Introduction to Finite Element Analysis and Design,9780470125397

Introduction to Finite Element Analysis and Design

by ;
Edition: 1
ISBN13: 9780470125397
ISBN10: 047012539X
Format: Paperback
Pub. Date: 2008-10-01
Publisher(s): Wiley
List Price: $178.95

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Summary

Finite Element Method (FEM) is one of the numerical methods of solving differential equations that describe many engineering problems. This new book covers the basic theory of FEM and includes appendices on each of the main FEA programs as reference. It introduces the concepts so that engineers can use the method efficiently and interpret the results properly. They'll learn about one-dimensional finite elements, including truss and beam elements, as well as two and three dimensional finite elements. Numerous examples are also included using ANSYS, ABAQUS, NASTRAN, Pro/Engineer, and I-DEAS. This approach will help engineers develop a thorough understanding of the theory behind FEM as well as its application.

Table of Contents

Prefacep. vii
Mathematical Preliminariesp. 1
Vectors and Matricesp. 1
Vector-Matrix Calculusp. 3
Matrix Equationsp. 8
Eigen Values and Eigen Vectorsp. 8
Quadratic Formsp. 12
Maxima and Minima of Functionsp. 13
Exercisep. 14
Stress-Strain Analysisp. 17
Stressp. 17
Strainp. 30
Stress-Strain Relationsp. 35
Boundary Value Problemsp. 39
Failure Theoriesp. 43
Safety Factorp. 49
Exercisep. 52
Uniaxial Bar and Truss Elements-Direct Methodp. 60
Illustration of the Direct Methodp. 61
Uniaxial Bar Elementp. 66
Plane Truss Elementsp. 73
Three-Dimensional Truss Elements (Space Truss)p. 83
Thermal Stressesp. 87
Projectsp. 94
Exercisep. 98
Weighted Residual and Energy Methods for One-Dimensional Problemsp. 108
Exact vs. Approximate Solutionp. 108
Galerkin Methodp. 109
Higher-Order Differential Equationsp. 114
Finite Element Approximationp. 117
Formal Procedurep. 124
Energy Methodsp. 129
Exercisep. 138
Finite Element Analysis of Beams and Framesp. 143
Review of Elementary Beam Theoryp. 143
Rayleigh-Ritz Methodp. 148
Finite Element Interpolationp. 153
Finite Element Equation for the Beam Elementp. 158
Bending Moment and Shear Force Distributionp. 166
Plane Framep. 171
Projectp. 175
Exercisep. 176
Finite Elements for Heat Transfer Problemsp. 185
Introductionp. 185
Fourier Heat Conduction Equationp. 186
Finite Element Analysis - Direct Methodp. 188
Galerkin Method for Heat Conduction Problemsp. 194
Convection Boundary Conditionsp. 200
Exercisep. 207
Finite Elements for Plane Solidsp. 211
Introductionp. 211
Types of Two-Dimensional Problemsp. 211
Principle of Minimum Potential Energyp. 214
Constant Strain Triangular (CST) Elementp. 216
Four-Node Rectangular Elementp. 229
Four-Node Iso-Parametric Quadrilateral Elementp. 237
Numerical Integrationp. 248
Projectp. 253
Exercisep. 254
Finite Element Procedures and Modelingp. 261
Finite Element Analysis Proceduresp. 261
Finite Element Modeling Techniquesp. 281
Projectp. 291
Exercisep. 292
Structural Design Using Finite Elementsp. 297
Introductionp. 297
Safety Margin in Designp. 298
Intuitive Design: Fully-Stressed Designp. 301
Design Parameterizationp. 304
Parameter Study - Sensitivity Analysisp. 307
Structural Optimizationp. 313
Project: Design Optimization of a Bracketp. 325
Exercisep. 327
Finite Element Analysis Using Pro/Engineerp. 333
Introductionp. 333
Getting Startp. 333
Plate with a Hole Analysisp. 334
Design Sensitivity Analysis/Parameter Studyp. 339
Design Optimizationp. 341
Finite Element Analysis Using NEi Nastranp. 343
Introductionp. 343
Getting Startp. 343
Plate with a Hole Analysisp. 343
Static Analysis of Beamsp. 350
Examples in the textp. 356
Finite Element Analysis Using ANSYSp. 363
Introductionp. 363
Getting Startp. 364
Static Analysis of a Corner Bracketp. 365
Examples in the Textp. 381
Finite Element Analysis Using MATLAB Toolboxp. 391
Finite Element Analysis of Bar and Trussp. 391
Finite Element Analysis Using Frame Elementsp. 403
Finite Element Analysis Using Plane Solid Elementsp. 408
Indexp. 417
Table of Contents provided by Ingram. All Rights Reserved.

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