Hartmann / Katz Structural Analysis with Finite Elements

2. Auflage 2007
ISBN: 978-3-540-49702-8
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 598 Seiten

This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.

Autoren/Hrsg.

Hartmann, Friedel

Katz, Casimir

Inhaltsverzeichnis

1;Preface;5
2;Preface to the second edition;7
3;Contents;8
4;1. What are finite elements?;12
4.1;1.1 Introduction;12
4.2;1.2 Key points of the FE method;12
4.3;1.3 Potential energy;17
4.4;1.4 Projection;19
4.5;1.5 The error of an FE solution;24
4.6;1.6 A beautiful idea that does not work;26
4.7;1.7 Set theory;27
4.8;1.8 Principle of virtual displacements;34
4.9;1.9 Taut rope;40
4.10;1.10 Least squares;44
4.11;1.11 Distance inside = distance outside;48
4.12;1.12 Scalar product and weak solution;51
4.13;1.13 Equivalent nodal forces;53
4.14;1.14 Concentrated forces;55
4.15;1.15 Green’s functions;62
4.16;1.16 Practical consequences;66
4.17;1.17 Why finite element results are wrong;68
4.18;1.18 Proof;75
4.19;1.19 Influence functions;80
4.20;1.20 Accuracy;91
4.21;1.21 Why resultant stresses are more accurate;97
4.22;1.22 Why stresses at midpoints are more accurate;99
4.23;1.23 Why stresses jump;110
4.24;1.24 Why finite element support reactions are relatively accurate;110
4.25;1.25 Gauss points;115
4.26;1.26 The Dirac energy;121
4.27;1.27 How to predict changes;124
4.28;1.28 The influence of a single element;137
4.29;1.29 Retrofitting structures;141
4.30;1.30 Local errors and pollution;147
4.31;1.31 Adaptive methods;158
4.32;1.32 St. Venant’s principle;183
4.33;1.33 Singularities;186
4.34;1.34 Actio = reactio?;188
4.35;1.35 The output;192
4.36;1.36 Support conditions;194
4.37;1.37 Equilibrium;195
4.38;1.38 Temperature changes and displacement of supports;198
4.39;1.39 Stability problems;204
4.40;1.40 Interpolation;208
4.41;1.41 Polynomials;210
4.42;1.42 Infinite energy;219
4.43;1.43 Conforming and nonconforming shape functions;220
4.44;1.44 Partition of unity;222
4.45;1.45 Generalized finite element methods;224
4.46;1.46 Elements;231
4.47;1.47 Stiffness matrices;232
4.48;1.48 Coupling degrees of freedom;235
4.49;1.49 Numerical details;237
4.50;1.50 Warning;246
5;2. What are boundary elements?;250
5.1;2.1 Influence functions or Betti’s theorem;251
5.2;2.2 Structural analysis with boundary elements;258
5.3;2.3 Comparison finite elements—boundary elements;273
6;3. Frames;280
6.1;3.1 Introduction;280
6.2;3.2 The FE approach;281
6.3;3.3 Finite elements and the slope deflection method;300
6.4;3.4 Stiffness matrices;303
6.5;3.5 Approximations for stiffness matrices;309
6.6;3.6 Cables;316
6.7;3.7 Hierarchical elements;320
6.8;3.8 Sensitivity analysis;324
7;4. Plane problems;338
7.1;4.1 Simple example;338
7.2;4.2 Strains and stresses;345
7.3;4.3 Shape functions;348
7.4;4.4 Plane elements;349
7.5;4.5 The patch test;355
7.6;4.6 Volume forces;357
7.7;4.7 Supports;358
7.8;4.8 Nodal stresses and element stresses;368
7.9;4.9 Truss and frame models;374
7.10;4.10 Two-bay wall;376
7.11;4.11 Multistory shear wall;376
7.12;4.12 Shear wall with suspended load;381
7.13;4.13 Shear wall and horizontal load;386
7.14;4.14 Equilibrium of resultant forces;389
7.15;4.15 Adaptive mesh refinement;394
7.16;4.16 Plane problems in soil mechanics;397
7.17;4.17 Incompressible material;404
7.18;4.18 Mixed methods;404
7.19;4.19 Influence functions for mixed formulations;410
7.20;4.20 Error analysis;412
7.21;4.21 Nonlinear problems;412
8;5. Slabs;426
8.1;5.1 Kirchhoff plates;427
8.2;5.2 The displacement model;432
8.3;5.3 Elements;433
8.4;5.4 Hybrid elements;436
8.5;5.5 Singularities of a Kirchhoff plate;440
8.6;5.6 Reissner–Mindlin plates;442
8.7;5.7 Singularities of a Reissner–Mindlin plate;447
8.8;5.8 Reissner–Mindlin elements;450
8.9;5.9 Supports;452
8.10;5.10 Columns;454
8.11;5.11 Shear forces;462
8.12;5.12 Variable thickness;463
8.13;5.13 Beam models;470
8.14;5.14 Wheel loads;471
8.15;5.15 Circular slabs;472
8.16;5.16 T beams;473
8.17;5.17 Foundation slabs;480
8.18;5.18 Direct design method;487
8.19;5.19 Point supports;488
8.20;5.20 Study;491
8.21;5.21 Sensitivity analysis;491
9;6. Shells;496
9.1;6.1 Shell equations;496
9.2;6.2 Shells of revolution;499
9.3;6.3 Volume elements and degenerate shell elements;501
9.4;6.4 Circular arches;502
9.5;6.5 Flat elements;504
9.6;6.6 Membranes;509
10;7. Theoretical details;514
10.1;7.1 Scalar product;514
10.2;7.2 Green’s identities;519
10.3;7.3 Green’s functions;527
10.4;7.4 Generalized Green’s functions;530
10.5;7.5 Nonlinear problems;537
10.6;7.6 The derivation of influence functions;540
10.7;7.7 Weak form of influence functions;546
10.8;7.8 Influence functions for other quantities;550
10.9;7.9 Shifted Green’s functions;552
10.10;7.10 The dual space;563
10.11;7.11 Some concepts of error analysis;571
10.12;7.12 Important equations and inequalities;579
11;References;590
12;Index;604