Author | Laporte, Emmanuel. author |
---|---|
Title | Numerical Methods in Sensitivity Analysis and Shape Optimization [electronic resource] / by Emmanuel Laporte, Patrick Le Tallec |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0069-7 |
Descript | XVII, 194 p. online resource |
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