Descript 
1 online resource (xxiii, 646 pages) : illustrations, digital ; 24 cm 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

text file PDF rda 
Series 
Springer optimization and its applications, 19316828 ; volume 164


Springer optimization and its applications ; volume 164

Note 
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 nonparametric shape optimization problems, systematically keeping in mind readers with an engineering background. Nonparametric 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 
Host Item 
Springer Nature eBook

Subject 
Shape theory (Topology)


Mathematical optimization


Engineering mathematics


Mathematical Applications in the Physical Sciences


Functional Analysis


Numerical Analysis


Partial Differential Equations


Math Applications in Computer Science

Alt Author 
SpringerLink (Online service)

