Numerical Structural Analysis: Methods, Models and PitfallsTo our sons, Mike, Andrew, Alex, who did not inherit their fathers' level of interest in applied mechanics, but who became sophisticated in software development and in this regard surpassed their parents. A.P., V.S. Hard times came, the god5 got angry. Children do not behave themselves and everybody wishes to write a book. Ancient Babylonian inscription X Preface Preface to the English Edition The book you are reading is a translation from Russian into English. Within a pretty short term this book saw two editions in Russian. The authors received in spiring responses from readers that both stimulated our continuing and improving this work and made sure it would not be in vain of us to try to multiply our readers by covering the English-speaking engineering community. When we prepared the present edition, we took into account interests of the Western readers, so we had to make some changes to our text published earlier. These changes include the following aspects. First, we excluded a lot of references and discussions regarding Russian engi neering codes. It seems to us those are of no real interest for Western engineers oriented at Eurocode or national construction design regulations. |
Contents
Object of Analysis and Problem of Modelling | 1 |
12 Principal Factors taken into Account during Creation of Design Models | 3 |
13 Incomplete Determinacy of an Objects Knowledge | 6 |
14 Experiment and Practical Experience | 7 |
15 General Issues of Modeling | 10 |
16 Majorant and Minorant Models | 12 |
17 Posterior Analysis of a Design Model | 13 |
References | 15 |
64 Characteristic Displacement | 259 |
65 Calculating Energy of Deformation | 262 |
66 Further Processing of Results | 264 |
References | 266 |
Uncertainty of Parameters | 267 |
72 Methods of Sensitivity Analysis | 274 |
73 Sensitivity of Natural Oscillations | 277 |
74 Estimating Extra Stresses Caused by Varied Stiffness | 282 |
Building a Design Model | 17 |
21 Determinative Parameters and the Number of Degrees of Freedom | 18 |
22 Model of Loading as a Part of the Design Model | 22 |
23 Validation and Means of Description of Design Models | 25 |
24 Some Tricks | 34 |
25 MonoConstraints and PolyConstraints in Design Models | 42 |
26 Perfectly Rigid Bodies as Finite Element Types | 46 |
261 OneDimensional Perfectly Rigid Bodies | 47 |
263 ThreeDimensional Perfectly Rigid Bodies | 48 |
27 On a Nonlinear Analysis | 51 |
28 Using Several Models at the same Time | 54 |
29 Comparison between Calculated and Experimental Data | 59 |
References | 62 |
Basic Relationships for Discrete Systems | 65 |
311 Slope Deflection Method | 67 |
312 Force Method | 71 |
313 Duality of the Slope Deflection Method and Force Method Projectors | 73 |
32 Static and Kinematical Analysis | 77 |
321 Note on Dislocations | 81 |
33 Polyconstraints Revisited Variational Formulation | 82 |
34 Null Elements | 91 |
35 Geometrical Nonlinearity Stability | 98 |
352 Geometrical Nonlinearity in Trusstype Bars | 99 |
353 Geometrically Nonlinear Equations in Variations | 105 |
36 Structural Nonlinearity Systems with Unilateral Constraints | 109 |
37 Cable Elements in Design Models | 114 |
371 Coordinate Axes | 118 |
372 Specification of Prestress | 119 |
373 On Linearized Models of Cable Structures | 120 |
374 Linearization of Cable Elements in a Design Model | 122 |
375 Linearization of Compressed and Bent Elements of a Design Model | 126 |
38 Dynamical Analysis | 128 |
39 Continual Systems in FiniteDimensional Representation | 133 |
391 A Note on Terminology | 135 |
References | 136 |
Finite Element Models | 139 |
42 Basic Concepts of the Finite Element Analysis | 140 |
43 Modeling of Bar Systems | 144 |
44 Finite Element Grid Modeling | 151 |
45 On Practical Convergence | 153 |
46 Convergence Validation for some Models | 154 |
47 Richardson Extrapolation | 158 |
48 Circumventing Singularities | 161 |
49 Finite Element Mesh Generation | 165 |
410 Using Hybrid Finite Elements | 169 |
| 173 | |
Mistakes and Pitfalls Special Techniques to Build Finite Element Models | 177 |
52 Building Continuous Stress Fields with FEM | 184 |
53 Mistakes and Traps in Coupling Elements of Different Dimensionality | 193 |
531 Bars + Plates | 194 |
532 Bars + Plane Stress | 200 |
533 Bars + Massive Elements | 211 |
54 A Paradox of Coupling Bernoulli and Timoshenko Bars in the Same Model | 216 |
55 Approximating Geometric Shapes and Fixations | 224 |
56 Computational Error and Ways to Dispose of it | 227 |
561 Notes on the SuperElement Application | 238 |
562 Notes on a Software Testing | 239 |
57 StepbyStep Procedure | 241 |
References | 246 |
Estimating and Interpreting Results | 249 |
62 What Analysis Results are Needed | 250 |
63 General Validation | 256 |
75 Theoretical Estimates in the Case of Uncertain Stiffness Properties | 285 |
76 Making Use of Experiment Planning Methods | 287 |
77 Limit Equilibrium under an Uncertain Load | 294 |
References | 296 |
A Review of some Problem Classes | 299 |
82 Erection | 302 |
821 Genetic Nonlinearity | 307 |
83 Prestressing | 315 |
84 Structures with Hydraulic Jacks | 318 |
841 Liquid Finite Element | 323 |
85 A Structure Foundation Model | 324 |
852 A Twoparametric Bed Model | 326 |
86 Assigning Properties of a Twoparametric Elastic Bed | 331 |
861 A CCC Bed Model | 334 |
87 Employing FiniteElement Foundation Models | 342 |
88 A Bimember Model of an Opensection Thinwalled Bar7 | 345 |
882 A Bimember Model of a Thinwalled Bar Reinforced by Lateral Slats | 351 |
883 A Thinwalled Bar Reinforced by a Lateral Diaphragm | 357 |
884 A Mathematical Interpretation of the Bimember Model and its Discrete Scheme | 358 |
89 Design Load Combinations | 361 |
| 367 | |
Buckling Problems and Related Issues | 369 |
92 Classic Problems of Equilibrium Stability | 375 |
93 Free Lengths of Compressed Bars | 379 |
94 Analysis of a Role Played by Particular Subsystems | 383 |
95 On the Influence of Additional Constraints upon the Stability of a System | 388 |
96 On a Paradox Encountered in a Bar Buckling Problem8 | 404 |
97 Allowing for Imperfections in a Real Construction | 410 |
98 Notes on Allowing for PA Effects | 415 |
References | 416 |
Problems of Dynamics | 419 |
1011 Dynamical Degrees of Freedom | 423 |
1012 Dynamic Condensation a Guyans Procedure | 424 |
102 lntegrating Motion Equations | 427 |
103 Forced Oscillations under a Harmonic Action | 432 |
1031 A Model by Gordeyeva | 439 |
104 Decrement of Oscillations | 443 |
1041 Finite Elements of an Elastic Material | 446 |
1042 A Dry Friction Element | 447 |
1044 A Nonlinear Viscous Friction Element | 448 |
105 Three Resonance Curves | 450 |
106 Analysis of Structures under Seismic Actions | 452 |
1062 Seismic Response | 453 |
1063 Analysis with Accelerograms | 459 |
107 Action of Pulse and Impact Loads | 461 |
108 Oscillations under an Action of Wind Flow Pulsations | 465 |
1082 A Dynamic Action of the Wind Loads Pulsation Component | 466 |
1083 Representation of a Pulsation Component of a Wind Load | 468 |
1084 Spectrum of Wind Velocity Pulsations | 470 |
1085 A Dynamical Component of a Design Factor | 471 |
1086 lssues of Numerical lmplementation | 472 |
References | 474 |
A Word Instead of a Conclusion | 477 |
| 483 | |
Appendix | 485 |
A1 Jordan Exclusions and their Role in Structural Mechanics | 486 |
A3 Jordan Exclusions with the Stiffness Matrix of a Structure | 488 |
A4 Stiffness Matrix of a Finite Element NonRigidly Attached to its Nodes | 492 |
A5 A Double Jordan Exclusion | 496 |
| 498 | |
| 499 | |
Other editions - View all
Numerical Structural Analysis: Methods, Models and Pitfalls Anatoly Perelmuter,Vladimir Slivker No preview available - 2012 |
Common terms and phrases
accuracy analysis of structures analyze applied approximation assume axis bar's behavior bending boundary conditions buckling C₁ C₂ cable calculated caused coefficient column components compressed computational controlling parameters coordinate cross-section deformation degrees of freedom design model determined discrete displacement vector displacements distribution dynamical eigenvalues elastic bed elasticity modulus energy engineering equations equilibrium error estimate example external finite element analysis finite element mesh finite element method flexural formula frequency functions geometrical nonlinearity Jordan exclusion kinematical linear load longitudinal force ment Moskow natural oscillation Nauka Publishing nodal nodes obtained oscillation particular perfectly rigid body performed plane plane stress plate poly-constraints pre-stress problem properties respective Richardson extrapolation rotation Russian SCAD seismic shear shown in Fig slope deflection method solution solve source data stability static stiffness matrix structural mechanics structure's technique theory thin-walled bar tion two-parametric unilateral constraints values vector zero