[PDF] Topological Derivative In Shape Optimization - eBooks Review

Topological Derivative In Shape Optimization


Topological Derivative In Shape Optimization
DOWNLOAD

Download Topological Derivative In Shape Optimization PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topological Derivative In Shape Optimization book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page





Topological Derivatives In Shape Optimization


Topological Derivatives In Shape Optimization
DOWNLOAD
Author : Antonio André Novotny
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-14

Topological Derivatives In Shape Optimization written by Antonio André Novotny and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.


The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.



Topological Derivative In Shape Optimization


Topological Derivative In Shape Optimization
DOWNLOAD
Author : Antonio Andre Novotny
language : en
Publisher:
Release Date : 2013

Topological Derivative In Shape Optimization written by Antonio Andre Novotny and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Asymptotic expansions categories.


The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested in the mathematical aspects of topological asymptotic analysis as well as in applications of topological derivatives in computational mechanics.



An Introduction To The Topological Derivative Method


An Introduction To The Topological Derivative Method
DOWNLOAD
Author : Antonio André Novotny
language : en
Publisher: Springer Nature
Release Date : 2020-01-21

An Introduction To The Topological Derivative Method written by Antonio André Novotny and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-21 with Mathematics categories.


This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis. This new concept in shape optimization has applications in many different fields such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms. Some exercises are offered at the end of each chapter, helping the reader to better understand the involved concepts.



Applications Of The Topological Derivative Method


Applications Of The Topological Derivative Method
DOWNLOAD
Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2018-12-28

Applications Of The Topological Derivative Method written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-28 with Technology & Engineering categories.


The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.



Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View


Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View
DOWNLOAD
Author : Harald Held
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30

Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View written by Harald Held and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-30 with Mathematics categories.


Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.



Shape Optimization Problems


Shape Optimization Problems
DOWNLOAD
Author : Hideyuki Azegami
language : en
Publisher: Springer Nature
Release Date : 2020-09-30

Shape Optimization Problems written by Hideyuki Azegami and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-30 with Mathematics categories.


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.



Shape Optimization And Optimal Design


Shape Optimization And Optimal Design
DOWNLOAD
Author : John Cagnol
language : en
Publisher: CRC Press
Release Date : 2017-08-02

Shape Optimization And Optimal Design written by John Cagnol and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-02 with Mathematics categories.


This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.



Introduction To Shape Optimization


Introduction To Shape Optimization
DOWNLOAD
Author : J. Haslinger
language : en
Publisher: SIAM
Release Date : 2003-01-01

Introduction To Shape Optimization written by J. Haslinger and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.


Treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.



Shape Optimization Using Constructive Representations


Shape Optimization Using Constructive Representations
DOWNLOAD
Author : Jiaqin Chen
language : en
Publisher:
Release Date : 2008

Shape Optimization Using Constructive Representations written by Jiaqin Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.




New Trends In Shape Optimization


New Trends In Shape Optimization
DOWNLOAD
Author : Aldo Pratelli
language : en
Publisher: Birkhäuser
Release Date : 2015-12-01

New Trends In Shape Optimization written by Aldo Pratelli and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-01 with Mathematics categories.


This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.