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| Author | : B. Kawohl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2000-11-16 |
| Genre | : Mathematics |
| ISBN | : 9783540679714 |
Download Optimal Shape Design Book in PDF, ePub and Kindle
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 | : O. Pironneau |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 179 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642877222 |
Download Optimal Shape Design for Elliptic Systems Book in PDF, ePub and Kindle
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 |
| Total Pages | : 397 |
| Release | : 2007-05-06 |
| Genre | : Mathematics |
| ISBN | : 3540444866 |
Download Optimal Shape Design Book in PDF, ePub and Kindle
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 |
| Publisher | : |
| Total Pages | : 360 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
Download Finite Element Approximation for Optimal Shape Design Book in PDF, ePub and Kindle
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 | : Martin P. Bendsøe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 564 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401118043 |
Download Topology Design of Structures Book in PDF, ePub and Kindle
Proceedings of the NATO Advanced Research Workshop, Sesimbra, Portugal, June 20-26, 1992
| Author | : John Cagnol |
| Publisher | : CRC Press |
| Total Pages | : 458 |
| Release | : 2017-08-02 |
| Genre | : Mathematics |
| ISBN | : 9780203904169 |
Download Shape Optimization And Optimal Design Book in PDF, ePub and Kindle
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 | : Jan Sokolowski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 254 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642581064 |
Download Introduction to Shape Optimization Book in PDF, ePub and Kindle
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 | : B. Mohammadi |
| Publisher | : Oxford University Press |
| Total Pages | : 251 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780198507437 |
Download Applied Shape Optimization for Fluids Book in PDF, ePub and Kindle
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 | : Martin P. Bendsoe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 278 |
| Release | : 2013-03-14 |
| Genre | : Technology & Engineering |
| ISBN | : 3662031159 |
Download Optimization of Structural Topology, Shape, and Material Book in PDF, ePub and Kindle
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.
| Author | : J. Haslinger |
| Publisher | : SIAM |
| Total Pages | : 291 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898718690 |
Download Introduction to Shape Optimization Book in PDF, ePub and Kindle
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.
