Shape Optimization Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Shape Optimization Problems write by Hideyuki Azegami. This book was released on 2020-09-30. Shape Optimization Problems available in PDF, EPUB and Kindle. 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.
Variational Methods in Shape Optimization Problems
Variational Methods in Shape Optimization Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variational Methods in Shape Optimization Problems write by Dorin Bucur. This book was released on 2006-09-13. Variational Methods in Shape Optimization Problems available in PDF, EPUB and Kindle. 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.
Introduction to Shape Optimization
Introduction to Shape Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Shape Optimization write by Jan Sokolowski. This book was released on 2012-12-06. Introduction to Shape Optimization available 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.
Existence and Regularity Results for Some Shape Optimization Problems
Existence and Regularity Results for Some Shape Optimization Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Existence and Regularity Results for Some Shape Optimization Problems write by Bozhidar Velichkov. This book was released on 2015-03-21. Existence and Regularity Results for Some Shape Optimization Problems available in PDF, EPUB and Kindle. 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.
Introduction to Shape Optimization
Introduction to Shape Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Shape Optimization write by J. Haslinger. This book was released on 2003-01-01. Introduction to Shape Optimization available in PDF, EPUB and Kindle. Treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.
