Numerical Methods in Sensitivity Analysis and Shape Optimization

Emmanuel Laporte, Patrick Le Tallec (Autoren)

Buch | Hardcover

194 Seiten

2002 | 2003 ed.
Birkhauser Boston Inc (Verlag)
978-0-8176-4322-5 (ISBN)

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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.

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.

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.

Erscheint lt. Verlag	13.12.2002
Reihe/Serie	Modeling and Simulation in Science, Engineering and Technology
Zusatzinfo	XVII, 194 p. With online files/update.
Verlagsort	Secaucus
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Technik
ISBN-10	0-8176-4322-2 / 0817643222
ISBN-13	978-0-8176-4322-5 / 9780817643225
Zustand	Neuware