Structural Analysis with Finite Elements

By: Friedel Hartmann, Casimir Katz

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Hardcover | 5 February 2007 | Edition Number 2

At a Glance

Hardcover
612 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 15.88 x 2.54

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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 and based on a foundation that enables structural engineers to address key questions that arise in computer modelling of structures with finite elements. 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.

Industry Reviews

From the reviews:

"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 modeling of structures with finite elements. ... The authors deserve full marks for a difficult assignment. Users of finite element software in mechanical and civil engineering will have reason to feel delighted to own a copy of the book. The book is certain to stimulate a heightened research interest in the vital area of finite elements." (Current Engineering Practice - online, Vol. 47, 2004/2005)

"This book explains the theoretical foundations of the finite element method and its application in civil engineering. ... the text is addressed to practitioners who wish to gain inside into a method which is widely applied in today's design processes. ... The book seems mainly intended for the civil engineer who already applies finite element software, but it also offers interesting insight for those studying numerical methods in engineering." (Technische Mechanik, Vol. 25 (3-4), 2005)

From the reviews of the second edition:

"The emphasis of the book is static structural design. ... The book is well written and would be a valuable addition for the library of a structural engineer." (J. Genin, Zentralblatt MATH, Vol. 1139 (17), 2008)

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What are finite elements?	p. 1
Introduction	p. 1
Key points of the FE method	p. 1
Potential energy	p. 6
Projection	p. 8
The error of an FE solution	p. 13
A beautiful idea that does not work	p. 15
Set theory	p. 16
Principle of virtual displacements	p. 23
Taut rope	p. 29
Least squares	p. 33
Distance inside = distance outside	p. 37
Scalar product and weak solution	p. 40
Equivalent nodal forces	p. 42
Concentrated forces	p. 44
Green's functions	p. 51
Practical consequences	p. 55
Why finite element results are wrong	p. 57
Proof	p. 64
Influence functions	p. 69
Accuracy	p. 80
Why resultant stresses are more accurate	p. 86
Why stresses at midpoints are more accurate	p. 88
Why stresses jump	p. 99
Why finite element support reactions are relatively accurate	p. 99
Gauss points	p. 104
The Dirac energy	p. 110
How to predict changes	p. 113
The influence of a single element	p. 126
Retrofitting structures	p. 130
Local errors and pollution	p. 136
Adaptive methods	p. 147
St.Venant's principle	p. 172
Singularities	p. 175
Actio = reactio?	p. 177
The output	p. 181
Support conditions	p. 183
Equilibrium	p. 184
Temperature changes and displacement of supports	p. 187
Stability problems	p. 193
Interpolation	p. 197
Polynomials	p. 199
Infinite energy	p. 208
Conforming and nonconforming shape functions	p. 209
Partition of unity	p. 211
Generalized finite element methods	p. 213
Elements	p. 220
Stiffness matrices	p. 221
Couplingdegrees offreedom	p. 224
Numerical details	p. 226
Warning	p. 235
What are boundary elements?	p. 239
Influence functions or Betti's theorem	p. 240
Structural analysis with boundary elements	p. 247
Comparison finite elements-boundary elements	p. 262
Frames	p. 269
Introduction	p. 269
The FE approach	p. 270
Finite elements and the slope deflection method	p. 289
Stiffness matrices	p. 292
Approximations for stiffness matrices	p. 298
Cables	p. 305
Hierarchical elements	p. 309
Sensitivity analysis	p. 313
Plane problems	p. 327
Simple example	p. 327
Strains and stresses	p. 334
Shape functions	p. 337
Plane elements	p. 338
Thepatchtest	p. 344
Volume forces	p. 346
Supports	p. 347
Nodal stresses and element stresses	p. 357
Truss and frame models	p. 363
Two-bay wall	p. 365
Multistory shear wall	p. 365
Shear wall with suspended load	p. 370
Shear wall and horizontal load	p. 375
Equilibrium ofresultant forces	p. 378
Adaptive mesh refinement	p. 383
Plane problems in soil mechanics	p. 386
Incompressible material	p. 393
Mixedmethods	p. 393
Influence functions for mixed formulations	p. 399
Error analysis	p. 401
Nonlinear problems	p. 401
Slabs	p. 415
Kirchhoff plates	p. 416
Thedisplacementmodel	p. 421
Elements	p. 422
Hybridelements	p. 425
Singularities of a Kirchhoff plate	p. 429
Reissner-Mindlin plates	p. 431
Singularities of a Reissner-Mindlin plate	p. 436
Reissner-Mindlinelements	p. 439
Supports	p. 441
Columns	p. 443
Shearforces	p. 451
Variable thickness	p. 452
Beammodels	p. 459
Wheel loads	p. 460
Circularslabs	p. 461
Tbeams	p. 462
Foundationslabs	p. 469
Direct design method	p. 476
Pointsupports	p. 477
Study	p. 480
Sensitivityanalysis	p. 480
Shells	p. 485
Shellequations	p. 485
Shellsofrevolution	p. 488
Volume elements and degenerate shell elements	p. 490
Circulararches	p. 491
Flatelements	p. 493
Membranes	p. 498
Theoretical details	p. 503
Scalar product	p. 503
Green's identities	p. 508
Green'sfunctions	p. 516
Generalized Green'sfunctions	p. 519
Nonlinear problems	p. 526
The derivation of influence functions	p. 529
Weak form of influence functions	p. 535
Influence functions for other quantities	p. 539
Shifted Green'sfunctions	p. 541
The dual space	p. 552
Someconceptsoferroranalysis	p. 560
Important equations and inequalities	p. 568
References	p. 579
Index	p. 593
Table of Contents provided by Publisher. All Rights Reserved.

Structural Analysis with Finite Elements

At a Glance

Hardcover

Industry Reviews

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