Numerical Methods In Sensitivity Analysis And Shape Optimization
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Numerical Methods In Sensitivity Analysis And Shape Optimization
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Author : Emmanuel Laporte
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods In Sensitivity Analysis And Shape Optimization written by Emmanuel Laporte 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 2012-12-06 with Technology & Engineering categories.
Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.
Introduction To Shape Optimization
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Author : Jan Sokolowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Shape Optimization written by Jan Sokolowski 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 2012-12-06 with Mathematics categories.
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.
Shape Design Sensitivity Analysis And Optimization Using The Boundary Element Method
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Author : Zhiye Zhao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Shape Design Sensitivity Analysis And Optimization Using The Boundary Element Method written by Zhiye Zhao 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 2012-12-06 with Technology & Engineering categories.
This book investigates the various aspects of shape optimization of two dimensional continuum structures, including shape design sensitivity analysis, structural analysis using the boundary element method (BEM), and shape optimization implementation. The book begins by reviewing the developments of shape optimization, followed by the presentation of the mathematical programming methods for solving optimization problems. The basic theory of the BEM is presented which will be employed later on as the numerical tool to provide the structural responses and the shape design sensitivities. The key issue of shape optimization, the shape design sensitivity analy sis, is fully investigated. A general formulation of stress sensitivity using the continuum approach is presented. The difficulty of the modelling of the ad joint problem is studied, and two approaches are presented for the modelling of the adjoint problem. The first approach uses distributed loads to smooth the concentrated adjoint loads, and the second approach employs the singu larity subtraction method to remove the singular boundary displacements and tractions from the BEM equation. A novel finite difference based approach to shape design sensitivity is pre sented, which overcomes the two drawbacks of the conventional finite difference method. This approach has the advantage of being simple in concept, and eas ier implementation. A shape optimization program for two-dimensional continuum structures is developed, including structural analysis using the BEM, shape design sensitiv ity analysis, mathematical programming, and the design boundary modelling.
Introduction To Shape Optimization
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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.
Computational Methods In Applied Sciences
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Author : Ch Hirsch
language : en
Publisher: Elsevier Publishing Company
Release Date : 1992
Computational Methods In Applied Sciences written by Ch Hirsch and has been published by Elsevier Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
The European Computational Fluid Dynamics Conference and the European Conference on Numerical Methods in Engineering are the initiative of national Scientific Societies of many countries in Europe engaged in these fields. The 28 papers in this volume give an extensive review on selected topics pertaining to basic methodologies, scientific developments and industrial applications, in fluid dynamics, in structural mechanics and other engineering applications. This multidisciplinary volume brings together specialists in a wide range of engineering activities who employ common analytical and experimental methods in their research. The contents are of world-wide interest and will help to stimulate future research and analysis in this broad field.
Sensitivity Analysis And Shape Optimization Of Geometrically Non Linear Structures
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Author :
language : pt-BR
Publisher:
Release Date : 2000
Sensitivity Analysis And Shape Optimization Of Geometrically Non Linear Structures written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Este trabalho propõe uma metodologia para a otimização de forma de estruturas geometricamente não-lineares. O objetivo desta metodologia é evitar os problemas deinstabilidade apresentados por estruturas otimizadas de acordo com a formulação clássica. Ela foi implementada para problemas bidimensionais e os resultados obtidos na otimização de diferentes estruturas demonstraram o seu sucesso. Utilizando-se conceitos de modelagem geométrica, a forma da estrutura é defini-da através das curvas de seu contorno. Assim, a representação paramétrica de curvas e adefinição destas em função de um conjunto de pontos de interpolação (pontos-chave) são discutidas detalhadamente. A ênfase é dada à interpolação através de B-splines, devidoa sua grande flexibilidade. O problema de otimização édefinido com base no modelo geométrico e as variáveis de projeto são as coordenadas dos pontos-chave. A simetria da estrutura é garantida através da ligação de variáveis. A estrutura é analisada através de elementos isoparametricos planos. Assim, antes de realizar a análise, é necessário discretizar a estrutura em um conjunto de elementos finitos. Para realizar esta tarefa foram implementados diferentes algoritmos de geração de malhas, tanto estruturadas quanto não-estruturadas. O método de Newton-Raphson é utilizado pa-ra determinar a configuração de equilíbrio e diferentes métodos podem ser aplicados para determinar os pontos críticos. Devido aos problemas de convergência apresentados pelos métodos diretos para a determinação dos pontos crticos, um método semi-direto foi desenvolvidoneste trabalho. Os resultados obtidos na análise de diferentes exemplos mostraram a adequação dos elementos finitos e dos métodos numéricos implementados. Os algoritmos de programação matemática utilizados neste trabalho precisam dos gradientes da função objetivo e das restrições, que são calculadas com base nos gradientesdas respostas da estrutura. Partindo-se de equações gerais válidas para quaisquer elementos, foram desenvolvidas expressões analíticas que permitem o cálculo exato das sensibilidades de elementos finitos isoparamétricos formulados através do procedimento Lagrangiano Total. O desenvolvimento e a implementação de expressões semelhantes para elementos mais complexos é uma tarefa bastante árdua. Por outro lado, o método das diferenças fi-nitas é simples e genérico, mas muito caro computacionalmente. O método semi-analítico mantémm as vantagens da utilização de diferenças finitas e possui um custo computacional baixo, porém pode apresentar sérios problemas de preciso. Devido a estes motivos, foidesenvolvido neste trabalho um procedimento para melhorar a qualidade das sensibilidades semi-analíticas de estruturas geometricamente não-lineares. O procedimento é baseado nadiferenciação exata dos movimentos de corpo rígido do elemento utilizado. Os resultados numéricos obtidos demonstraram a sua eficácia.
Multi Scale Computational Techniques For Design Of Polycrystalline Materials
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Author : Veeraraghavan Sundararaghyavan
language : en
Publisher:
Release Date : 2007
Multi Scale Computational Techniques For Design Of Polycrystalline Materials written by Veeraraghavan Sundararaghyavan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Microstructures play an important role in controlling distribution of properties in engineering materials. It is possible to develop components with tailored distribution of properties such as strength and stiffness by controlling microstructure evolution during the manufacturing process. When forming metallic components by imposing large deformations, mechanisms such as slip and lattice rotation drive formation of texture in the underlying polycrystalline microstructure. Such microstructural changes affect the final distribution of material properties in the component. By carefully designing the imposed deformation, one could potentially tailor the microstructure and obtain desired property distributions. This thesis focuses on development of novel computational strategies for designing deformation processes to realize materials with desired properties. The techniques presented are an interplay of several new tools developed recently, such as reduced order modeling, graphical cross-plots, statistical learning, microstructure homogenization and multi-scale sensitivity analysis. The primary outcomes of this thesis are listed below: Development of reduced-order representations and graphical methodologies for representing process-property-texture relationships. Development of adaptive reduced-order optimization techniques for identification of processing paths that lead to desirable microstructure-sensitive properties. Development of homogenization techniques for predicting microstructure evolution in large deformation processes. Development of multi-scale sensitivity analysis of poly-crystalline material deformation for optimizing microstructure-sensitive properties during industrial forming processes. The framework for design of polycrystalline microstructures leads to increased product yield in industrial forming processes and simultaneously allows control distribution of properties such as stiffness and strength in forged products. Multiscale design problems leading to billions of unknowns have been solved using parallel computing techniques. The computational framework can be readily used for selecting optimal processing paths for achieving desired properties. The methodology developed is a fundamental effort at providing detailed deformation process design solutions needed for controlling properties of performance-critical hardware components in automotive, structural and aerospace applications. (Abstract).
Asme Technical Papers
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Author :
language : en
Publisher:
Release Date : 1998
Asme Technical Papers written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mechanical engineering categories.
Mathematical Modeling And Optimization Of Complex Structures
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Author : Pekka Neittaanmäki
language : en
Publisher: Springer
Release Date : 2015-10-07
Mathematical Modeling And Optimization Of Complex Structures written by Pekka Neittaanmäki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-07 with Technology & Engineering categories.
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimization algorithms; * Optimal control problems with distributed and discrete control; * Shape optimization and shape design problems in science and engineering; * Sensitivity analysis and parameters optimization of complex systems.
Design Sensitivity Analysis And Optimization Of Electromagnetic Systems
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Author : Il Han Park
language : en
Publisher: Springer
Release Date : 2018-08-27
Design Sensitivity Analysis And Optimization Of Electromagnetic Systems written by Il Han Park and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-27 with Technology & Engineering categories.
This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems. It treats the subject in a unified manner, providing numerical methods and design examples. The specific focus is on continuum design sensitivity analysis, which offers significant advantages over discrete design sensitivity methods. Continuum design sensitivity formulas are derived from the material derivative in continuum mechanics and the variational form of the governing equation. Continuum sensitivity analysis is applied to Maxwell equations of electrostatic, magnetostatic and eddy-current systems, and then the sensitivity formulas for each system are derived in a closed form; an integration along the design interface. The book also introduces the recent breakthrough of the topology optimization method, which is accomplished by coupling the level set method and continuum design sensitivity. This topology optimization method enhances the possibility of the global minimum with minimised computational time, and in addition the evolving shapes during the iterative design process are easily captured in the level set equation. Moreover, since the optimization algorithm is transformed into a well-known transient analysis algorithm for differential equations, its numerical implementation becomes very simple and convenient. Despite the complex derivation processes and mathematical expressions, the obtained sensitivity formulas are very straightforward for numerical implementation. This book provides detailed explanation of the background theory and the derivation process, which will help readers understand the design method and will set the foundation for advanced research in the future.