Homogenization And Structural Topology Optimization

Author : Behrooz Hassani,Ernest Hinton
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447108917

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Homogenization and Structural Topology Optimization by Behrooz Hassani,Ernest Hinton Pdf

Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.

Author : Martin P. Bendsoe
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 45,5 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662031155

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Optimization of Structural Topology, Shape, and Material by Martin P. Bendsoe Pdf

In the past, the possibilities of structural optimization were restricted to an optimal choice of profiles and shape. Further improvement can be obtained by selecting appropriate advanced materials and by optimizing the topology, i.e. finding the best position and arrangement of structural elements within a construction. The optimization of structural topology permits the use of optimization algorithms at a very early stage of the design process. The method presented in this book has been developed by Martin Bendsoe in cooperation with other researchers and can be considered as one of the most effective approaches to the optimization of layout and material design.

Author : Daicong Da
Publisher : John Wiley & Sons
Page : 200 pages
File Size : 42,7 Mb
Release : 2020-02-26
Category : Mathematics
ISBN : 9781786305589

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Topology Optimization Design of Heterogeneous Materials and Structures by Daicong Da Pdf

This book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue. The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high industrial and practical relevance. Part 1 starts by testing the limits of the homogenization-based approach when the size of the representative volume element is non-negligible compared to the structure. The book then introduces a non-local homogenization scheme to take into account the strain gradient effects. Using a phase field method, Part 2 offers three significant contributions concerning optimal placement of the inclusion phases. Respectively, these contributions take into account fractures in quasi-brittle materials, interface cracks and periodic composites. The topology optimization proposed has significantly increased the fracture resistance of the composites studied.

Author : George I. N. Rozvany,Tomasz Lewinski
Publisher : Springer Science & Business Media
Page : 471 pages
File Size : 41,8 Mb
Release : 2013-09-20
Category : Science
ISBN : 9783709116432

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Topology Optimization in Structural and Continuum Mechanics by George I. N. Rozvany,Tomasz Lewinski Pdf

The book covers new developments in structural topology optimization. Basic features and limitations of Michell’s truss theory, its extension to a broader class of support conditions, generalizations of truss topology optimization, and Michell continua are reviewed. For elastic bodies, the layout problems in linear elasticity are discussed and the method of relaxation by homogenization is outlined. The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case. For structures subjected to dynamic loads, it is explained how they can be designed so that the structural eigenfrequencies of vibration are as far away as possible from a prescribed external excitation frequency (or a band of excitation frequencies) in order to avoid resonance phenomena with high vibration and noise levels. For diffusive and convective transport processes and multiphysics problems, applications of the density method are discussed. In order to take uncertainty in material parameters, geometry, and operating conditions into account, techniques of reliability-based design optimization are introduced and reviewed for their applicability to topology optimization.

Author : G.I.N. Rozvany
Publisher : Springer
Page : 325 pages
File Size : 44,6 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709125663

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Topology Optimization in Structural Mechanics by G.I.N. Rozvany Pdf

Topology optimization is a relatively new and rapidly expanding field of structural mechanics. It deals with some of the most difficult problems of mechanical sciences but it is also of considerable practical interest, because it can achieve much greater savings than mere cross-section or shape optimization.

Author : Liang Xia
Publisher : Elsevier
Page : 184 pages
File Size : 41,8 Mb
Release : 2016-04-27
Category : Technology & Engineering
ISBN : 9780081011867

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Multiscale Structural Topology Optimization by Liang Xia Pdf

Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain. Presents the first attempts towards topology optimization design of nonlinear highly heterogeneous structures Helps with simultaneous design of the topologies of both macroscopic structure and microscopic materials Helps with development of computer codes for the designs of nonlinear structures and of materials with extreme constitutive properties Focuses on the simultaneous design of both macroscopic structure and microscopic materials Includes a reduce database model from a set of numerical experiments in the space of effective strain

Author : Martin Philip Bendsoe,Ole Sigmund
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 46,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662050866

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Topology Optimization by Martin Philip Bendsoe,Ole Sigmund Pdf

The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition, has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also materials and MEMS.

Author : Y.M. Xie,Grant P. Steven
Publisher : Springer
Page : 200 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781447109853

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Evolutionary Structural Optimization by Y.M. Xie,Grant P. Steven Pdf

Evolutionary Structural Optimization (ESO) is a design method based on the simple concept of gradually removing inefficient material from a structure as it is being designed. Through this method, the resulting structure will evolve towards its optimum shape. The latest techniques and results of ESO are presented here, illustrated by numerous clear and detailed examples. Sections cover the fundamental aspects of the method, the application to multiple load cases and multiple support environments, frequency optimization, stiffness and displacement constraints, buckling, jointed frame structures, shape optimization, and stress reduction. This is followed by a section describing Evolve97, a software package which will allow readers to try the ideas of ESO themselves and to solve their optimization problems. This software is provided on a computer diskette which accompanies the book.

Author : Osvaldo M. Querin,Mariano Victoria,Cristina Alonso Gordoa,Rubén Ansola,Pascual Martí
Publisher : Butterworth-Heinemann
Page : 204 pages
File Size : 54,8 Mb
Release : 2017-06-09
Category : Mathematics
ISBN : 9780080999890

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Topology Design Methods for Structural Optimization by Osvaldo M. Querin,Mariano Victoria,Cristina Alonso Gordoa,Rubén Ansola,Pascual Martí Pdf

Topology Design Methods for Structural Optimization provides engineers with a basic set of design tools for the development of 2D and 3D structures subjected to single and multi-load cases and experiencing linear elastic conditions. Written by an expert team who has collaborated over the past decade to develop the methods presented, the book discusses essential theories with clear guidelines on how to use them. Case studies and worked industry examples are included throughout to illustrate practical applications of topology design tools to achieve innovative structural solutions. The text is intended for professionals who are interested in using the tools provided, but does not require in-depth theoretical knowledge. It is ideal for researchers who want to expand the methods presented to new applications, and includes a companion website with related tools to assist in further study. Provides design tools and methods for innovative structural design, focusing on the essential theory Includes case studies and real-life examples to illustrate practical application, challenges, and solutions Features accompanying software on a companion website to allow users to get up and running fast with the methods introduced Includes input from an expert team who has collaborated over the past decade to develop the methods presented

Author : Martin P. Bendsøe,Carlos A. Mota Soares
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401118040

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Topology Design of Structures by Martin P. Bendsøe,Carlos A. Mota Soares Pdf

Proceedings of the NATO Advanced Research Workshop, Sesimbra, Portugal, June 20-26, 1992

Author : Gregoire Allaire
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781468492866

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Shape Optimization by the Homogenization Method by Gregoire Allaire Pdf

This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.

Author : Xiaodong Huang,Mike Xie
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 54,9 Mb
Release : 2010-03-11
Category : Technology & Engineering
ISBN : 0470689471

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Evolutionary Topology Optimization of Continuum Structures by Xiaodong Huang,Mike Xie Pdf

Evolutionary Topology Optimization of Continuum Structures treads new ground with a comprehensive study on the techniques and applications of evolutionary structural optimization (ESO) and its later version bi-directional ESO (BESO) methods. Since the ESO method was first introduced by Xie and Steven in 1992 and the publication of their well-known book Evolutionary Structural Optimization in 1997, there have been significant improvements in the techniques as well as important practical applications. The authors present these developments, illustrated by numerous interesting and detailed examples. They clearly demonstrate that the evolutionary structural optimization method is an effective approach capable of solving a wide range of topology optimization problems, including structures with geometrical and material nonlinearities, energy absorbing devices, periodical structures, bridges and buildings. Presents latest developments and applications in this increasingly popular & maturing optimization approach for engineers and architects; Authored by leading researchers in the field who have been working in the area of ESO and BESO developments since their conception; Includes a number of test problems for students as well as a chapter of case studies that includes several recent practical projects in which the authors have been involved; Accompanied by a website housing ESO/BESO computer programs at http://www.wiley.com/go/huang and test examples, as well as a chapter within the book giving a description and step-by-step instruction on how to use the software package BESO2D. Evolutionary Topology Optimization of Continuum Structures will appeal to researchers and graduate students working in structural design and optimization, and will also be of interest to civil and structural engineers, architects and mechanical engineers involved in creating innovative and efficient structures.

Author : Martin P. Bends?e
Publisher : Unknown
Page : 0 pages
File Size : 51,7 Mb
Release : 1995
Category : Structural optimization
ISBN : 0387590579

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Optimization of Structural Topology, Shape, and Material by Martin P. Bends?e Pdf

Author : B. Kawohl
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 50,7 Mb
Release : 2000-11-16
Category : Mathematics
ISBN : 3540679715

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Optimal Shape Design by B. Kawohl Pdf

Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.

Author : Peter W. Christensen,Anders Klarbring
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 43,7 Mb
Release : 2008-10-20
Category : Technology & Engineering
ISBN : 9781402086656

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An Introduction to Structural Optimization by Peter W. Christensen,Anders Klarbring Pdf

This book has grown out of lectures and courses given at Linköping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying—frequently very many— variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.