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Группа авторов. Modern Trends in Structural and Solid Mechanics 3
Table of Contents
List of Illustrations
List of Tables
Guide
Pages
Modern Trends in Structural and Solid Mechanics 3. Non-deterministic Mechanics
Preface. Short Bibliographical Presentation of Prof. Isaac Elishakoff
Books by Elishakoff
Books edited or co-edited by Elishakoff
1. Optimization in Mitochondrial Energetic Pathways. 1.1. Optimization in neural and cell biology
1.2. Mitochondria
1.3. General morphology; fission and fusion
1.4. Mechanical aspects
1.5. Mitochondrial motility
1.6. Cristae, ultrastructure and supercomplexes
1.7. Mitochondrial diseases and neurodegenerative disorders
1.8. Modeling
1.9. Concluding summary
1.10. Acknowledgments
1.11. Appendix
1.12. References
2. The Concept of Local and Non-Local Randomness for Some Mechanical Problems. 2.1. Introduction
2.2. Preliminary concepts
2.2.1. Statically determinate stochastic beams
2.2.2. Statically indeterminate stochastic beams
2.3. Local and non-local randomness
2.3.1. Statically determinate stochastic beams
2.3.2. Statically indeterminate stochastic beams
2.3.3. Comments on the results
2.4. Conclusion
2.5. References
3. On the Applicability of First-Order Approximations for Design Optimization under Uncertainty. 3.1. Introduction
3.2. Summary of first- and second-order Taylor series approximations for uncertainty quantification
3.2.1. Approximations of stochastic moments
3.2.2. Probabilistic lower bound approximation
3.2.3. Convex anti-optimization
3.2.4. Correlation of probabilistic approaches and convex anti-optimization
3.3. Design optimization under uncertainty
3.3.1. Robust design optimization
3.3.2. Reliability-based design optimization
3.3.3. Optimization with convex anti-optimization
3.4. Numerical examples
3.4.1. Imperfect von Mises truss analysis
3.4.2. Three-bar truss optimization
3.4.2.1. Cross-section as design and random parameters – first-order works
3.4.2.2. Load as a random variable – first-order fails
3.4.3. Topology optimization
3.4.3.1. Load as a random variable – first-order fails
3.4.3.2. Young’s modulus as a random field – first-order works
3.5. Conclusion and outlook
3.6. References
4. Understanding Uncertainty. 4.1. Introduction
4.2. Uncertainty and uncertainties
4.3. Design and uncertainty. 4.3.1. Decision modules
4.3.1.1. Requirements
4.3.1.2. Architecture
4.3.1.3. Engineering
4.3.1.4. Lifetime
4.3.2. Designing in uncertain
4.4. Knowledge entity
4.4.1. Structure of a knowledge entity
4.4.1.1. Definition
4.4.1.2. Entity level
4.4.1.3. Entity maturity
4.5. Robust and reliable engineering. 4.5.1. Definitions
4.5.2. Robustness
4.5.3. Reliability
4.5.4. Optimization
4.5.5. Reliable and robust optimization
4.6. Conclusion
4.7. References
5. New Approach to the Reliability Verification of Aerospace Structures1. 5.1. Introduction
5.2. Factor of safety and probability of failure
5.3. Reliability verification of aerospace structural systems
5.3.1. Reliability demonstration is integrated into the design process
5.3.2. Analysis of failure mechanism and failure modes
5.3.3. Modeling the structural behavior, verifying the model by tests
5.3.4. Design of structural development tests to surface failure modes
5.3.5. Design of development tests to find unpredicted failure modes
5.3.6. “Cleaning” failure mechanism and failure modes
5.3.7. Determination of required safety and confidence in models
5.3.8. Determination of the reliability by “orders of magnitude”
5.4. Summary
5.5. References
6. A Review of Interval Field Approaches for Uncertainty Quantification in Numerical Models. 6.1. Introduction
6.2. Interval finite element analysis
6.3. Convex-set analysis
6.4. Interval field analysis
6.4.1. Explicit interval field formulation
6.4.2. Interval fields based on KL expansion
6.4.3. Interval fields based on convex descriptors
6.5. Conclusion
6.6. Acknowledgments
6.7. References
7. Convex Polytopic Models for the Static Response of Structures with Uncertain-but-bounded Parameters. 7.1. Introduction
7.2. Problem statements
7.3. Analysis and solution of the convex polytopic model for the static response of structures
7.4. Vertex solution theorem of the convex polytopic model for the static response of structures
7.5. Review of the vertex solution theorem of the interval model for the static response of structures
7.6. Numerical examples
7.6.1. Two-step bar
7.6.2. Ten-bar truss
7.6.3. Plane frame
7.7. Conclusion
7.8. Acknowledgments
7.9. References
8. On the Interval Frequency Response of Cracked Beams with Uncertain Damage
8.1. Introduction
8.2. Crack modeling for damaged beams. 8.2.1. Finite element crack model
8.2.2. Continuous crack model
8.3. Statement of the problem
8.3.1. Interval model for the uncertain crack depth
8.3.2. Governing equations of damaged beams
8.3.3. Finite element model versus continuous model
8.4. Interval frequency response of multi-cracked beams
8.4.1. Interval deflection function in the FE model
8.4.2. Interval deflection function in the continuous model
8.5. Numerical applications
8.6. Concluding remarks
8.7. Acknowledgments
8.8. References
9. Quantum-Inspired Topology Optimization
9.1. Introduction
9.2. General statements
9.2.1. Density-based continuum structural topology optimization formulation
9.2.2. Characteristics of quantum computing
9.3. Topology optimization design model based on quantum-inspired evolutionary algorithms
9.3.1. Classic procedure of topology optimization based on the SIMP method and optimality criteria
9.3.2. The fundamental theory of a quantum-inspired evolutionary algorithm – DCQGA. 9.3.2.1. Double chains encoding and decoding for quantum chromosomes
9.3.2.2. The rotation angle of quantum rotation gates
9.3.3. Implementation of the integral topology optimization framework
9.4. A quantum annealing operator to accelerate the calculation and jump out of local extremum
9.5. Numerical examples
9.5.1. Example of a short cantilever
9.5.2. Example of a wing rib
9.6. Conclusion
9.7. Acknowledgments
9.8. References
10. Time Delay Vibrations and Almost Sure Stability in Vehicle Dynamics
10.1. Introduction to road vehicle dynamics
10.2. Delay resonances of half-car models on road
10.3. Extensions to multi-body vehicles on a random road
10.4. Non-stationary road excitations applying sinusoidal models
10.5. Resonance reduction or induction by means of colored noise
10.6. Lyapunov exponents and rotation numbers in vehicle dynamics
10.7. Concluding remarks and main new results
10.8. References
11. Order Statistics Approach to Structural Optimization Considering Robustness and Confidence of Responses
11.1. Introduction
11.2. Overview of order statistics
11.2.1. Definition of order statistics
11.2.2. Tolerance intervals and confidence intervals of quantiles
11.3. Robust design. 11.3.1. Overview of the robust design problem
11.3.2. Worst-case-based method
11.3.3. Order statistics-based method
11.4. Numerical examples. 11.4.1. Design response spectrum
11.4.2. Optimization of the building frame considering seismic responses
11.4.3. Multi-objective optimization considering robustness
11.5. Conclusion
11.6. References
List of Authors
Index. A, B, C
D, E, F
G, I, K
L, M, N
O, P, Q
R, S, T
U, V, W
Summary of Volume 1
Summary of Volume 2
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