An Introduction to the Finite Element Method Book

	Preface to the Second Edition
	Preface to the First Edition
Pt. 1	Preliminaries
1.1	General Comments	3
1.2	Historical Background	5
1.3	The Basic Concept of the Finite Element Method	5
1.4	The Present Study	15
2	Integral Formulations and Variational Methods	18
2.1	Need for Weighted-Integral Forms	18
2.2	Some Mathematical Concepts and Formulae	20
2.3	Weak Formulation of Boundary Value Problems	28
2.4	Variational Methods of Approximation	40
Pt. 2	Finite Element Analysis of One-Dimensional Problems
3	Second-Order Boundary Value Problems	67
3.2	Basic Steps of Finite Element Analysis	70
3.3	Applications	105
4	Bending of Beams	143
4.2	The Euler-Bernoulli Beam Element	143
4.3	Plane Truss and Euler-Bernoulli Frame Elements	167
4.4	The Timoshenko Beam and Frame Elements	177
4.5	Inclusion of Constraint Equations	187
5	Finite Element Error Analysis	199
5.1	Approximation Errors	199
5.2	Various Measures of Errors	200
5.3	Convergence of Solution	201
5.4	Accuracy of the Solution	202
6	Eigenvalue and Time-Dependent Problems	209
6.1	Eigenvalue Problems	209
6.2	Time-Dependent Problems	224
7	Numerical Integration and Computer Implementation	246
7.1	Isoparametric Formulations and Numerical Integration	246
7.2	Computer Implementation	258
7.3	Applications of the Computer Program FEM1DV2	270
Pt. 3	Finite Element Analysis of Two-Dimensional Problems
8	Single-Variable Problems	295
8.2	Boundary Value Problems	297
8.3	Some Comments on Mesh Generation and Imposition of Boundary Conditions	334
8.4	Applications	340
8.5	Eigenvalue and Time-Dependent Problems	370
9	Interpolation Functions, Numerical Integration, and Modeling Considerations	404
9.1	Library of Elements and Interpolation Functions	404
9.2	Numerical Integration	421
9.3	Modeling Considerations	439
10	Plane Elasticity	455
10.2	Governing Equations	456
10.3	Weak Formulations	459
10.4	Finite Element Model	461
10.5	Evaluation of Integrals	465
10.6	Assembly and Boundary and Initial Conditions	468
11	Flows of Viscous Incompressible Fluids	482
11.2	Governing Equations	483
11.3	Velocity-Pressure Finite Element Model	484
11.4	Penalty-Finite Element Model	488
12	Bending of Elastic Plates	508
12.2	Classical Plate Model	510
12.3	Shear Deformable Plate Model	516
12.4	Eigenvalue and Time-Dependent Problems	520
13	Computer Implementation	533
13.2	Preprocessor	534
13.3	Element Computations: Processor	535
13.4	Applications of the Computer Program FEM2DV2	540
Pt. 4	Advanced Topics
14	Weighted-Residual Finite Element Models, and Finite Element Models of Nonlinear and Three-Dimensional Problems	579
14.2	Alternative Formulations	580
14.3	Nonlinear Problems	594
14.4	Three-Dimensional Problems	599
	App. 1 Fortran Listing of FEM1DV2	609
	App. 2 Fortran Listing of FEM2DV2	640
	Index	679