Skip to main content
SpringerLink
Log in

Shape Optimization Problems

  • Book
  • © 2020

Overview

Authors:
  1. Hideyuki Azegami

    1. Graduate School of Informatics, Nagoya University, Nagoya, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Introduces most theories related to non-parametric shape optimization problems
  • Summarizes basic theories in the first six chapters, with Chap. 4 especially valuable for engineers
  • Devotes the three final chapters to shape and topology optimization problems after providing their abstract framework

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 164)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxiii
    Download chapter PDF

  2. Basics of Optimal Design

    • Hideyuki Azegami
    Pages 1-43

  3. Basics of Optimization Theory

    • Hideyuki Azegami
    Pages 45-103

  4. Basics of Mathematical Programming

    • Hideyuki Azegami
    Pages 105-158

  5. Basics of Variational Principles and Functional Analysis

    • Hideyuki Azegami
    Pages 159-222

  6. Boundary Value Problems of Partial Differential Equations

    • Hideyuki Azegami
    Pages 223-257

  7. Fundamentals of Numerical Analysis

    • Hideyuki Azegami
    Pages 259-329

  8. Abstract Optimum Design Problem

    • Hideyuki Azegami
    Pages 331-357

  9. Topology Optimization Problems of Density Variation Type

    • Hideyuki Azegami
    Pages 359-426

  10. Shape Optimization Problems of Domain Variation Type

    • Hideyuki Azegami
    Pages 427-566

  11. Back Matter

    Pages 567-646
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

“The book is written clearly. Key points of the presentation are summarized, and the theorems are formulated using well-known mathematical results. … The book is appropriate for use in a graduate course or for self-study. Each chapter ends with a diverse list of exercises. Again, the solutions to these exercises can be found at the end of the book. This book will be a valuable resource for engineering graduate students or experts on structural optimization problems and related areas.” (Andrzej M. Myśliński, Mathematical Reviews, March, 2022)

Authors and Affiliations

  • Graduate School of Informatics, Nagoya University, Nagoya, Japan

    Hideyuki Azegami

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation