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Author: Antoine Henrot
Publisher:
Published: 2018
Total Pages: 365
ISBN-13: 9783037191781
DOWNLOAD EBOOKDownload 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
Published: 2020-09-30
Total Pages: 646
ISBN-13: 9811576181
DOWNLOAD EBOOKThis 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.
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
Published: 2006-09-13
Total Pages: 218
ISBN-13: 0817644032
DOWNLOAD EBOOKShape 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.
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
Published: 2012-12-06
Total Pages: 254
ISBN-13: 3642581064
DOWNLOAD EBOOKThis 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.
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: Catherine Bandle
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2023-06-19
Total Pages: 292
ISBN-13: 3111025438
DOWNLOAD EBOOKThis 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.
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: J. Haslinger
Publisher: SIAM
Published: 2003-01-01
Total Pages: 276
ISBN-13: 0898715369
DOWNLOAD EBOOKTreats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.
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: Morton I. Kamien
Publisher: Courier Corporation
Published: 2013-04-17
Total Pages: 402
ISBN-13: 0486310280
DOWNLOAD EBOOKSince 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.
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: Bijan Mohammadi
Publisher: Oxford University Press
Published: 2010
Total Pages: 292
ISBN-13: 0199546908
DOWNLOAD EBOOKContents: 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.
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: M. C. Delfour
Publisher: SIAM
Published: 2011-01-01
Total Pages: 637
ISBN-13: 0898719364
DOWNLOAD EBOOKPresents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.
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: Martin P. Bendsøe
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 564
ISBN-13: 9401118043
DOWNLOAD EBOOKProceedings of the NATO Advanced Research Workshop, Sesimbra, Portugal, June 20-26, 1992
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
