Programming Finite Elements in Java™

✍ Scribed by Gennadiy Nikishkov (auth.)

• Publisher: Springer-Verlag London
• Year: 2010
• Tongue: English
• Leaves: 395
• Edition: 1
• Category: Library

✦ Synopsis

The finite element method (FEM) is a computational technique for solving problems which are described by partial differential equations or which can be formulated as functional minimization. The FEM is commonly used in the design and development of products, especially where structural analysis is involved. The simple object model of the Java™ programming language lends itself to efficient implementation of FEM analysis.

Programming Finite Elements in Java™ teaches the reader FEM algorithms and their programming in Java™ through a single finite element Java™ program. The compact, simple code makes it straightforward to understand the algorithms and their implementation, thereby encouraging developers to extend the code to their own tasks. All of the main aspects of finite element techniques are considered:

• finite element solution;

• generation of finite element meshes; and

• visualization of finite element models and results with Java 3D™.

The step-by-step presentation includes algorithm programming and code explanation at each point. Problems and exercises are provided for each chapter, with Java™ source code and problem data sets available from http://extras.springer.com/2010/978-1-84882-971-8.

Graduate students using the FEM will find the simple but detailed object-oriented programming methods presented in this textbook to be of great assistance in understanding the FEM, including mesh generation and visualization. Programming Finite Elements in Java™ will also be of interest to senior undergraduates doing special studies encompassing the FEM. Researchers and practicing engineers already familiar with the FEM but seeking an alternative approach will find this book readily suited to self study.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Introduction....Pages 3-11
Finite Element Equations for Heat Transfer....Pages 13-19
FEM for Solid Mechanics Problems....Pages 21-31
Finite Element Program....Pages 33-39
Front Matter....Pages 41-41
Finite Element Processor....Pages 43-61
Finite Element Model....Pages 63-73
Elastic Material....Pages 75-81
Elements....Pages 83-92
Numerical Integration....Pages 93-99
Two-dimensional Isoparametric Elements....Pages 101-112
Implementation of Two-dimensional Quadratic Element....Pages 113-128
Three-dimensional Isoparametric Elements....Pages 129-140
Implementation of Three-dimensional Quadratic Element....Pages 141-159
Assembly and Solution....Pages 161-171
Direct Equation Solver....Pages 173-186
Iterative Equation Solver....Pages 187-197
Load Data and Load Vector Assembly....Pages 199-211
Stress Increment, Residual Vector and Results....Pages 213-221
Elastic–Plastic Problems....Pages 223-246
Front Matter....Pages 247-247
Mesh Generator....Pages 249-255
Front Matter....Pages 247-247
Two-dimensional Mesh Generators....Pages 257-270
Generation of Three-dimensional Meshes by Sweeping....Pages 271-281
Pasting Mesh Blocks....Pages 283-288
Mesh Transformations....Pages 289-296
Copying, Writing and Reading Mesh Blocks....Pages 297-302
Front Matter....Pages 303-303
Introduction to Java 3D™....Pages 305-311
Visualizer....Pages 313-323
Visualization Scene Graph....Pages 325-331
Surface Geometry....Pages 333-342
Edge and Face Subdivision....Pages 343-352
Surface Subdivision....Pages 353-362
Results Field, Color Scale, Interaction and Lights....Pages 363-376
Back Matter....Pages 377-402

✦ Subjects

Theoretical and Applied Mechanics; Programming Techniques; Computational Mathematics and Numerical Analysis