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Author: Juan Casado-Díaz Publisher: Springer Nature ISBN: 3030981916 Category : Mathematics Languages : en Pages : 119
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
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: H.C. Rodrigues Publisher: Springer ISBN: 3319977733 Category : Technology & Engineering Languages : en Pages : 1486
Book Description
The papers in this volume focus on the following topics: design optimization and inverse problems, numerical optimization techniques,efficient analysis and reanalysis techniques, sensitivity analysis and industrial applications. The conference EngOpt brings together engineers, applied mathematicians and computer scientists working on research, development and practical application of optimization methods in all engineering disciplines and applied sciences.
Author: Daicong Da Publisher: John Wiley & Sons ISBN: 1119687578 Category : Mathematics Languages : en Pages : 206
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
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: Linda M. Collins Publisher: Springer ISBN: 3319722069 Category : Social Science Languages : en Pages : 319
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: P. Ponte Castaneda Publisher: Springer Science & Business Media ISBN: 1402026234 Category : Technology & Engineering Languages : en Pages : 371
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: Ali Jahan Publisher: Butterworth-Heinemann ISBN: 0081005415 Category : Technology & Engineering Languages : en Pages : 254
Book Description
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials in Product Design, Second Edition, provides readers with tactics they can use to optimally select materials to satisfy complex design problems when they are faced with the vast range of materials available. Current approaches to materials selection range from the use of intuition and experience, to more formalized computer-based methods, such as electronic databases with search engines to facilitate the materials selection process. Recently, multi-criteria decision-making (MCDM) methods have been applied to materials selection, demonstrating significant capability for tackling complex design problems. This book describes the rapidly growing field of MCDM and its application to materials selection. It aids readers in producing successful designs by improving the decision-making process. This new edition updates and expands previous key topics, including new chapters on materials selection in the context of design problem-solving and multiple objective decision-making, also presenting a significant amount of additional case studies that will aid in the learning process. - Describes the advantages of Quality Function Deployment (QFD) in the materials selection process through different case studies - Presents a methodology for multi-objective material design optimization that employs Design of Experiments coupled with Finite Element Analysis - Supplements existing quantitative methods of materials selection by allowing simultaneous consideration of design attributes, component configurations, and types of material - Provides a case study for simultaneous materials selection and geometrical optimization processes
Author: Juan Casado-Díaz
Author: Juan Casado-Díaz
Author: Fernando Fraternali
Author: United States. Office of Saline Water
Author: H.C. Rodrigues
Author: Daicong Da
Author: C Soutis
Author: Linda M. Collins
Author: P. Ponte Castaneda
Author: Ali Jahan
Author: