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Shape optimization problems

Azegami, Hideyuki.

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Shape optimization problems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Shape optimization problems/ by Hideyuki Azegami.
Author:	Azegami, Hideyuki.
Published:	Singapore :Springer Singapore : : 2020.,
Description:	xxiii, 646 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface -- Notation -- Chapter 1: Basics of Optimal Design -- Chapter 2: Basics of Optimization Theory -- Chapter 3: Basics of Mathematical Programming -- Chapter 4: Basics of Variational Principles and Functional Analysis -- Chapter 5: Boundary Value Problems of Partial Differential Equations -- Chapter 6: Fundamentals of Numerical Analysis -- Chapter 7: Abstract Optimum Design Problem -- Chapter 8: Topology Optimization Problem of Density Variation Type -- Chapter 9: Shape Optimization Problems of Domain Variation Type -- Answers to Practice Problems -- Afterword -- References -- Index.
Contained By:	Springer Nature eBook
Subject:	Shape theory (Topology) -
Online resource:	https://doi.org/10.1007/978-981-15-7618-8
ISBN:	9789811576188

Shape optimization problems
Azegami, Hideyuki.

Shape optimization problems[electronic resource] /by Hideyuki Azegami. - Singapore :Springer Singapore :2020. - xxiii, 646 p. :ill., digital ;24 cm. - Springer optimization and its applications,v.1641931-6828 ;. - Springer optimization and its applications ;v.164..

Preface -- Notation -- Chapter 1: Basics of Optimal Design -- Chapter 2: Basics of Optimization Theory -- Chapter 3: Basics of Mathematical Programming -- Chapter 4: Basics of Variational Principles and Functional Analysis -- Chapter 5: Boundary Value Problems of Partial Differential Equations -- Chapter 6: Fundamentals of Numerical Analysis -- Chapter 7: Abstract Optimum Design Problem -- Chapter 8: Topology Optimization Problem of Density Variation Type -- Chapter 9: Shape Optimization Problems of Domain Variation Type -- Answers to Practice Problems -- Afterword -- References -- Index.

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.

ISBN: 9789811576188

Standard No.: 10.1007/978-981-15-7618-8doiSubjects--Topical Terms:

726529
Shape theory (Topology)

LC Class. No.: QA612.7 / .A95 2020

Dewey Class. No.: 514.24

Shape optimization problems
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245 1 0 $a Shape optimization problems $h [electronic resource] / $c by Hideyuki Azegami.
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300 $a xxiii, 646 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer optimization and its applications, $x 1931-6828 ; $v v.164
505 0 $a Preface -- Notation -- Chapter 1: Basics of Optimal Design -- Chapter 2: Basics of Optimization Theory -- Chapter 3: Basics of Mathematical Programming -- Chapter 4: Basics of Variational Principles and Functional Analysis -- Chapter 5: Boundary Value Problems of Partial Differential Equations -- Chapter 6: Fundamentals of Numerical Analysis -- Chapter 7: Abstract Optimum Design Problem -- Chapter 8: Topology Optimization Problem of Density Variation Type -- Chapter 9: Shape Optimization Problems of Domain Variation Type -- Answers to Practice Problems -- Afterword -- References -- Index.
520 $a 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.
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650 0 $a Mathematical optimization. $3 517763
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650 1 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
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650 2 4 $a Partial Differential Equations. $3 890899
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856 4 0 $u https://doi.org/10.1007/978-981-15-7618-8
950 $a Mathematics and Statistics (SpringerNature-11649)