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THE ANALYSIS OF CONSTRUCTION Ч 

MODELS AND INTERPRETATION

A.V.Perelmuter

e-mail: aperel@i.com.ua

V.I.Slivker

e-mail: slivker@VS3491.spb.edu

 

CONTENTS

PREFACE

9

1. THE SUBJECTS OF ANALYSIS AND PROBLEMS OF MODELING

15

1.1. Multidimension and multifunctionality

15

1.2.  Main factors taken into account while creating an analytical model

16

1.3.  Uncertainties in our knowledge of the subject

19

1.4.  Experiment and practical experience

21

1.5.  General problems of modeling

23

1.6.  Majorant models and minorant models

26

1.7.  A posteriori analysis of mechanical model

27

References to chapter 1

28

2. CREATION OF ANALYTICAL MODEL

31

2.1. Determinative parameters and number of degrees of freedom

32

2.2. Loading model as a part of analytical model

36

2.3. Check of analytical model and means of its description

39

2.4. Some techniques

47

2.5. Mono-constraints and poly-constraints

54

2.6. Absolutely rigid bodies as finite element types

58

1-dimensional rigid bodies

59

2-dimensional rigid bodies

59

3-dimensional rigid bodies

60

2.7. Simultaneous use of number of analytical models

63

2.8. Confrontation of analytical and experimental data

69

References to chapter 2

72

3. GENERAL EQUATIONS FOR DISCRETE SYSTEMS

75

3.1. Determinative equations

75

Displacement method

77

Force method

81

Dualism of displacement method and force method. Projectors

82

3.2. Kinematic analysis

87

Remarks on dislocations

91

3.3. More about poly-constraints. Variational problem

92

3.4. Null-elements

100

3.5. Geometrical nonlinearity. Stability

106

Four storeys of geometrically nonlinear problems

106

Geometrical nonlinearity for truss members

108

Geometrical nonlinearity Ч incremental equations

113

3.6. Constructive nonlinearity Ч mechanical systems with unilateral constraints

116

3.7. Dynamic analysis

122

3.8. Continued mechanical systems and their finite element description

127

Remarks on terminology

128

References to chapter 3

129

4. FINITE ELEMENT MODELS

133

4.1. Remarks on physical lumping

133

4.2. General conceptions of finite element method

134

4.3. Models for member systems

139

4.4. Models and finite element mesh

143

4.5. Practical convergence

145

4.6. Check of convergence for some models

147

4.7. Richardson's extrapolation

150

4.8. Roundabout way of singular points

154

4.9. Finite element mesh generation

158

4.10. Application of hybrid elements

161

References to chapter 4

165

5. SOME TRAPS AND PITFALLS, SPECIAL TECHNIQUE IN CREATING FINITE ELEMENT MODELS

 

167

5.1. Fragmentation

167

5.2. Development of continuous stress field in finite element method

175

5.3. Traps and pitfalls at joining elements with different dimensions

182

1+2. Members + plates

183

1+3. Members + plane elements

189

1+4. Members + 3D elements

198

2+3. Plates + plane elements (shell elements coupling)

198

5.4. A paradox in combination of Bernoulli's members and Timoshenko's members

203

5.5. Approximation of geometrical form and boundary conditions

210

5.6. Numerical errors and how we can battle against them

213

Remarks on the application of superelements

224

Remarks on testing engineering software

225

5.7 Step by step procedure

226

References to chapter 5

232

6. ANALYSIS AND INTERPRETATION OF RESULTS

235

6.1. The problem of analysis

235

6.2. What kind of the results we need

236

6.3. General approval

240

6.4. Characteristic displacement

244

6.5. Computation of energy of deformation

247

6.6. The following treatment of results

248

References to chapter 6

250

 

 

7. UNCERTAINTIES OF PARAMETERS

251

7.1. Basic sources of uncertainties

251

7.2. Methods of analysis of sensitivities

257

7.3. Sensitivity of natural vibrations

261

7.4. Evaluation of additional stresses while changing rigidity

266

7.5. Theoretical evaluations in case of uncertain rigidity

269

7.6. Application of test planning

271

7.7. Extreme balance under uncertain loading

276

References to chapter 7

279

8. ANALYSIS OF SOME CLASSES OF PROBLEMS

281

8.1. Trusses

281

8.2. Mounting

284

Genetic nonlinearity

289

8.3. Initial prestress

296

8.4. Constructions with hydraulic jacks

299

Liquid-spring finite element

304

8.5. Model "building Ц foundation"

305

Taking into account a distributive capability of elastic foundation

305

Model of foundation with two parameters

307

Elastic characteristics of foundation

312

8.6. Setting characteristics of double parameterized elastic foundation

315

"CCC" foundation model

319

8.7. An application of finite element model of foundation

326

8.8. Bi-member model of thin-walled member of open cross section

327

Construction of bi-member model

328

The bi-member model for a thin-walled member reinforced with cross-sectional slats

334

Thin-walled member with a crosscut diaphragm

339

Mathematical treatment of bi-member model and its discrete scheme

340

8.9. Extreme loading combinations

342

References to chapter 8

349

9. THE PROBLEM OF STABILITY AND ADJOINING PROBLEMS

351

9.1. Control of stability

351

9.2. Classic problem of stability

356

9.3. Effective lengths of compressed members

360

9.4. The role of separate subsystems

364

9.5. The influence of additional restraints on the stability

369

9.6. Taking into consideration the imperfections of real construction

370

References to chapter 9

374

10. PROBLEMS OF DYNAMIC ANALYSIS

 

10.1. Analytical models in dynamic analysis

377

Dynamic degrees of freedom

377

Dynamic condensation Ц Guyan's procedure

381

10.2. Direct integration

383

10.3. Vibrations under harmonic loading

386

Gordeeva's model

390

10.4. Seismic action

397

Earthquake spectrum

401

Seismic response

401

Accelerations as external loading

402

Storey response spectrum

407

10.5. Impact and percussive actions

408

10.6. Oscillations under wind loading

410

Modelling of wind action

414

Dynamic action of wind excited oscillation

414

Introduction of oscillated component of wind loading

415

Spectrum of wind speed

417

Dynamic component of the analyzed factor

420

Numerical problems

420

References to chapter 10

421

11. IN PLACE OF CONCLUSION

423

References to the final section

427

 

433

 

435




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