Shape Optimization
DOWNLOAD
Download Shape Optimization PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Shape Optimization book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Introduction To Shape Optimization
DOWNLOAD
Author : Jan Sokolowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Shape Optimization written by Jan Sokolowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.
Introduction To Shape Optimization
DOWNLOAD
Author : J. Haslinger
language : en
Publisher: SIAM
Release Date : 2003-01-01
Introduction To Shape Optimization written by J. Haslinger and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization comprehensively, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Applications include contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics. Audience: the book is written primarily for students of applied mathematics, scientific computing, and mechanics. Most of the material is directed toward graduate students, although a portion of it is suitable for senior undergraduate students. Readers are assumed to have some knowledge of partial differential equations and their numerical solution, as well as modern programming language such as C++ Fortran 90.
Topological Derivatives In Shape Optimization
DOWNLOAD
Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2012-12-14
Topological Derivatives In Shape Optimization written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.
Variational Methods In Shape Optimization Problems
DOWNLOAD
Author : Dorin Bucur
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-13
Variational Methods In Shape Optimization Problems written by Dorin Bucur and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-13 with Mathematics categories.
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Shape Optimization By The Homogenization Method
DOWNLOAD
Author : Gregoire Allaire
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Shape Optimization By The Homogenization Method written by Gregoire Allaire and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest tar geted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equa tion (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is al ways assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literat ure in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258].
Optimization Of Structural Topology Shape And Material
DOWNLOAD
Author : Martin P. Bendsoe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Optimization Of Structural Topology Shape And Material written by Martin P. Bendsoe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Technology & Engineering categories.
In the past, the possibilities of structural optimization were restricted to an optimal choice of profiles and shape. Further improvement can be obtained by selecting appropriate advanced materials and by optimizing the topology, i.e. finding the best position and arrangement of structural elements within a construction. The optimization of structural topology permits the use of optimization algorithms at a very early stage of the design process. The method presented in this book has been developed by Martin Bendsoe in cooperation with other researchers and can be considered as one of the most effective approaches to the optimization of layout and material design.
Profile Optimization Method For Robust Airfoil Shape Optimization In Viscous Flow
DOWNLOAD
Author : Wu Li
language : en
Publisher:
Release Date : 2003
Profile Optimization Method For Robust Airfoil Shape Optimization In Viscous Flow written by Wu Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Aerofoils categories.
Applied Shape Optimization For Fluids
DOWNLOAD
Author : Bijan Mohammadi
language : en
Publisher: Oxford University Press
Release Date : 2010
Applied Shape Optimization For Fluids written by Bijan Mohammadi and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Language Arts & Disciplines categories.
Contents: PREFACE; ACKNOWLEDGEMENTS; 1. Introduction; 2. Optimal shape design; 3. Partial differential equations for fluids; 4. Some numerical methods for fluids; 5. Sensitivity evaluation and automatic differentiation; 6. Parameterization and implementation issues; 7. Local and global optimization; 8. Incomplete sensitivities; 9. Consistent approximations and approximate gradients; 10. Numerical results on shape optimization; 11. Control of unsteady flows; 12. From airplane design to microfluidic; 13. Toplogical optimization for fluids; 14. Conclusion and perspectives; INDEX.
Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View
DOWNLOAD
Author : Harald Held
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30
Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View written by Harald Held and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-30 with Mathematics categories.
Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.
An Introduction To Structural Optimization
DOWNLOAD
Author : Peter W. Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
An Introduction To Structural Optimization written by Peter W. Christensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-20 with Technology & Engineering categories.
This book has grown out of lectures and courses given at Linköping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying—frequently very many— variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.