Introductory Finite Element Method

Front Cover
CRC Press, May 18, 2001 - Technology & Engineering - 520 pages
Although there are many books on the finite element method (FEM) on the market, very few present its basic formulation in a simple, unified manner. Furthermore, many of the available texts address either only structure-related problems or only fluid or heat-flow problems, and those that explore both do so at an advanced level.

Introductory Finite Element Method examines both structural analysis and flow (heat and fluid) applications in a presentation specifically designed for upper-level undergraduate and beginning graduate students, both within and outside of the engineering disciplines. It includes a chapter on variational calculus, clearly presented to show how the functionals for structural analysis and flow problems are formulated. The authors provide both one- and two-dimensional finite element codes and a wide range of examples and exercises. The exercises include some simpler ones to solve by hand calculation-this allows readers to understand the theory and assimilate the details of the steps in formulating computer implementations of the method.

Anyone interested in learning to solve boundary value problems numerically deserves a straightforward and practical introduction to the powerful FEM. Its clear, simplified presentation and attention to both flow and structural problems make Introductory Finite Element Method the ideal gateway to using the FEM in a variety of applications.
 

Contents

Principles and Laws
7
Steps in the Finite Element Method
13
TwoDimensional Problems
41
Summary
47
OneDimensional Stress Deformation
53
Principle of Minimum Potential Energy
61
Integration
75
Boundary Conditions
82
Boundary Conditions
261
ThreeDimensional Formulation
284
Comparisons of Numerical Predictions and Closed Form Solutions
309
Review and Comments
327
1888888
345
Static Condensation
354
References
360
Stream Function Formulation
371

Strains and Stresses
88
Formulation by Galerkins Method
92
Bounds
112
References
120
Problems
135
TimeDependent Problems
144
OneDimensional Consolidation
162
Problems
169
References
175
Users Guide for Code DFTC1DFE
184
Users Guide for Field2D
195
BeamColumn
219
Problems
228
References
237
References
248
Thermal or Heat Flow Problem
377
Electromagnetic Problems
384
References
392
Finite Element Formulation
400
Computer Code
418
Problems
428
References
436
Computer Code
447
Transformation of Coordinates
455
Solution of Beam
459
Comparisons of the Methods
469
Solution Procedure
475
References
482
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