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Author : Antoine Henrot
Publisher :
ISBN 13 : 9783037191781
Total Pages : 365 pages
Book Rating : 4.1/5 (917 download)
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:
Author : Hideyuki Azegami
Publisher : Springer Nature
ISBN 13 : 9811576181
Total Pages : 646 pages
Book Rating : 4.8/5 (115 download)
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.
Author : Dorin Bucur
Publisher : Springer Science & Business Media
ISBN 13 : 0817644032
Total Pages : 218 pages
Book Rating : 4.8/5 (176 download)
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.
Author : Jan Sokolowski
Publisher : Springer Science & Business Media
ISBN 13 : 3642581064
Total Pages : 254 pages
Book Rating : 4.6/5 (425 download)
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.
Author : Bozhidar Velichkov
Publisher : Springer
ISBN 13 : 8876425276
Total Pages : 362 pages
Book Rating : 4.8/5 (764 download)
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 362 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.
Author : Catherine Bandle
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111025438
Total Pages : 292 pages
Book Rating : 4.1/5 (11 download)
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.
Author : M. C. Delfour
Publisher : SIAM
ISBN 13 : 0898719364
Total Pages : 637 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Morton I. Kamien
Publisher : Courier Corporation
ISBN 13 : 0486310280
Total Pages : 402 pages
Book Rating : 4.4/5 (863 download)
Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Author : Martin P. Bendsøe
Publisher : Springer Science & Business Media
ISBN 13 : 9401118043
Total Pages : 564 pages
Book Rating : 4.4/5 (11 download)
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
Author : Donald A. Pierre
Publisher : Courier Corporation
ISBN 13 : 0486136957
Total Pages : 640 pages
Book Rating : 4.4/5 (861 download)
Download or read book Optimization Theory with Applications written by Donald A. Pierre and published by Courier Corporation. This book was released on 2012-07-12 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.
Author : J. Haslinger
Publisher : SIAM
ISBN 13 : 0898715369
Total Pages : 276 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Yannis Tsompanakis
Publisher : Taylor & Francis
ISBN 13 : 1134055064
Total Pages : 669 pages
Book Rating : 4.1/5 (34 download)
Download or read book Structural Design Optimization Considering Uncertainties written by Yannis Tsompanakis and published by Taylor & Francis. This book was released on 2008-02-07 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainties play a dominant role in the design and optimization of structures and infrastructures. In optimum design of structural systems due to variations of the material, manufacturing variations, variations of the external loads and modelling uncertainty, the parameters of a structure, a structural system and its environment are not given, fixed coefficients, but random variables with a certain probability distribution. The increasing necessity to solve complex problems in Structural Optimization, Structural Reliability and Probabilistic Mechanics, requires the development of new ideas, innovative methods and numerical tools for providing accurate numerical solutions in affordable computing times. This book presents the latest findings on structural optimization considering uncertainties. It contains selected contributions dealing with the use of probabilistic methods for the optimal design of different types of structures and various considerations of uncertainties. The first part is focused on reliability-based design optimization and the second part on robust design optimization. Comprising twenty-one, self-contained chapters by prominent authors in the field, it forms a complete collection of state-of-the-art theoretical advances and applications in the fields of structural optimization, structural reliability, and probabilistic computational mechanics. It is recommended to researchers, engineers, and students in civil, mechanical, naval and aerospace engineering and to professionals working on complicated costs-effective design problems.
Author : R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
ISBN 13 : 3642024319
Total Pages : 747 pages
Book Rating : 4.6/5 (42 download)
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author : Daniel Liberzon
Publisher : Princeton University Press
ISBN 13 : 0691151873
Total Pages : 255 pages
Book Rating : 4.6/5 (911 download)
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Author : Dominique Thévenin
Publisher : Springer Science & Business Media
ISBN 13 : 3540721533
Total Pages : 301 pages
Book Rating : 4.5/5 (47 download)
Download or read book Optimization and Computational Fluid Dynamics written by Dominique Thévenin and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical optimization of practical applications has been an issue of major importance for the last 10 years. It allows us to explore reliable non-trivial configurations, differing widely from all known solutions. The purpose of this book is to introduce the state-of-the-art concerning this issue and many complementary applications are presented.
Author : Bijan Mohammadi
Publisher : Oxford University Press
ISBN 13 : 0199546908
Total Pages : 292 pages
Book Rating : 4.1/5 (995 download)
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.
Author : Paul G. Constantine
Publisher : SIAM
ISBN 13 : 1611973864
Total Pages : 105 pages
Book Rating : 4.6/5 (119 download)
Download or read book Active Subspaces written by Paul G. Constantine and published by SIAM. This book was released on 2015-03-17 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.
