Variational Methods In Shape Optimization Problems PDF Download
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Author | : Dorin Bucur |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2006-09-13 |
Genre | : Mathematics |
ISBN | : 0817644032 |
Download Variational Methods in Shape Optimization Problems Book 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.
Author | : Dorin Bucur |
Publisher | : Edizioni della Normale |
Total Pages | : 217 |
Release | : 2002-10-01 |
Genre | : Mathematics |
ISBN | : 9788876422973 |
Download Variational methods in some shape optimization problems Book in PDF, ePub and Kindle
The study of shape optimization problems is a very wide field, both classical, as the isoperimetric problem and Newton problem of the best aerodynamical shape show, and modern, for all the recent results obtained in the last two, three decades. The fascinating feature is that the competing objects are shapes, i.e. domains of Rn, instead of functions, as usually occurs in problems of calculus of variations. This constraint often produces additional difficulties that lead to a lack of existence of a solution and the introduction of suitable relaxed formulations of the problem. However, in a few cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restriction on the class of competing domains. This volume collects the lecture notes of two courses given in the academic year 2000/01 by the authors at the University of Pisa and at the Scuola Normale Superiore respectively. The courses were mainly addressed to Ph. D. students and required a background in the topics in functional analysis that are usually taught in undergraduate courses.
Author | : Andrej Cherkaev |
Publisher | : Springer Science & Business Media |
Total Pages | : 561 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461211883 |
Download Variational Methods for Structural Optimization Book in PDF, ePub and Kindle
This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
Author | : Hideyuki Azegami |
Publisher | : Springer Nature |
Total Pages | : 646 |
Release | : 2020-09-30 |
Genre | : Mathematics |
ISBN | : 9811576181 |
Download Shape Optimization Problems Book 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.
Author | : Dumitru Motreanu |
Publisher | : Springer Science & Business Media |
Total Pages | : 400 |
Release | : 2003-05-31 |
Genre | : Mathematics |
ISBN | : 9781402013850 |
Download Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems Book in PDF, ePub and Kindle
This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
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.
Author | : Donald R. Smith |
Publisher | : Courier Corporation |
Total Pages | : 406 |
Release | : 1998-01-01 |
Genre | : Mathematics |
ISBN | : 9780486404554 |
Download Variational Methods in Optimization Book in PDF, ePub and Kindle
Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
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 | : Roland Herzog |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 386 |
Release | : 2022-03-07 |
Genre | : Mathematics |
ISBN | : 3110696002 |
Download Optimization and Control for Partial Differential Equations Book in PDF, ePub and Kindle
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Author | : Kazufumi Ito |
Publisher | : SIAM |
Total Pages | : 354 |
Release | : 2008-11-06 |
Genre | : Mathematics |
ISBN | : 0898716497 |
Download Lagrange Multiplier Approach to Variational Problems and Applications Book in PDF, ePub and Kindle
Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.