Overview

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.

Full Product Details

Author:   Emmanuel Laporte ,  Patrick Le Tallec
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 2003
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.338kg
ISBN:  

9781461265986

ISBN 10:   1461265983
Pages:   194
Publication Date:   19 April 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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.

Reviews

The focus of this book is finite-dimensional constrained optimization problems which arise by discretizing shape optimization problems of [a particular] type.... In the major part of the book the authors recall the basic principles of constrained optimization, describe variants of Newton's algorithm to solve the necessary optimality conditions and discuss analytic and automatic techniques to calculate the derivative of j with respect to the design variable z. -Mathematical Reviews Many illustrative examples and numerical results clarify the presentation. The book will be of interest to graduate students involved in mathematical modeling and simulation, as well as to engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design. -Zentralblatt Math

The focus of this book is finite-dimensional constrained optimization problems which arise by discretizing shape optimization problems of [a particular] type.... In the major part of the book the authors recall the basic principles of constrained optimization, describe variants of Newton's algorithm to solve the necessary optimality conditions and discuss analytic and automatic techniques to calculate the derivative of j with respect to the design variable z. -Mathematical Reviews Many illustrative examples and numerical results clarify the presentation. The book will be of interest to graduate students involved in mathematical modeling and simulation, as well as to engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design. -Zentralblatt Math

The focus of this book is finite-dimensional constrained optimization problems which arise by discretizing shape optimization problems of [a particular] type... In the major part of the book the authors recall the basic principles of constrained optimization, describe variants of Newton's algorithm to solve the necessary optimality conditions and discuss analytic and automatic techniques to calculate the derivative of j with respect to the design variable z. -Mathematical Reviews Many illustrative examples and numerical results clarify the presentation. The book will be of interest to graduate students involved in mathematical modeling and simulation, as well as to engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design. -Zentralblatt Math

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