Structural Analysis with Finite Elements (2004. 450 p.)

Structural Analysis with Finite Elements (2004. 450 p.)

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  • 製本 Hardcover:ハードカバー版/ページ数 450 p.
  • 商品コード 9783540404163

Full Description


Structural Analysis with Finite Elements develops the foundations and applications of the finite element method in structural analysis in a language which is familiar to structural engineers. At the same time, it uncovers the structural mechanics behind the finite element method. This innovative text explores and explains issues such as: why finite element results are 'wrong,' why support reactions are relatively accurate, why stresses at midpoints are more reliable, why averaging the stresses sometimes may not help or why the equilibrium conditions are violated. An additional chapter treats the boundary element method, and related software is available at www winfem.de. Structural Analysis with Finite Elements provides a new foundation for the finite element method that enables structural engineers to address key questions that arise in computer modelling of structures with finite elements.

Table of Contents

1 What are finite elements?                        1  (180)
1.1 Introduction 1 (1)
1.2 Key points of the FE method 1 (4)
1.3 Potential energy 5 (3)
1.4 Projection 8 (4)
1.5 The error of an FE solution 12 (3)
1.6 A beautiful idea that does not work 15 (1)
1.7 Set theory 16 (7)
1.8 Principle of virtual displacements 23 (5)
1.9 Taut rope 28 (5)
1.10 Least squares 33 (3)
1.11 Distance inside = distance outside 36 (3)
1.12 Scalar product and weak solution 39 (2)
1.13 Equivalent nodal forces 41 (2)
1.14 Concentrated forces 43 (7)
1.15 Green's functions 50 (2)
1.16 Practical consequences 52 (3)
1.17 Why finite element results are wrong 55 (7)
1.18 Proof 62 (5)
1.19 Influence functions 67 (8)
1.20 Accuracy 75 (5)
1.21 Why resultant stresses are more accurate 80 (4)
1.22 Why stresses at midpoints are more 84 (9)
accurate
1.23 Why stresses jump 93 (1)
1.24 Why finite element support reactions are 94 (5)
relatively accurate
1.25 Gauss points 99 (6)
1.26 Local errors and pollution 105(7)
1.27 Adaptive methods 112(15)
1.28 St. Venant's principle 127(2)
1.29 Singularities 129(3)
1.30 Actio = reactio? 132(3)
1.31 The output 135(2)
1.32 Support conditions 137(1)
1.33 Equilibrium 138(3)
1.34 Changes in the temperature and 141(3)
displacement of supports
1.35 Stability problems 144(4)
1.36 Interpolation 148(3)
1.37 Polynomials 151(7)
1.38 Infinite energy 158(2)
1.39 Conforming and nonconforming shape 160(1)
functions
1.40 Partition of unity 161(2)
1.41 Elements 163(1)
1.42 Stiffness matrices 164(3)
1.43 Coupling degrees of freedom 167(3)
1.44 Numerical details 170(8)
1.45 Warning 178(3)
2 What are boundary elements? 181(30)
2.1 Influence functions or Betti's theorem 182(7)
2.2 Structural analysis with boundary 189(15)
elements
2.3 Comparison finite elements-boundary 204(7)
elements
3 Frames 211(30)
3.1 Introduction 211(1)
3.2 The FE approach 212(15)
3.3 Finite elements and the slope 227(4)
deflection method
3.4 Stiffness matrices 231(6)
3.5 Approximations for stiffness matrices 237(4)
4 Plane problems 241(84)
4.1 Simple example 241(7)
4.2 Strains and stresses 248(3)
4.3 Shape functions 251(1)
4.4 Plane elements 252(6)
4.5 The patch test 258(2)
4.6 Volume forces 260(1)
4.7 Supports 261(10)
4.8 Nodal stresses and element stresses 271(6)
4.9 Truss models 277(1)
4.10 Two-bay wall 278(2)
4.11 Multistory shear wall 280(7)
4.12 Shear wall with suspended load 287(2)
4.13 Shear wall and horizontal load 289(3)
4.14 Equilibrium of resultant forces 292(4)
4.15 Adaptive mesh refinement 296(4)
4.16 Plane problems in soil mechanics 300(6)
4.17 Incompressible material 306(1)
4.18 Mixed methods 307(5)
4.19 Influence functions 312(1)
4.20 Error analysis 313(1)
4.21 Nonlinear problems 314(11)
5 Slabs 325(66)
5.1 Kirchhoff plates 326(5)
5.2 The displacement model 331(1)
5.3 Elements 332(3)
5.4 Hybrid elements 335(4)
5.5 Singularities of a Kirchhoff plate 339(2)
5.6 Reissner-Mindlin plates 341(5)
5.7 Singularities of a Reissner-Mindlin 346(3)
plate
5.8 Reissner-Mindlin elements 349(2)
5.9 Supports 351(2)
5.10 Columns 353(8)
5.11 Shear forces 361(1)
5.12 Variable thickness 362(2)
5.13 Beam models 364(5)
5.14 Wheel loads 369(1)
5.15 Circular slabs 369(3)
5.16 T beams 372(6)
5.17 Foundation slabs 378(6)
5.18 Direct design method 384(2)
5.19 Point supports 386(1)
5.20 Study 386(5)
6 Shells 391(18)
6.1 Shell equations 391(3)
6.2 Shells of revolution 394(2)
6.3 Volume elements and degenerate shell 396(1)
elements
6.4 Circular arches 397(2)
6.5 Flat elements 399(5)
6.6 Membranes 404(5)
7 Theoretical details 409(62)
7.1 Scalar product 409(5)
7.2 Green's identities 414(5)
7.3 Green's functions 419(2)
7.4 Generalized Green's functions 421(7)
7.5 Nonlinear problems 428(4)
7.6 The derivation of influence functions 432(5)
7.7 Shifted Green's functions 437(10)
7.8 The dual space 447(6)
7.9 Some concepts of error analysis 453(8)
7.10 Important equations and inequalities 461(10)
References 471