A variational approach to structural analysis

David V Wallerstein

406 pages, parution le 17/12/2001

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Résumé

The finite element method (FEM) is a key analytical tool for today's engineers. Written by an author who has spent almost twenty years as one of the major developers of the world's most heavily used FEM code, this book covers the basic underpinnings of FEM to give engineers a crucial "grass roots" understanding of the calculations that occur behind the code that they run during FEM analysis.

Table of Contents

Preface 1
Introduction 1

2 Preliminaries 7

2.1 Variational Notation 7
2.2 The Gradient 10
2.3 Integration by Parts 11
2.4 Stokes's Theorem 13
2.5 Green's Theorem in the Plane 15
2.6 Adjoint Equations 16
2.7 Meaning of [actual symbol not reproducible] 19
2.8 Total Differentials 20
2.9 Legendre Transformation 21
2.10 Lagrange Multipliers 24
2.11 Differential Equations of Equilibrium 27
2.12 Strain-Displacement Relations 29
2.13 Compatibility Conditions of Strain 33
2.14 Thermodynamic Considerations 35

3 Principle of Virtual Work 40

3.1 Virtual Work Definition 40
3.2 Generalized Coordinates 41
3.3 Virtual Work of a Deformable Body 42
3.4 Thermal Stress, Initial Strain, and Initial Stress 47
3.5 Some Constitutive Relationships 48
3.6 Accounting for All Work 51
3.7 Axially Loaded Members 53
3.8 The Unit-Displacement Method 60
3.9 Finite Elements for Axial Members 65
3.10 Coordinate Transformations 71
3.11 Review of the Simple Beam Theory 74
3.12 Shear Stress in Simple Beams 92
3.13 Shear Deflection in Straight Beams 95
3.14 Beams with Initial Curvature 99
3.15 Thermal Strain Correction in Curved Beams 112
3.16 Shear and Radial Stress in Curved Beams 114
3.17 Thin Walled Beams of Open Section 121
3.18 Shear in Open Section Beams 147
3.19 Slope-Deflection Equations 155
3.20 Approximate Methods 165

4 Complementary Virtual Work 196

4.1 Complementary Virtual Work Definition 196
4.2 Complementary Virtual Work of a Deformable Body 197
4.3 Symmetry 210
4.4 The Unit Load Method 217
4.5 Force Elements 235
4.6 Generalized Force-Displacement Transformations 239

5 Some Energy Methods 261

5.1 Conservative Forces and Potential Functions 261
5.2 Stationary Potential Energy 271
5.3 Castigliano's First Theorem 274
5.4 Complementary Energy 277
5.5 Stationary Complementary Potential Energy 280
5.6 Engesser-Crotti Theorem 282
5.7 Variational Statements 287
5.8 The Galerkin Method 290
5.9 Derived Variational Principles 300

6 Some Static and Dynamic Stability Concepts 318

6.1 Linear-Stability Analysis 318
6.2 Geometric Measure of Strain 322
6.3 A Beam with Initial Curvature Revisited 330
6.4 Thin Walled Open Beams Revisited 337
6.5 Some Stability Concepts 349
6.6 Energy Criterion of Stability 350
6.7 Stiffness 353
6.8 Stiffening and Unstiffening Models 360
6.9 Bifurcation Analysis 369
6.10 Imperfection Analysis 372
6.11 Circulatory Dynamic Stability 377
6.12 Instationary Dynamic Stability 384

References 396
Index 401

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	David V Wallerstein
Parution	17/12/2001
Nb. de pages	406
Format	16 x 24,2
Couverture	Relié
Poids	720g
Intérieur	Noir et Blanc
EAN13	9780471395935
ISBN13	978-0-471-39593-5