.2 Basic Equations of the Fluid Flow 1D Element;401
20.3;17.3 MATLAB Functions Used in the Fluid Flow 1D Element;403
21;References;405
22;Answers to Problems;407
23;Contents of the Accompanying CD-ROM;427
24;Index;428

Leseproben

"1 Introduction (p. 1-5)

This short introductory chapter is divided into two parts. In the ?rst part there is a summary of the steps of the ?nite element method. The second part includes a short tutorial on MATLAB.

1.1 Steps of the Finite Element Method

There are many excellent textbooks available on ?nite element analysis like those in [1–18]. Therefore this book will not present any theoretical formulations or derivations of ?nite element equations. Only the main equations are summarized for each chapter followed by examples. In addition only problems from linear elastic structural mechanics are used throughout the book. The ?nite element method is a numerical procedure for solving engineering problems. Linear elastic behavior is assumed throughout this book. The problems in this book are taken from structural engineering but the method can be applied to other ?elds of engineering as well. In this book six steps are used to solve each problem using ?nite elements. The six steps of ?nite element analysis are summarized as follows:

1. Discretizing the domain – this step involves subdividing the domain into elements and nodes. For discrete systems like trusses and frames the system is already discretized and this step is unnecessary. In this case the answers obtained are exact. However, for continuous systems like plates and shells this step becomes very important and the answers obtained are only approximate. In this case, the accuracy of the solution depends on the discretization used. In this book this step will be performed manually (for continuous systems).

2. Writing the element stiffness matrices – the element stiffness equations need to be written for each element in the domain. In this book this step will be performed using MATLAB.

3. Assembling the global stiffness matrix – this will be done using the direct stiffness approach. In this book this step will be performed using MATLAB.

4. Applying the boundary conditions – like supports and applied loads and displacements. In this book this step will be performed manually.

5. Solving the equations – this will be done by partitioning the global stiffness matrix and then solving the resulting equations using Gaussian elimination. In this book the partitioning process will be performed manually while the solution part will be performed using MATLAB with Gaussian elimination.

6. Post-processing – to obtain additional information like the reactions and element forces and stresses. In this book this step will be performed using MATLAB. It is seen from the above steps that the solution process involves using a combination of MATLAB and some limited manual operations. The manual operations employed are very simple dealing only with discretization (step 1), applying boundary conditions (step 4) and partitioning the global stiffness matrix (part of step 5)."