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Topology Optimization In Engineering Structure Design

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Topology Optimization in Engineering Structure Design

Topology Optimization in Engineering Structure Design Book
Author : Jihong Zhu,Tong Gao
Publisher : Elsevier
Release : 2016-11-08
ISBN : 0081021194
Language : En, Es, Fr & De

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Book Description :

Topology Optimization in Engineering Structure Design explores the recent advances and applications of topology optimization in engineering structures design, with a particular focus on aircraft and aerospace structural systems. To meet the increasingly complex engineering challenges provided by rapid developments in these industries, structural optimization techniques have developed in conjunction with them over the past two decades. The latest methods and theories to improve mechanical performances and save structural weight under static, dynamic and thermal loads are summarized and explained in detail here, in addition to potential applications of topology optimization techniques such as shape preserving design, smart structure design and additive manufacturing. These new design strategies are illustrated by a host of worked examples, which are inspired by real engineering situations, some of which have been applied to practical structure design with significant effects. Written from a forward-looking applied engineering perspective, the authors not only summarize the latest developments in this field of structure design but also provide both theoretical knowledge and a practical guideline. This book should appeal to graduate students, researchers and engineers, in detailing how to use topology optimization methods to improve product design. Combines practical applications and topology optimization methodologies Provides problems inspired by real engineering difficulties Designed to help researchers in universities acquire more engineering requirements

Topology Design Methods for Structural Optimization

Topology Design Methods for Structural Optimization Book
Author : Osvaldo M. Querin,Mariano Victoria,Cristina Alonso Gordoa,Rubén Ansola,Pascual Martí
Publisher : Butterworth-Heinemann
Release : 2017-06-09
ISBN : 0080999891
Language : En, Es, Fr & De

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Book Description :

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

Topology Optimization in Structural Mechanics

Topology Optimization in Structural Mechanics Book
Author : G.I.N. Rozvany
Publisher : Springer
Release : 2014-05-04
ISBN : 3709125669
Language : En, Es, Fr & De

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Book Description :

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.

Topology Optimization

Topology Optimization Book
Author : Martin Philip Bendsoe,Ole Sigmund
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 3662050862
Language : En, Es, Fr & De

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Book Description :

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.

Optimization of Structural and Mechanical Systems

Optimization of Structural and Mechanical Systems Book
Author : Jasbir S. Arora
Publisher : World Scientific
Release : 2007
ISBN : 9812779671
Language : En, Es, Fr & De

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Book Description :

This book provides a discussion of the general impact of WTO membership on both sides of the Taiwan Strait, and addresses the political and economic impact on cross-Strait relations of common membership. The book begins with an introduction which analyzes the state of cross-Strait economic and political relations on the eve of dual accession to the WTO and briefly introduces the chapters which follow. The first chapter discusses the concessions made by both sides in their accession agreements and is followed by two chapters which describe the manner in which the Taiwan economy was reformed to achieve compliance as well as the specific, restrictive trade regime that was put into place to manage mainland trade. The next two chapters deal with the implications of that restrictive trade regime for the Taiwan economy in Asia and with the nature of the interactions between the two sides within the WTO. The final four chapters of the volume examine the impact of membership on four sectors of the economy: finance; agriculture; electronics and automobiles. There is a post-script which briefly covers developments since the chapters were completed.

Optimization of Structural Topology Shape and Material

Optimization of Structural Topology  Shape  and Material Book
Author : Martin P. Bendsoe
Publisher : Springer Science & Business Media
Release : 2013-03-14
ISBN : 3662031159
Language : En, Es, Fr & De

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Book Description :

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.

Topology Optimization of Structures and Composite Continua

Topology Optimization of Structures and Composite Continua Book
Author : George I. N. Rozvany,N. Olhoff
Publisher : Springer Science & Business Media
Release : 2001-01-31
ISBN : 9780792368076
Language : En, Es, Fr & De

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Book Description :

Topology optimization of structures and composite materials is a new and rapidly expanding field of mechanics which now plays an ever-increasing role in most branches of technology, such as aerospace, mechanical, structural, civil and ma terials engineering, with important implications for energy production as well as building and environmental sciences. It is a truly "high-tech" field which requires advanced computer facilities and computational methods, whilst involving unusual theoretical considerations in pure mathematics. Topology optimization deals with some of the most difficult problems of mechanical sciences, but it is also of consid erable practical interest because it can achieve much greater savings than conven tional (sizing or shape) optimization. Extensive research into topology optimization is being carried out in most of the developed countries of the world. The workshop addressed the state of the art of the field, bringing together re searchers from a diversity of backgrounds (mathematicians, information scientists, aerospace, automotive, mechanical, structural and civil engineers) to span the full breadth and depth of the field and to outline future developments in research and avenues of cooperation between NATO and Partner countries. The program cov ered • theoretical (mathematical) developments, • computer algorithms, software development and computational difficulties, and • practical applications in various fields of technology. A novel feature of the workshop was that, in addition to shorter discussions after each lecture, a 30 minutes panel discussion took place in each sesssion, which made this ARW highly interactive and more informal.

Recent Advances in Optimal Structural Design

Recent Advances in Optimal Structural Design Book
Author : Scott A. Burns
Publisher : ASCE Publications
Release : 2002-01-01
ISBN : 9780784475249
Language : En, Es, Fr & De

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Book Description :

Sponsored by the Technical Committee on Structural Design of the Technical Administrative Committee on Analysis and Computation of the Technical Activities Division of the Structural Engineering Institute of ASCE. This report documents the dramatic new developments in the field of structural optimization over the last two decades. Changes in both computational techniques and applications can be seen by developments in computational methods and solution algorithms, the role of optimization during the various stages of structural design, and the stochastic nature of design in relation to structural optimization. Topics include: Ømethods for discrete variable structural optimization; Ødecomposition methods in structural optimization; Østate of the art on the use of genetic algorithms in design of steel structures; Øconceptual design optimization of engineering structures; Øtopology and geometry optimization of trusses and frames; Øevolutionary structural optimization; Ødesign and optimization of semi-rigid framed structures; Øoptimized performance-based design for buildings; Ømulti-objective optimum design of seismic-resistant structures; and Øreliability- and cost-oriented optimal bridge maintenance planning. The book concludes with an extensive bibliography of journal papers on structural optimization published between 1987 and 1999.

Modeling Solving and Application for Topology Optimization of Continuum Structures ICM Method Based on Step Function

Modeling  Solving and Application for Topology Optimization of Continuum Structures  ICM Method Based on Step Function Book
Author : Yunkang Sui,Xirong Peng
Publisher : Butterworth-Heinemann
Release : 2017-08-29
ISBN : 0128126566
Language : En, Es, Fr & De

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Book Description :

Modelling, Solving and Applications for Topology Optimization of Continuum Structures: ICM Method Based on Step Function provides an introduction to the history of structural optimization, along with a summary of the existing state-of-the-art research on topology optimization of continuum structures. It systematically introduces basic concepts and principles of ICM method, also including modeling and solutions to complex engineering problems with different constraints and boundary conditions. The book features many numerical examples that are solved by the ICM method, helping researchers and engineers solve their own problems on topology optimization. This valuable reference is ideal for researchers in structural optimization design, teachers and students in colleges and universities working, and majoring in, related engineering fields, and structural engineers. Offers a comprehensive discussion that includes both the mathematical basis and establishment of optimization models Centers on the application of ICM method in various situations with the introduction of easily coded software Provides illustrations of a large number of examples to facilitate the applications of ICM method across a variety of disciplines

Structural Seismic Design Optimization and Earthquake Engineering Formulations and Applications

Structural Seismic Design Optimization and Earthquake Engineering  Formulations and Applications Book
Author : Plevris, Vagelis
Publisher : IGI Global
Release : 2012-05-31
ISBN : 1466616415
Language : En, Es, Fr & De

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Book Description :

Throughout the past few years, there has been extensive research done on structural design in terms of optimization methods or problem formulation. But, much of this attention has been on the linear elastic structural behavior, under static loading condition. Such a focus has left researchers scratching their heads as it has led to vulnerable structural configurations. What researchers have left out of the equation is the element of seismic loading. It is essential for researchers to take this into account in order to develop earthquake resistant real-world structures. Structural Seismic Design Optimization and Earthquake Engineering: Formulations and Applications focuses on the research around earthquake engineering, in particular, the field of implementation of optimization algorithms in earthquake engineering problems. Topics discussed within this book include, but are not limited to, simulation issues for the accurate prediction of the seismic response of structures, design optimization procedures, soft computing applications, and other important advancements in seismic analysis and design where optimization algorithms can be implemented. Readers will discover that this book provides relevant theoretical frameworks in order to enhance their learning on earthquake engineering as it deals with the latest research findings and their practical implementations, as well as new formulations and solutions.

Multiscale Structural Topology Optimization

Multiscale Structural Topology Optimization Book
Author : Liang Xia
Publisher : Elsevier
Release : 2016-04-27
ISBN : 0081011865
Language : En, Es, Fr & De

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Book Description :

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

Evolutionary Topology Optimization of Continuum Structures

Evolutionary Topology Optimization of Continuum Structures Book
Author : Xiaodong Huang,Mike Xie
Publisher : John Wiley & Sons
Release : 2010-03-11
ISBN : 9780470689479
Language : En, Es, Fr & De

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Book Description :

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.

Topology Optimization Design of Heterogeneous Materials and Structures

Topology Optimization Design of Heterogeneous Materials and Structures Book
Author : Daicong Da
Publisher : John Wiley & Sons
Release : 2020-01-09
ISBN : 1786305585
Language : En, Es, Fr & De

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Book Description :

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.

Advanced Topology Optimization Techniques for Engineering and Biomedical Problems

Advanced Topology Optimization Techniques for Engineering and Biomedical Problems Book
Author : Jaejong Park
Publisher : Unknown
Release : 2018
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Modern manufacturing advances such as layer-by-layer material joining process in 3D printing have added a new dimension to engineering design problems by providing greater flexibility. Sophisticated structural features in the internal architecture or complex geometries can be manipulated and implemented to enhance the performance of the final structure. Topology optimization is a powerful numerical tool that provides engineers an efficient way to realize innovative designs at an early design stage. It seeks the optimum distribution of limited material volume within a predefined design domain for the optimization objective against a set of constraints. This makes it an attractive tool for obtaining the non-intuitive mechanical design of complex structures in the aerospace, automotive and biomedical industries among others. Effective and systematic topology optimization methods that can fully leverage the capabilities of the recent manufacturing developments needs to be developed. In this thesis work, novel topology optimization methods are formulated which allows the design of multi-material, geometrically complex structures, and functional microstructures. A robust and effcient multi-material method for 3D topology optimization problems is formulated that breaks the original multi-material problem into a series of binary phase topology optimization problems then solves sequentially similar to the Gauss-Seidel method. The efficiency and accuracy are improved by implementing the multi-resolution technique. Using relatively coarser mesh for displacement field compared to the design and density variables allows reduced CPU time for solving the system equation. Also, a topology optimization technique to design structures in microscale is provided. Homogenization method allows analysis of composite materials by considering an effective continuum with repetitive microstructures. An objective is formulated in topology optimization that designs microstructure so that when it is repeated through the macroscopic domain, the structure can obtain a certain target elastic properties. Finally, the topological complexity can be controlled by introducing an additional geometric constraint in the formulation. Lower bound in the perimeter value, which is defined as the sum of inner and outer boundaries, can drive the final topology to have more holes. This leads to a structure with more refined load transfer paths, and it can generate structurally sound internal architectures for an effective light weighting of currently existing engineering solutions. The addition of design capabilities of multi-material, microstructures, complex geometries in this work will provide the basis of advanced manufacturing centric topology optimization framework.

Topology Design of Structures

Topology Design of Structures Book
Author : Martin P Bendse
Publisher : Kluwer Academic Pub
Release : 1993
ISBN : 9780792320555
Language : En, Es, Fr & De

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Book Description :

The efficient use of materials is of great importance, and the choice of the basic topology for the design of structures and mechanical elements is crucial for the performance of sizing of shape optimization. This volume provides a comprehensive review of the state of the art in topology design, spanning fundamental mathematical, mechanical and implementation issues. Topology design of discrete structures involves large scale computational problems and the need to select structural elements from a discrete set of possibilities. The formulation and solution of discrete design problems are described, including new applications of genetic algorithms and dual methods. For continuum problems the emphasis is on the `homogenization method', which employs composite materials as the basis for defining shape in terms of material density, unifying macroscopic structural design optimization and micromechanics. All aspects of this field are covered, including computational aspects and the use of the homogenization method in a computer-aided design environment.

Homogenization and Structural Topology Optimization

Homogenization and Structural Topology Optimization Book
Author : Behrooz Hassani,Ernest Hinton
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1447108914
Language : En, Es, Fr & De

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Book Description :

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.

An Introduction to Structural Optimization

An Introduction to Structural Optimization Book
Author : Peter W. Christensen,A. Klarbring
Publisher : Springer Science & Business Media
Release : 2008-10-14
ISBN : 1402086660
Language : En, Es, Fr & De

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Book Description :

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.

Frame Topology Optimization with Standard Cross Sections

Frame Topology Optimization with Standard Cross Sections Book
Author : Navid Changizi
Publisher : Unknown
Release : 2016
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Topology optimization is a free-form design tool that allows identification of optimized material distribution within the design domain while engineering constraints are fulfilled. Topology optimization is used to arrive at high-performance designs in a variety of engineering disciplines (e.g., such as aerospace design, micro-structure design, photonic devices and structural engineering). Structural engineering has adopted topology optimization for recommending innovative structural layouts. However, most of the research in this area uses simplified mechanics, design objectives and assumes deterministic design conditions. The simplifications in mechanics is usually manifested with employing truss finite-element models that are only capable of transferring axial loads using members with simple geometry cross sectional shapes (e.g., squares), and simple objective functions include displacement-based metrics which are directly found using finite-element method. However real-world structures are capable of transferring loads via bending and shear in addition to axial forces, and are built from standard cross-sections such as wide flange I-beams. Many of these structures are mainly designed for stress constraints, and their applications are almost always accompanied with uncertainties. These uncertainties could be, for example, due to incomplete knowledge about external loads or a result of manufacturing errors, which is the focus of this thesis. However, due to numerical and theoretical challenges, incorporation of these necessary elements within structural topology optimization is not fully developed yet. This thesis addresses these challenges for taking the initial steps towards bringing topology optimization applications closer to realistic design conditions and constraints.This thesis begins with developing a methodology to efficiently incorporate members with standard cross sections such as I-beams in structural topology optimization. To this end, standard I-beams from the American Institute of Steel Construction Design manual are selected and a relationship between cross-sectional area and other section properties such as moment of inertia is developed through advanced regression analysis. This approach allows using member cross-sectional area as the independent design variable, and explicit derivation of gradients. These gradients are used in gradient-based optimizers for increasing computational efficiency. The next contribution of this thesis is implementation of an efficient methodology for controlling von Mises yield criterion within the structure. This criterion is suitable for stress-based design of steel frames. The proposed approach determines this criterion in a set of candidate points for each element, and then approximates their maximum with an analytical function. Therefore, stress-based performance of the structure was expressed analytically with a single scalar. Moreover, gradients were derived analytically, which resulted in computational efficiency. A comparison of stress-based designs and traditional compliance-based design demonstrated the significant changes in final topology and reduction of stress maximum. Moreover, designs for optimizing a combination of compliance and stress criteria were explored. The next contribution of this thesis the incorporation of global buckling constraints to stress-based design structural topology optimization to control instability and stress modes of failures simultaneously. Global buckling was controlled with determining the minimum value of buckling load factor that is given by solving the eigenvalue problem of linear buckling analysis. In the last part of this thesis, the focus is shifted to design under uncertainty. More specifically, geometric uncertainties were considered and were modeled with random variables that defined the geometry of the structure. These uncertainties were efficiently propagated to the structural response level, measured with both stress and displacement-based criteria, using stochastic perturbation method. The design objective was to arrive at topologies that are robust (insensitive) in the presence of these geometric uncertainties. Monte Carlo simulation was used to verify the predictions and designs from the proposed methodology, and an excellent agreement was observed.

Topology Optimization in Structural and Continuum Mechanics

Topology Optimization in Structural and Continuum Mechanics Book
Author : George I. N. Rozvany,Tomasz Lewinski
Publisher : Springer Science & Business Media
Release : 2013-09-20
ISBN : 3709116430
Language : En, Es, Fr & De

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Book Description :

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.

Evolutionary Structural Optimization

Evolutionary Structural Optimization Book
Author : Y.M. Xie,Grant P. Steven
Publisher : Springer
Release : 2012-12-06
ISBN : 1447109856
Language : En, Es, Fr & De

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Book Description :

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.