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Author: Juan Casado-Díaz
Publisher: Springer Nature
ISBN: 3030981916
Category : Mathematics
Languages : en
Pages : 119
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Book Description
This book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book. It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of these more general materials. In general, we do not dispose of an explicit representation, and then, to numerically solve the problem, it is necessary to design strategies that allow the functional to be replaced by upper or lower approximations. The book is divided in four chapters. The first is devoted to recalling some classical results related to the homogenization of a sequence of linear elliptic partial differential problems. In the second one, we define the control problem that we are mainly interested in solving in the book. We obtain a relaxed formulation and their main properties, including an explicit representation of the new cost functional, at least in the boundary of its domain. In the third chapter, we study the optimality conditions of the relaxed problem, and we describe some algorithms to numerically solve the problem. We also provide some numerical experiments carried out using such algorithms. Finally, the fourth chapter is devoted to briefly describe some extensions of the results obtained in Chapters 2 and 3 to the case of dealing with several state equations and the case of evolutive problems. The problems covered in the book are interesting for mathematicians and engineers whose work is related to mathematical modeling and the numerical resolution of optimal design problems in material sciences. The contents extend some previous results obtained by the author in collaboration with other colleagues.
Author: Juan Casado-Díaz
Publisher: Springer Nature
ISBN: 3030981916
Category : Mathematics
Languages : en
Pages : 119
Get Book Here
Book Description
This book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book. It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of these more general materials. In general, we do not dispose of an explicit representation, and then, to numerically solve the problem, it is necessary to design strategies that allow the functional to be replaced by upper or lower approximations. The book is divided in four chapters. The first is devoted to recalling some classical results related to the homogenization of a sequence of linear elliptic partial differential problems. In the second one, we define the control problem that we are mainly interested in solving in the book. We obtain a relaxed formulation and their main properties, including an explicit representation of the new cost functional, at least in the boundary of its domain. In the third chapter, we study the optimality conditions of the relaxed problem, and we describe some algorithms to numerically solve the problem. We also provide some numerical experiments carried out using such algorithms. Finally, the fourth chapter is devoted to briefly describe some extensions of the results obtained in Chapters 2 and 3 to the case of dealing with several state equations and the case of evolutive problems. The problems covered in the book are interesting for mathematicians and engineers whose work is related to mathematical modeling and the numerical resolution of optimal design problems in material sciences. The contents extend some previous results obtained by the author in collaboration with other colleagues.
Author: P. Pedersen
Publisher: Elsevier
ISBN: 0444600302
Category : Technology & Engineering
Languages : en
Pages : 528
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Book Description
Optimal design with advanced materials is becoming a very progressive and challenging domain within applied mechanics. The increasing use of advanced materials, such as anisotropic fiber composites and ceramics, is instigating new developments to be made within constitutive modelling and the computational methods of analysis, sensitivity analysis and optimization. A new dimension of optimal design is being realised by the direct tailoring and building of new materials. Research in this area is accelerating rapidly with the results already being applied to high technology industries. Two vital high technology research areas covered in this volume include homogenization and smart materials/structures. The 31 papers will prove an indispensable reference source for all those involved in the interdisciplinary research and development aspects of mechanics, materials and mathematics in the design of advanced materials.
Author: Fernando Fraternali
Publisher: Frontiers Media SA
ISBN: 2889631850
Category :
Languages : en
Pages : 180
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Book Description
Author: Linda M. Collins
Publisher: Springer
ISBN: 3319722069
Category : Social Science
Languages : en
Pages : 319
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Book Description
This book presents a framework for development, optimization, and evaluation of behavioral, biobehavioral, and biomedical interventions. Behavioral, biobehavioral, and biomedical interventions are programs with the objective of improving and maintaining human health and well-being, broadly defined, in individuals, families, schools, organizations, or communities. These interventions may be aimed at, for example, preventing or treating disease, promoting physical and mental health, preventing violence, or improving academic achievement. This volume introduces the multiphase optimization strategy (MOST), pioneered at The Methodology Center at the Pennsylvania State University, as an alternative to the classical approach of relying solely on the randomized controlled trial (RCT). MOST borrows heavily from perspectives taken and approaches used in engineering, and also integrates concepts from statistics and behavioral science, including the RCT. As described in detail in this book, MOST consists of three phases: preparation, in which the conceptual model underlying the intervention is articulated; optimization, in which experimentation is used to gather the information necessary to identify the optimized intervention; and evaluation, in which the optimized intervention is evaluated in a standard RCT. Through numerous examples, the book demonstrates that MOST can be used to develop interventions that are more effective, efficient, economical, and scalable. Optimization of Behavioral, Biobehavioral, and Biomedical Interventions: The Multiphase Optimization Strategy is the first book to present a comprehensive introduction to MOST. It will be an essential resource for behavioral, biobehavioral, and biomedical scientists; statisticians, biostatisticians, and analysts working in epidemiology and public health; and graduate-level courses in development and evaluation of interventions.
Author: United States. Office of Saline Water
Publisher:
ISBN:
Category : Saline water conversion
Languages : en
Pages : 918
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Book Description
Author: Daicong Da
Publisher: John Wiley & Sons
ISBN: 1119687578
Category : Mathematics
Languages : en
Pages : 200
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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.
Author: C Soutis
Publisher: Elsevier
ISBN: 1845690842
Category : Technology & Engineering
Languages : en
Pages : 525
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Book Description
One of the most important and exciting areas of composites research is the development of modelling techniques to predict the response of composite materials to different types of stress. Predictive modelling provides the opportunity both to understand better how composites behave in different conditions and to develop materials with enhanced performance for particular industrial applications. Multi-scale modelling of composite material systems summarises the key research in this area and its implications for industry.The book covers modelling approaches ranging from the micron to the metre in scale, and from the single fibre to complete composite structures. Individual chapters discuss a variety of material types from laminates and fibre-reinforced composites to monolithic and sandwich composites. They also analyse a range of types of stress and stress response from fracture and impact to wear and fatigue. Authors also discuss the strengths and weaknesses of particular models.With its distinguished editors and international team of contributors, Multi-scale modelling of composite material systems is a standard reference for both academics and manufacturers in such areas as aerospace, automotive and civil engineering. Extensive coverage of this important and exciting area of composites research Understand how composites behave in different circumstances Compiled by an expert panel of authors and editors
Author: P. Ponte Castaneda
Publisher: Springer Science & Business Media
ISBN: 1402026234
Category : Technology & Engineering
Languages : en
Pages : 371
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Book Description
Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended. The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods – both analytical and computational – for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior. All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods.
Author: Xiujuan Zhang
Publisher: Open Dissertation Press
ISBN: 9781374719798
Category : Technology & Engineering
Languages : en
Pages : 250
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Book Description
This dissertation, "An Effective Design Method for Components Made of a Multiphase Perfect Material" by Xiujuan, Zhang, 張秀娟, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled An Effective Design Method for Components Made of a Multiphase Perfect Material Submitted by Zhang, Xiujuan for the Degree of Doctor of Philosophy at The University of Hong Kong in November 2004 As technology continues to develop rapidly, requirements for special functions of components are becoming ever more demanding. Since different regions of a component may have different special requirements, components made of a single material cannot meet all special requirements in their different regions. It is therefore necessary to use components made of different materials and also optimize the use of different materials, in much the same way as materials such as bamboo, tooth, and bone have naturally evolved over time to fulfill their functions perfectly. A component with a perfect combination of different materials in its different regions for a specific application is termed a component made of a multiphase perfect material (CMMPM). Such components need to satisfy many requirements and their corresponding constraints. A systematic design method has therefore been developed and is implemented from functional requirements to the component configuration, to material properties, and to material microstructures and constituent compositions. Based on the new design method, this study further develops the detailed approaches and their computer software prototypes for determining the optimal material iproperties needed in different regions of the component according to its functional requirements, and for selecting the optimal material constituent compositions and microstructures in different regions of the component according to the optimal material properties required. For determining optimal material properties, an algorithm of sensitivity analysis and optimization for the implicit relationship expression determined by the finite element analysis is developed, because the relationship between the component's objective performances and the material properties in different regions is very difficult to be expressed in the form of accurate functions and thus conventional optimization methods cannot be applied. For selecting materials, a material database for designing CMMPMs and an improved Genetic Algorithm (GA) are developed. The database is developed to cover homogeneous materials and different types of heterogeneous materials, and includes a novel sub-database for heterogeneous materials with a periodic microstructure developed from topology optimization and homogenization theories. In the improved GA, the "family tree" concept is adopted to evaluate the degree of homology between chromosomes, in order to reduce inbreeding and premature convergence. During the material selection using the improved GA, a special constraint was considered, namely the material affinity of two adjacent material regions. The criteria of chemical affinity and physical affinity between different materials were defined, developed, and used to evaluate the priority of two different materials to be selected. iiSome design examples are introduced using the approaches developed. Components that could not be obtained by conventional design methods were designed successfully, demonstrating that designers can use the method to design their CMMPMs to meet special functional requirements in high-tech applications effec
Author:
Publisher:
ISBN:
Category : Engineering design
Languages : en
Pages : 712
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Book Description
