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...

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Bibliographic Details
Main Authors: Laporte, Emmanuel, Le Tallec, Patrick (Author)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 2003, 2003
Edition:1st ed. 2003
Series:Modeling and Simulation in Science, Engineering and Technology
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