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Shape And Variation And Optimization
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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 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Shape Optimization by : Catherine Bandle
Download or read book Shape Optimization written by Catherine Bandle and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-06-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications.
Book Synopsis Shape Variation and Optimization by : Antoine Henrot
Download or read book Shape 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:
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.
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:
Book Synopsis Shape Optimization And Optimal Design by : John Cagnol
Download or read book Shape Optimization And Optimal Design written by John Cagnol and published by CRC Press. This book was released on 2017-08-02 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.
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.
Book Synopsis Optimal Shape Design for Elliptic Systems by : O. Pironneau
Download or read book Optimal Shape Design for Elliptic Systems written by O. Pironneau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" This book is an applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most numerical simulations of physical systems are solved not to gain better understanding of the phenomena but to obtain better control and design. Problems of this type are described in Chapter 2. Traditionally, optimal shape design has been treated as a branch of the calculus of variations and more specifically of optimal control. This subject interfaces with no less than four fields: optimization, optimal control, partial differential equations (PDEs), and their numerical solutions-this is the most difficult aspect of the subject. Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).
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 Oxford University Press. This book was released on 2010 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Constrained Optimization In The Calculus Of Variations and Optimal Control Theory by : J Gregory
Download or read book Constrained Optimization In The Calculus Of Variations and Optimal Control Theory written by J Gregory and published by CRC Press. This book was released on 2018-01-18 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.
Book Synopsis Advances in Mathematical Modeling, Optimization and Optimal Control by : Jean-Baptiste Hiriart-Urruty
Download or read book Advances in Mathematical Modeling, Optimization and Optimal Control written by Jean-Baptiste Hiriart-Urruty and published by Springer. This book was released on 2016-05-19 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.
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 . This book was released on 2015 with total page 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.
Book Synopsis Shape Optimization and Free Boundaries by : Michel C. Delfour
Download or read book Shape Optimization and Free Boundaries written by Michel C. Delfour and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Shape Design Sensitivity Analysis and Optimization Using the Boundary Element Method by : Zhiye Zhao
Download or read book Shape Design Sensitivity Analysis and Optimization Using the Boundary Element Method written by Zhiye Zhao and published by Springer. This book was released on 1991 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the various aspects of shape optimization of two dimensional continuum structures, including shape design sensitivity analysis, structural analysis using the boundary element method (BEM), and shape optimization implementation. The book begins by reviewing the developments of shape optimization, followed by the presentation of the mathematical programming methods for solving optimization problems. The basic theory of the BEM is presented which will be employed later on as the numerical tool to provide the structural responses and the shape design sensitivities. The key issue of shape optimization, the shape design sensitivity analy sis, is fully investigated. A general formulation of stress sensitivity using the continuum approach is presented. The difficulty of the modelling of the ad joint problem is studied, and two approaches are presented for the modelling of the adjoint problem. The first approach uses distributed loads to smooth the concentrated adjoint loads, and the second approach employs the singu larity subtraction method to remove the singular boundary displacements and tractions from the BEM equation. A novel finite difference based approach to shape design sensitivity is pre sented, which overcomes the two drawbacks of the conventional finite difference method. This approach has the advantage of being simple in concept, and eas ier implementation. A shape optimization program for two-dimensional continuum structures is developed, including structural analysis using the BEM, shape design sensitiv ity analysis, mathematical programming, and the design boundary modelling.
Book Synopsis Research in Shape Analysis by : Asli Genctav
Download or read book Research in Shape Analysis written by Asli Genctav and published by Springer. This book was released on 2018-05-17 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the second Women in Shape (WiSH) workshop held in Sirince, Turkey in June 2016, these proceedings offer the latest research on shape modeling and analysis and their applications. The 10 peer-reviewed articles in this volume cover a broad range of topics, including shape representation, shape complexity, and characterization in solving image-processing problems. While the first six chapters establish understanding in the theoretical topics, the remaining chapters discuss important applications such as image segmentation, registration, image deblurring, and shape patterns in digital fabrication. The authors in this volume are members of the WiSH network and their colleagues, and most were involved in the research groups formed at the workshop. This volume sheds light on a variety of shape analysis methods and their applications, and researchers and graduate students will find it to be an invaluable resource for further research in the area.
Book Synopsis Applied Shape Optimization for Fluids by : B. Mohammadi
Download or read book Applied Shape Optimization for Fluids written by B. Mohammadi and published by Oxford University Press. This book was released on 2001 with total page 251 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. The present book deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Stokes), and with the numerical simulation of these problems. Automatic differentiation, approximate gradients, and automatic mesh refinement as the new tools of optimal shape design are introduced, and their implementation into the industrial environments of aerospace and automobile equipment industry explained and illustrated.
