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PREFACE |
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1. THE SUBJECTS OF ANALYSIS AND PROBLEMS OF MODELING |
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1.1. Multidimension and multifunctionality
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1.2. Main factors taken into account while creating an analytical model
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1.3. Uncertainties in our knowledge of the subject
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1.4. Experiment and practical experience
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1.5. General problems of modeling
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1.6. Majorant models and minorant models
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1.7. A posteriori analysis of mechanical model
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References to chapter 1
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2. CREATION OF ANALYTICAL MODEL |
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2.1. Determinative parameters and number of degrees of freedom
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2.2. Loading model as a part of analytical model
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2.3. Check of analytical model and means of its description
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2.4. Some techniques
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2.5. Mono-constraints and poly-constraints
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2.6. Absolutely rigid bodies as finite element types
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1-dimensional rigid bodies
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2-dimensional rigid bodies
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3-dimensional rigid bodies
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2.7. Simultaneous use of number of analytical models
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2.8. Confrontation of analytical and experimental data
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References to chapter 2
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3. GENERAL EQUATIONS FOR DISCRETE SYSTEMS |
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3.1. Determinative equations
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Displacement method
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Force method
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Dualism of displacement method and force method. Projectors
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3.2. Kinematic analysis
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Remarks on dislocations
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3.3. More about poly-constraints. Variational problem
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3.4. Null-elements
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3.5. Geometrical nonlinearity. Stability
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106 |
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Four storeys of geometrically nonlinear problems
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106 |
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Geometrical nonlinearity for truss members
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108 |
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Geometrical nonlinearity Ч incremental equations
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3.6. Constructive nonlinearity Ч mechanical systems with unilateral constraints
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3.7. Dynamic analysis
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3.8. Continued mechanical systems and their finite element description
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Remarks on terminology
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References to chapter 3
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4. FINITE ELEMENT MODELS |
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4.1. Remarks on physical lumping
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4.2. General conceptions of finite element method
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4.3. Models for member systems
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4.4. Models and finite element mesh
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4.5. Practical convergence
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4.6. Check of convergence for some models
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4.7. Richardson's extrapolation
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4.8. Roundabout way of singular points
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4.9. Finite element mesh generation
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4.10. Application of hybrid elements
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References to chapter 4
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5. SOME TRAPS AND PITFALLS, SPECIAL TECHNIQUE IN CREATING FINITE ELEMENT MODELS
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5.1. Fragmentation
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5.2. Development of continuous stress field in finite element method
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5.3. Traps and pitfalls at joining elements with different dimensions
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1+2. Members + plates
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1+3. Members + plane elements
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1+4. Members + 3D elements
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2+3. Plates + plane elements (shell elements coupling)
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5.4. A paradox in combination of Bernoulli's members and Timoshenko's members
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5.5. Approximation of geometrical form and boundary conditions
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5.6. Numerical errors and how we can battle against them
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Remarks on the application of superelements
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Remarks on testing engineering software
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5.7 Step by step procedure
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References to chapter 5
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6. ANALYSIS AND INTERPRETATION OF RESULTS |
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6.1. The problem of analysis
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6.2. What kind of the results we need
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6.3. General approval
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6.4. Characteristic displacement
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6.5. Computation of energy of deformation
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6.6. The following treatment of results
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References to chapter 6
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7. UNCERTAINTIES OF PARAMETERS |
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7.1. Basic sources of uncertainties
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7.2. Methods of analysis of sensitivities
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7.3. Sensitivity of natural vibrations
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7.4. Evaluation of additional stresses while changing rigidity
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7.5. Theoretical evaluations in case of uncertain rigidity
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7.6. Application of test planning
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7.7. Extreme balance under uncertain loading
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References to chapter 7
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8. ANALYSIS OF SOME CLASSES OF PROBLEMS |
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8.1. Trusses
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8.2. Mounting
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Genetic nonlinearity
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8.3. Initial prestress
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8.4. Constructions with hydraulic jacks
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Liquid-spring finite element
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8.5. Model "building Ц foundation"
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Taking into account a distributive capability of elastic foundation
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Model of foundation with two parameters
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Elastic characteristics of foundation
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8.6. Setting characteristics of double parameterized elastic foundation
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"CCC" foundation model
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8.7. An application of finite element model of foundation
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8.8. Bi-member model of thin-walled member of open cross section
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327 |
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Construction of bi-member model
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328 |
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The bi-member model for a thin-walled member reinforced with cross-sectional slats
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334 |
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Thin-walled member with a crosscut diaphragm
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339 |
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Mathematical treatment of bi-member model and its discrete scheme
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340 |
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8.9. Extreme loading combinations
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References to chapter 8
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9. THE PROBLEM OF STABILITY AND ADJOINING PROBLEMS |
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9.1. Control of stability
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9.2. Classic problem of stability
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356 |
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9.3. Effective lengths of compressed members
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9.4. The role of separate subsystems
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364 |
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9.5. The influence of additional restraints on the stability
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369 |
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9.6. Taking into consideration the imperfections of real construction
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370 |
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References to chapter 9
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374 |
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10. PROBLEMS OF DYNAMIC ANALYSIS |
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10.1. Analytical models in dynamic analysis
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Dynamic degrees of freedom
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377 |
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Dynamic condensation Ц Guyan's procedure
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381 |
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10.2. Direct integration
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383 |
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10.3. Vibrations under harmonic loading
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Gordeeva's model
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390 |
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10.4. Seismic action
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397 |
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Earthquake spectrum
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401 |
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Seismic response
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401 |
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Accelerations as external loading
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402 |
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Storey response spectrum
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407 |
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10.5. Impact and percussive actions
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408 |
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10.6. Oscillations under wind loading
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410 |
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Modelling of wind action
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414 |
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Dynamic action of wind excited oscillation
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414 |
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Introduction of oscillated component of wind loading
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415 |
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Spectrum of wind speed
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417 |
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Dynamic component of the analyzed factor
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420 |
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Numerical problems
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420 |
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References to chapter 10
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421 |
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11. IN PLACE OF CONCLUSION |
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References to the final section
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