Numerical Methods in Sensitivity Analysis and Shape Optimization

Numerical Methods in Sensitivity Analysis and Shape Optimization by Emmanuel Laporte, Patrick Le Tallec.

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design...

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Bibliographic Details
Main Authors: Laporte, Emmanuel (Author), Le Tallec, Patrick (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2003.
Edition:1st ed. 2003.
Series:Modeling and Simulation in Science, Engineering and Technology,
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Probabilities.
Computer mathematics.
Mathematical optimization.
Computational intelligence.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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