Optimal Shape Design

Author : O. Pironneau
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642877223

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Optimal Shape Design for Elliptic Systems by O. Pironneau Pdf

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).

Author : B. Kawohl
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 42,6 Mb
Release : 2000-11-16
Category : Mathematics
ISBN : 3540679715

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Optimal Shape Design by B. Kawohl Pdf

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.

Author : J. Haslinger,Pekka Neittaanmäki
Publisher : Unknown
Page : 360 pages
File Size : 46,7 Mb
Release : 1988
Category : Mathematics
ISBN : WISC:89008959652

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Finite Element Approximation for Optimal Shape Design by J. Haslinger,Pekka Neittaanmäki Pdf

A text devoted to the mathematical basis of optimal shape design, to finite element approximation and to numerical realization by applying optimization techniques. The aim is to computerize the design process, thus reducing the time needed to design or to improve an existing design.

Author : B. Kawohl,O. Pironneau,L. Tartar,J.-P. Zolesio
Publisher : Springer
Page : 397 pages
File Size : 42,6 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540444862

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Optimal Shape Design by B. Kawohl,O. Pironneau,L. Tartar,J.-P. Zolesio Pdf

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.

Author : Martin P. Bendsøe,Carlos A. Mota Soares
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401118040

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Topology Design of Structures by Martin P. Bendsøe,Carlos A. Mota Soares Pdf

Proceedings of the NATO Advanced Research Workshop, Sesimbra, Portugal, June 20-26, 1992

Author : John Cagnol,Michael P. Polis,Jean-Paul Zolesio
Publisher : CRC Press
Page : 458 pages
File Size : 43,7 Mb
Release : 2017-08-02
Category : Mathematics
ISBN : 0203904168

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Shape Optimization And Optimal Design by John Cagnol,Michael P. Polis,Jean-Paul Zolesio Pdf

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.

Author : B. Mohammadi,Olivier Pironneau
Publisher : Oxford University Press
Page : 251 pages
File Size : 40,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0198507437

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Applied Shape Optimization for Fluids by B. Mohammadi,Olivier Pironneau Pdf

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.

Author : Gregoire Allaire
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 54,7 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 : J. Haslinger,R. A. E. Makinen
Publisher : SIAM
Page : 276 pages
File Size : 52,8 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 : Jan Sokolowski,Jean-Paul Zolesio
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 54,7 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 : James Bennett
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461594833

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The Optimum Shape by James Bennett Pdf

This book contains the papers presented at the International Symposium, "The Optimum Shape: Automated Structural Design," held at the General Motors Research Laboratories on September 3D-October 1, 1985. This was the 30th symposium in a series which the Research Laboratories began sponsoring in 1957. Each symposium has focused on a topic that is both under active study at the Research Laboratories and is also of interest to the larger technical community. While attempts to produce a structure which performs a certain task with the minimum amount of resources probably predates recorded civilization, the idea of coupling formal optimization techniques with computer-based structural analysis techniques was first proposed in the early 1960s. Although it was recognized at this time that the most fundamental description of the problem would be in terms of the shape or contours of the structure, much of the early work described the problem in terms of structural sizing parameters instead of geometrical descriptions. Within the past few years, several research groups have started to explore this more fundamental area of shape design. Initial research has raised many new questions about appropriate selection of design variables, methods of calculating derivatives, and generation of the underlying analysis problem.

Author : Raino Mäkinen
Publisher : Unknown
Page : 20 pages
File Size : 49,6 Mb
Release : 1989
Category : Computer-aided design
ISBN : PSU:000016091818

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On Computer Aided Optimal Shape Design by Raino Mäkinen Pdf

Author : J. Haslinger,Pekka Neittaanmäki
Publisher : Wiley
Page : 442 pages
File Size : 43,8 Mb
Release : 1996-08-06
Category : Mathematics
ISBN : 0471958506

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Finite Element Approximation for Optimal Shape, Material and Topology Design by J. Haslinger,Pekka Neittaanmäki Pdf

This book addresses the formulation, approximation and numerical solution of optimal shape design problems: from the continuous model through its discretization and approximation results, to sensitivity analysis and numerical realization. Shape optimization of structures is addressed in the first part, using variational inequalities of elliptic type. New results, such as contact shape optimization for bodies made of non-linear material, sensitivity analysis based on isoparametric technique, and analysis of cost functionals related to contact stress distribution are included. The second part presents new concepts of shape optimization based on a fictitious domain approach. Finally, the application of the shape optimization methodology in the material design is discussed. This second edition is a fully revised and up-dated version of Finite Element Method for Optimal Shape Design. Numerous numerical examples illustrate the theoretical results, and industrial applications are given.

Author : Bijan Mohammadi,Olivier Pironneau
Publisher : Oxford University Press
Page : 292 pages
File Size : 45,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780199546909

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Applied Shape Optimization for Fluids by Bijan Mohammadi,Olivier Pironneau Pdf

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.

Author : Martin P. Bendsoe
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 48,5 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662031155

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Optimization of Structural Topology, Shape, and Material by Martin P. Bendsoe Pdf

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.