Programming Finite Elements in Javaâ¢

By: Gennadiy P. Nikishkov

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Hardcover | 4 February 2010

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Hardcover
420 Pages

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22.86 x 15.88 x 2.54

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Programming Finite Elements in Java (TM) teaches the reader how to programme the algorithms of the finite element method (FEM) in Java (TM). The compact, simple code helps the student to read the algorithms, to understand them and thus to be able to refine them. 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 (TM).

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

Industry Reviews

From the reviews:

"Throughout the book, the author provides, in an object-oriented paradigm, clear and compact Java code snippets extracted from his own software application. ... The intended audience includes advanced undergraduate students in finite element analysis courses and graduate students in introductory FEM courses. Scientists and engineers who are familiar with FEM techniques can benefit from the book's discussion of object-oriented implementation. ... this book would also be highly valuable for computer scientists who want to learn about computational science and engineering and the FEM." (Alin Anton, ACM Computing Reviews, January, 2013)

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Programming & Software Development Object-Oriented Programming or OOP Mathematics Calculus & Mathematical Analysis Numerical Analysis Engineering & Technology Technology in General Maths for Engineers Mechanical Engineering & Materials Materials Science

Mechanics of Solids Mechanical Engineering Applied Mathematics

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Paperback

Published: 29th November 2014

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Finite Element Formulation
Introduction	p. 3
Basic Ideas of FEM	p. 3
Formulation of Finite Element Equations	p. 4
Galerkin Method	p. 5
Variational Formulation	p. 8
Example of Shape-function Determination	p. 9
Problems	p. 10
Finite Element Equations for Heat Transfer	p. 13
Problem Statement	p. 13
Finite Element Discretization of Heat Transfer Equations	p. 14
Different Type Problems	p. 16
Triangular Element	p. 17
Problems	p. 19
FEM for Solid Mechanics Problems	p. 21
Problem Statement	p. 21
Finite Element Equations	p. 23
Stiffness Matrix of a Triangular Element	p. 26
Assembly of the Global Equation System	p. 27
Example of the Global Matrix Assembly	p. 29
Problems	p. 30
Finite Element Program	p. 33
Object-oriented Approach to Finite Element Programming	p. 33
Requirements for the Finite Element Application	p. 34
Overall Description	p. 34
User Description	p. 35
User Interface	p. 35
Functions	p. 35
Other Requirements	p. 36
General Structure of the Finite Element Code	p. 36
Problems	p. 38
Finite Element Solution
Finite Element Processor	p. 43
Class Structure	p. 43
Problem Data	p. 49
Data Statements	p. 49
Model Data	p. 51
Load Specification	p. 52
Data Example	p. 54
Data Scanner	p. 57
Problems	p. 61
Finite Element Model	p. 63
Data for the Finite Element Model	p. 63
Class for the Finite Element Model	p. 66
Adding New Data Item	p. 72
Problems	p. 72
Elastic Material	p. 75
Hooke's Law	p. 75
Class for a Material	p. 76
Class for Elastic Material	p. 79
Problems	p. 81
Elements	p. 83
Element Methods	p. 83
Abstract Class Element	p. 84
Element Data	p. 84
Element Constructor	p. 85
Methods of Particular Elements	p. 87
Methods Common to All Elements	p. 88
Container for Stresses	p. 90
Adding New Element Type	p. 91
Problems	p. 92
Numerical Integration	p. 93
Gauss Integration Rule	p. 93
Implementation of Numerical Integration	p. 95
Problems	p. 99
Two-dimensional Isoparametric Elements	p. 101
Shape Functions	p. 101
Strain-Displacement Matrix	p. 104
Element Properties	p. 107
Nodal Equivalent of the Surface Load	p. 108
Example: Computing Nodal Equivalents of a Distributed Load	p. 109
Calculation of Strains and Stresses	p. 110
Problems	p. 111
Implementation of Two-dimensional Quadratic Element	p. 113
Class for Shape Functions and Their Derivatives	p. 113
Element Degeneration	p. 114
Shape Functions	p. 115
Derivatives of Shape Functions	p. 116
One-dimensional Shape Functions and Their Derivatives	p. 118
Class for Eight-node Element	p. 118
Stiffness Matrix	p. 119
Displacement Differentiation Matrix	p. 121
Thermal Vector	p. 122
Nodal Equivalent of a Distributed Load	p. 123
Equivalent Stress Vector	p. 125
Extrapolation from Integration Points to Nodes	p. 126
Other Methods	p. 127
Problems	p. 128
Three-dimensional Isoparametric Elements	p. 129
Shape Functions	p. 129
Strain-Displacement Matrix	p. 131
Element Properties	p. 133
Efficient Evaluation of Element Matrices and Vectors	p. 134
Calculation of Nodal Equivalents for External Loads	p. 134
Example: Nodal Equivalents of a Distributed Load	p. 136
Calculation of Strains and Stresses	p. 138
Extrapolation of Strains and Stresses	p. 138
Problems	p. 139
Implementation of Three-dimensional Quadratic Element	p. 141
Class for Shape Functions and Their Derivatives	p. 141
Element Degeneration	p. 141
Shape Functions	p. 143
Derivatives of Shape Functions	p. 144
Shape Functions and Their Derivatives for an Element Face	p. 147
Class for Twenty-node Element	p. 149
Stiffness Matrix	p. 150
Thermal Vector	p. 152
Nodal Equivalent of a Distributed Load	p. 153
Equivalent Stress Vector	p. 154
Extrapolation from Integration Points to Nodes	p. 155
Other Methods	p. 156
Problems	p. 158
Assembly and Solution	p. 161
Disassembly and Assembly	p. 161
Disassembly of Vectors	p. 161
Assembly of Vectors	p. 163
Assembly Algorithm for Matrices	p. 164
Displacement Boundary Conditions	p. 166
Explicit Specification of Displacement Boundary Conditions	p. 166
Method of Large Number	p. 167
Solution of Finite Element Equations	p. 167
Abstract Solver Class	p. 168
Adding New Equation Solver	p. 170
Problems	p. 171
Direct Equation Solver	p. 173
LDU Solution Method	p. 173
Assembly of Matrix in Symmetric Profile Format	p. 174
LDU Solution Algorithm	p. 178
Tuning of the LDU Factorization	p. 182
Problems	p. 186
Iterative Equation Solver	p. 187
Preconditioned Conjugate Gradient Method	p. 187
Assembly of Matrix in Sparse-row Format	p. 188
PCG Solution	p. 193
Problems	p. 196
Load Data and Load Vector Assembly	p. 199
Data Describing the Load	p. 199
Load Data Input	p. 201
Load Vector Assembly	p. 207
Element Face Load	p. 209
Problems	p. 211
Stress Increment, Residual Vector and Results	p. 213
Computing Stress Increment	p. 213
Residual Vector	p. 215
Results	p. 217
Solution of a Simple Test Problem	p. 219
Problems	p. 220
Elastic-Plastic Problems	p. 223
Constitutive Relations for Elastic-Plastic Material	p. 223
Computing Finite Stress Increments	p. 225
Determining Elastic Fraction of Stress Increment	p. 226
Subincrementation for Computing Stress Increment	p. 226
Material Deformation Curve	p. 227
Implementation of Elastic-Plastic Material Relations	p. 228
Midpoint Integration of Constitutive Relations	p. 234
Nonlinear Solution Procedure	p. 239
Newton-Raphson Method	p. 240
Initial Stress Method	p. 241
Convergence Criteria	p. 242
Example: Solution of an Elastic-Plastic Problem	p. 243
Problems	p. 245
Mesh Generation
Mesh Generator	p. 249
Block Decomposition Method	p. 249
Class Structure	p. 250
Mesh-generation Modules	p. 252
Adding New Module	p. 253
Problems	p. 254
Two-dimensional Mesh Generators	p. 257
Rectangular Block	p. 257
Mesh Inside Eight-node Macroelement	p. 261
Algorithm of Double-quadratic Transformation	p. 261
Implementation of Mesh Generation	p. 264
Example of Mesh Generation	p. 269
Problems	p. 270
Generation of Three-dimensional Meshes by Sweeping	p. 271
Sweeping Technique	p. 271
Implementation	p. 272
Input Data	p. 272
Node Numbering	p. 275
Element Connectivities and Nodal Coordinates	p. 276
Example of Mesh Generation	p. 279
Problems	p. 281
Pasting Mesh Blocks	p. 283
Pasting Technique	p. 283
Implementation	p. 284
Data Input	p. 284
Finding Coincident Nodes	p. 286
Pasting	p. 287
Problems	p. 288
Mesh Transformations	p. 289
Transformation Relations	p. 289
Implementation	p. 291
Input Data	p. 291
Performing Transformations	p. 293
Example of Using Transformations	p. 295
Problems	p. 296
Copying, Writing and Reading Mesh Blocks	p. 297
Copying	p. 297
Writing Mesh to File	p. 299
Reading Mesh from File	p. 300
Problems	p. 302
Visualization of Meshes and Results
Introduction to Java 3D™	p. 305
Rendering Three-dimensional Objects	p. 305
Scene Graph	p. 306
Scene Graph Nodes	p. 307
Group Nodes	p. 307
Leaf Nodes	p. 308
Node Components	p. 309
Geometry	p. 309
Appearance and Attributes	p. 311
Problems	p. 311
Visualizer	p. 313
Visualization Algorithm	p. 313
Surface of the Finite Element Model	p. 314
Subdivision of Quadratic Surfaces	p. 315
Class Structure of the Visualizer	p. 315
Visualizer Class	p. 316
Input Data	p. 318
Input Data File	p. 318
Class for Data Input	p. 319
Problems	p. 322
Visualization Scene Graph	p. 325
Schematic of the Scene Graph	p. 325
Implementation of the Scene Graph	p. 326
Shape Objects	p. 328
Problems	p. 331
Surface Geometry	p. 333
Creating Geometry of the Model Surface	p. 333
Surface Faces	p. 335
Surface Edges and Nodes	p. 338
Modification of Nodal Coordinates	p. 340
Problems	p. 342
Edge and Face Subdivision	p. 343
Subdivision for Quality Visualization	p. 343
Edge Subdivision	p. 344
Face Subdivision	p. 347
Problems	p. 352
Surface Subdivision	p. 353
Subdivision of the Model Surface	p. 353
Subdivision of Faces into Triangles	p. 356
Arrays for Java 3D	p. 359
Problems	p. 362
Results Field, Color Scale, Interaction and Lights	p. 363
Results Field	p. 363
Color Scale	p. 368
Mouse Interaction	p. 370
Lights and Background	p. 372
Visualization Example	p. 373
Problems	p. 375
Data for Finite Element Solver	p. 377
Data Statements	p. 377
Data Statement	p. 377
Comment Statement	p. 377
Including File	p. 377
End Statement	p. 378
Model Data	p. 378
Parameters	p. 378
Material Properties	p. 378
Finite Element Mesh	p. 379
Displacement Boundary Conditions	p. 379
Load-Specification	p. 380
Load Step Name	p. 380
Parameters	p. 380
Nodal Forces	p. 381
Surface Forces	p. 381
Surface Forces Inside a Box	p. 381
Nodal Temperatures	p. 382
Data for Mesh Generation	p. 383
Mesh-generation Modules	p. 383
Rectangular Mesh Block	p. 384
Mesh Inside Eight-node Macroelement	p. 384
Three-dimensional Mesh by Sweeping	p. 384
Reading Mesh from File	p. 385
Writing Mesh to File	p. 385
Copying Mesh	p. 385
Mesh Transformations	p. 385
Connecting Two Mesh Blocks	p. 386
Data for Visualizer	p. 387
Visualization Data	p. 387
Input Data	p. 387
Example of Problem Solution	p. 389
Problem Statement	p. 389
Mesh Generation	p. 390
Problem Solution	p. 391
Visualization	p. 393
References	p. 397
Index	p. 399
Table of Contents provided by Ingram. All Rights Reserved.

Programming Finite Elements in Javaâ¢

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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