Shape Optimization

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Shape Optimization Problems

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Author : Hideyuki Azegami
Publisher : Springer Nature
ISBN 13 : 9811576181
Total Pages : 646 pages
Book Rating : 4.8/5 (115 download)

Book Synopsis Shape Optimization Problems by : Hideyuki Azegami

Download or read book Shape Optimization Problems written by Hideyuki Azegami and published by Springer Nature. This book was released on 2020-09-30 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.

Introduction to Shape Optimization

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Author : Jan Sokolowski
Publisher : Springer Science & Business Media
ISBN 13 : 3642581064
Total Pages : 254 pages
Book Rating : 4.6/5 (425 download)

Book Synopsis Introduction to Shape Optimization by : Jan Sokolowski

Download or read book Introduction to Shape Optimization written by Jan Sokolowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Shape Optimization by the Homogenization Method

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Author : Gregoire Allaire
Publisher : Springer Science & Business Media
ISBN 13 : 1468492861
Total Pages : 470 pages
Book Rating : 4.4/5 (684 download)

Book Synopsis Shape Optimization by the Homogenization Method by : Gregoire Allaire

Download or read book Shape Optimization by the Homogenization Method written by Gregoire Allaire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.

Topological Derivatives in Shape Optimization

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Author : Antonio André Novotny
Publisher : Springer Science & Business Media
ISBN 13 : 3642352456
Total Pages : 423 pages
Book Rating : 4.6/5 (423 download)

Book Synopsis Topological Derivatives in Shape Optimization by : Antonio André Novotny

Download or read book Topological Derivatives in Shape Optimization written by Antonio André Novotny and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author : Dorin Bucur
Publisher : Springer Science & Business Media
ISBN 13 : 0817644032
Total Pages : 218 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Variational Methods in Shape Optimization Problems by : Dorin Bucur

Download or read book Variational Methods in Shape Optimization Problems written by Dorin Bucur and published by Springer Science & Business Media. This book was released on 2006-09-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Existence and Regularity Results for Some Shape Optimization Problems

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Author : Bozhidar Velichkov
Publisher : Springer
ISBN 13 : 8876425276
Total Pages : 349 pages
Book Rating : 4.8/5 (764 download)

Book Synopsis Existence and Regularity Results for Some Shape Optimization Problems by : Bozhidar Velichkov

Download or read book Existence and Regularity Results for Some Shape Optimization Problems written by Bozhidar Velichkov and published by Springer. This book was released on 2015-03-21 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.

Shape and Variation and Optimization

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Author : Antoine Henrot
Publisher :
ISBN 13 : 9783037191781
Total Pages : 365 pages
Book Rating : 4.1/5 (917 download)

Book Synopsis Shape and Variation and Optimization by : Antoine Henrot

Download or read book Shape and Variation and Optimization written by Antoine Henrot and published by . This book was released on 2018 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Shape Optimization

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Author : J. Haslinger
Publisher : SIAM
ISBN 13 : 0898715369
Total Pages : 276 pages
Book Rating : 4.8/5 (987 download)

Book Synopsis Introduction to Shape Optimization by : J. Haslinger

Download or read book Introduction to Shape Optimization written by J. Haslinger and published by SIAM. This book was released on 2003-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.

Optimization of Structural Topology, Shape, and Material

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Author : Martin P. Bendsoe
Publisher : Springer Science & Business Media
ISBN 13 : 3662031159
Total Pages : 278 pages
Book Rating : 4.6/5 (62 download)

Book Synopsis Optimization of Structural Topology, Shape, and Material by : Martin P. Bendsoe

Download or read book Optimization of Structural Topology, Shape, and Material written by Martin P. Bendsoe and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods in Sensitivity Analysis and Shape Optimization

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Author : Emmanuel Laporte
Publisher : Springer Science & Business Media
ISBN 13 : 1461200695
Total Pages : 202 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Numerical Methods in Sensitivity Analysis and Shape Optimization by : Emmanuel Laporte

Download or read book Numerical Methods in Sensitivity Analysis and Shape Optimization written by Emmanuel Laporte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Shape Optimization and Spectral Theory

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Author : Antoine Henrot
Publisher : De Gruyter Open
ISBN 13 : 9783110550856
Total Pages : 474 pages
Book Rating : 4.5/5 (58 download)

Book Synopsis Shape Optimization and Spectral Theory by : Antoine Henrot

Download or read book Shape Optimization and Spectral Theory written by Antoine Henrot and published by De Gruyter Open. This book was released on 2017-05-08 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noel Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartlomiej A., Velichkov Bozhidar

Optimal Shape Design

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Author : B. Kawohl
Publisher : Springer Science & Business Media
ISBN 13 : 9783540679714
Total Pages : 404 pages
Book Rating : 4.6/5 (797 download)

Book Synopsis Optimal Shape Design by : B. Kawohl

Download or read book Optimal Shape Design written by B. Kawohl and published by Springer Science & Business Media. This book was released on 2000-11-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.

Topology Design of Structures

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Author : Martin P. Bendsøe
Publisher : Springer Science & Business Media
ISBN 13 : 9401118043
Total Pages : 564 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis Topology Design of Structures by : Martin P. Bendsøe

Download or read book Topology Design of Structures written by Martin P. Bendsøe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Sesimbra, Portugal, June 20-26, 1992

Conceptual Shape Optimization of Entry Vehicles

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Author : Dominic Dirkx
Publisher : Springer
ISBN 13 : 3319460552
Total Pages : 280 pages
Book Rating : 4.3/5 (194 download)

Book Synopsis Conceptual Shape Optimization of Entry Vehicles by : Dominic Dirkx

Download or read book Conceptual Shape Optimization of Entry Vehicles written by Dominic Dirkx and published by Springer. This book was released on 2016-12-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the parameterization of entry capsules, including Apollo capsules and planetary probes, and winged entry vehicles such as the Space Shuttle and lifting bodies. The aerodynamic modelling is based on a variety of panel methods that take shadowing into account, and it has been validated with flight and wind tunnel data of Apollo and the Space Shuttle. The shape optimization is combined with constrained trajectory analysis, and the multi-objective approach provides the engineer with a Pareto front of optimal shapes. The method detailed in Conceptual Shape Optimization of Entry Vehicles is straightforward, and the output gives the engineer insight in the effect of shape variations on trajectory performance. All applied models and algorithms used are explained in detail, allowing for reconstructing the design tool to the researcher’s requirements. Conceptual Shape Optimization of Entry Vehicles will be of interest to both researchers and graduate students in the field of aerospace engineering, and to practitioners within the aerospace industry.

New Trends in Shape Optimization

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Author : Aldo Pratelli
Publisher : Birkhäuser
ISBN 13 : 3319175637
Total Pages : 314 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis New Trends in Shape Optimization by : Aldo Pratelli

Download or read book New Trends in Shape Optimization written by Aldo Pratelli and published by Birkhäuser. This book was released on 2015-12-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

Applied Shape Optimization for Fluids

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Author : Bijan Mohammadi
Publisher : OUP Oxford
ISBN 13 : 019157421X
Total Pages : 296 pages
Book Rating : 4.1/5 (915 download)

Book Synopsis Applied Shape Optimization for Fluids by : Bijan Mohammadi

Download or read book Applied Shape Optimization for Fluids written by Bijan Mohammadi and published by OUP Oxford. This book was released on 2009-09-24 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of computational fluid dynamics (CFD) and optimal shape design (OSD) have received considerable attention in the recent past, and are of practical importance for many engineering applications. This new edition of Applied Shape Optimization for Fluids deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Strokes, but also those for microfluids) and with the numerical simulation of these problems. It presents the state of the art in shape optimization for an extended range of applications involving fluid flows. Automatic differentiation, approximate gradients, unstructured mesh adaptation, multi-model configurations, and time-dependent problems are introduced, and their implementation into the industrial environments of aerospace and automobile equipment industry explained and illustrated. With the increases in the power of computers in industry since the first edition, methods which were previously unfeasible have begun giving results, namely evolutionary algorithms, topological optimization methods, and level set algortihms. In this edition, these methods have been treated in separate chapters, but the book remains primarily one on differential shape optimization. This book is essential reading for engineers interested in the implementation and solution of optimization problems using commercial packages or in-house solvers and graduates and researchers in applied mathematics, aerospace, or mechanical engineering, fluid dynamics, and CFD. More generally, anyone needing to understand and solve design problems or looking for new exciting areas for research and development in this area will find this book useful, especially in applying the methodology to practical problems.

Shapes and Geometries

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Author : M. C. Delfour
Publisher : SIAM
ISBN 13 : 0898719364
Total Pages : 637 pages
Book Rating : 4.8/5 (987 download)

Book Synopsis Shapes and Geometries by : M. C. Delfour

Download or read book Shapes and Geometries written by M. C. Delfour and published by SIAM. This book was released on 2011-01-01 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.