Numerical Methods in Sensitivity Analysis and Shape Optimization

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.