Numerical Methods in Sensitivity Analysis and Shape Optimization
Key features of this original, progressive, and comprehensive approach: * description of mathematical background and underlying tools * up-to-date review of grid construction and control, optimization algorithms, software differentiation and gradient calculations * practical solutions for implementa...
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
Boston, MA
Birkhäuser
2003, 2003
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Edition: | 1st ed. 2003 |
Series: | Modeling and Simulation in Science, Engineering and Technology
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Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Basic Formulations
- 1.1 A generic example
- 1.2 Abstract formulation of a shape optimization problem
- 1.3 Sensitivity analysis
- 1.4 Shape parametrization
- 1.5 Mesh construction and deformation
- 1.6 Exercises
- 2 Finite Dimensional Optimization
- 2.1 Basic problem and notation
- 2.2 Necessary conditions of optimality
- 2.3 Optimality conditions of Euler-Lagrange
- 2.4 Exercises
- 3 Newton's Algorithms
- 3.1 The problem to solve
- 3.2 Newton's algorithm
- 3.3 Unconstrained optimization
- 3.4 Thermodynamic equilibrium.
- 3.5 Additional remarks and conclusions.
- References
- 4 Modeling of Soil Behaviour: from Micro-Mechanical Analysis to Macroscopic Description
- 4.1 Introduction
- 4.2 Elementary considerations
- 4.3 Behaviour in proportional compression tests
- 4.4 A simple elasto-plastic strain-hardening model
- 4.5 Derivation of the failure condition
- 4.6 Non-normality and material instabilities
- 4.7 Three-dimensional loading conditions
- 4.8 Unlimited pore pressure generation
- 4.9 Drained shear banding
- 4.10 Locally undrained shear banding
- 4.11 Influence of induced anisotropy
- 4.12 Regularisation of the numerical response
- 4.13 Plasticity at very small strains
- 4.14 Conclusions
- References
- 5 Dynamic Thermo-Poro-Mechanical Stability Analysis of Simple Shear on Frictional Materials
- 5.1 Introduction
- 5.2 Mass balance
- 5.3 Energy balance in porous soils
- 5.4 The infinite slide
- 5.5 Drained soil behavior.
- 5.6 Governing equations.
- 5.7 Viscous regularization
- 5.8 Gradient regularization.
- 5.9 Summary of main results
- References
- II Flow and Transport Phenomena in Particulate Materials
- 6 Mathematical Models for Soil Consolidation Problems: a State of the Art Report
- 7 Applications
- 8 One Shot Methods
- 9 Conclusions