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 to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. 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 implementation in many real-life problems * solution of illustrative examples and exercises * basic mathematical programming techniques used to solve constrained minimization problems are presented; these fairly self-contained chapters can serve as an introduction to the numerical solution of generic constrained optimization problems * supplementary online source files and data; readers can test different solution strategies to determine their relevance and efficiency * supplementary files also offer software building, updating computational grids, performing automatic code differentiation, and computing basic aeroelastic solutions Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design. The work is suitable as a textbook for graduate courses in any of the topics mentioned above, and as a reference text
CONTENT
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
Engineering
Applied mathematics
Engineering mathematics
Computer mathematics
Mathematical optimization
Probabilities
Computational intelligence
Engineering
Appl.Mathematics/Computational Methods of Engineering
