Shape Optimization And Free Boundaries

Author : Michel C. Delfour
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401127103

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Shape Optimization and Free Boundaries by Michel C. Delfour Pdf

Shape optimization deals with problems where the design or control variable is no longer a vector of parameters or functions but the shape of a geometric domain. They include engineering applications to shape and structural optimization, but also original applications to image segmentation, control theory, stabilization of membranes and plates by boundary variations, etc. Free and moving boundary problems arise in an impressingly wide range of new and challenging applications to change of phase. The class of problems which are amenable to this approach can arise from such diverse disciplines as combustion, biological growth, reactive geological flows in porous media, solidification, fluid dynamics, electrochemical machining, etc. The objective and orginality of this NATO-ASI was to bring together theories and examples from shape optimization, free and moving boundary problems, and materials with microstructure which are fundamental to static and dynamic domain and boundary problems.

Author : Jan Sokolowski,Jean-Paul Zolesio
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581069

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Introduction to Shape Optimization by Jan Sokolowski,Jean-Paul Zolesio Pdf

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.

Author : Dorin Bucur,Giuseppe Buttazzo
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 53,6 Mb
Release : 2006-09-13
Category : Mathematics
ISBN : 9780817644031

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Variational Methods in Shape Optimization Problems by Dorin Bucur,Giuseppe Buttazzo Pdf

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.

Author : Hideyuki Azegami
Publisher : Springer Nature
Page : 646 pages
File Size : 45,5 Mb
Release : 2020-09-30
Category : Mathematics
ISBN : 9789811576188

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Shape Optimization Problems by Hideyuki Azegami Pdf

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.

Author : M. C. Delfour,J.-P. Zolesio
Publisher : SIAM
Page : 637 pages
File Size : 52,6 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780898719369

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Shapes and Geometries by M. C. Delfour,J.-P. Zolesio Pdf

Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Author : Antonio André Novotny,Jan Sokołowski
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 47,6 Mb
Release : 2012-12-14
Category : Technology & Engineering
ISBN : 9783642352454

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Topological Derivatives in Shape Optimization by Antonio André Novotny,Jan Sokołowski Pdf

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.

Author : J. Haslinger,R. A. E. Makinen
Publisher : SIAM
Page : 276 pages
File Size : 43,6 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9780898715361

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Introduction to Shape Optimization by J. Haslinger,R. A. E. Makinen Pdf

Treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.

Author : Miloslav Feistauer,Vit Dolejší,Peter Knobloch,Karel Najzar
Publisher : Springer Science & Business Media
Page : 873 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642187759

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Numerical Mathematics and Advanced Applications by Miloslav Feistauer,Vit Dolejší,Peter Knobloch,Karel Najzar Pdf

These proceedings collect the major part of the lectures given at ENU MATH2003, the European Conference on Numerical Mathematics and Ad vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men tion fluid dynamics, continuum mechanics, electromagnetism, phase transi tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.

Author : Gregoire Allaire
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781468492866

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Shape Optimization by the Homogenization Method by Gregoire Allaire Pdf

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.

Author : Michel C. Delfour,J. P. Zolesio
Publisher : SIAM
Page : 512 pages
File Size : 54,5 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0898714893

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Shapes and Geometries by Michel C. Delfour,J. P. Zolesio Pdf

The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.

Author : Roland Glowinski,Jean-Paul Zolesio
Publisher : CRC Press
Page : 474 pages
File Size : 50,9 Mb
Release : 2007-06-06
Category : Mathematics
ISBN : 9781420011159

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Free and Moving Boundaries by Roland Glowinski,Jean-Paul Zolesio Pdf

Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of mo

Author : Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 49,7 Mb
Release : 2012-01-03
Category : Mathematics
ISBN : 9783034801331

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Constrained Optimization and Optimal Control for Partial Differential Equations by Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich Pdf

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

Author : Bozhidar Velichkov
Publisher : Springer
Page : 349 pages
File Size : 45,5 Mb
Release : 2015-03-21
Category : Mathematics
ISBN : 9788876425271

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Existence and Regularity Results for Some Shape Optimization Problems by Bozhidar Velichkov Pdf

​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.

Author : Timo Tiihonen
Publisher : Unknown
Page : 24 pages
File Size : 51,5 Mb
Release : 1987
Category : Boundary value problems
ISBN : PSU:000013349646

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Shape Optimization and Unilateral Boundary Value Problems by Timo Tiihonen Pdf

Author : Weihong Zhang,Ying Zhou
Publisher : Elsevier
Page : 350 pages
File Size : 49,9 Mb
Release : 2020-11-05
Category : Computers
ISBN : 9780128213315

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The Feature-Driven Method for Structural Optimization by Weihong Zhang,Ying Zhou Pdf

The Feature-Driven Method for Structural Optimization details a novel structural optimization method within a CAD framework, integrating structural optimization and feature-based design. The book presents cutting-edge research on advanced structures and introduces the feature-driven structural optimization method by regarding engineering features as basic design primitives. Consequently, it presents a method that allows structural optimization and feature design to be done simultaneously so that feature attributes are preserved throughout the design process. The book illustrates and supports the effectiveness of the method described, showing potential applications through numerical modeling techniques and programming. This volume presents a high-performance optimization method adapted to engineering structures—a novel perspective that will help engineers in the computation, modeling and design of advanced structures. Integrates two independent methods - structural optimization and feature-based design—into one framework Adapts the high performance optimization method to the practice of designing engineering structures Provides numerical evidence for the effectiveness and potential of the methods described Works within a computer-aided design framework to develop a novel structural optimization methodology Presents engineering features as the basic design primitives in structural optimization