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Author : Jaroslav Haslinger
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (897 download)
Download or read book A shape optimization approach to free boundary value problems written by Jaroslav Haslinger and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jan Sokolowski
Publisher : Springer Science & Business Media
ISBN 13 : 3642581064
Total Pages : 254 pages
Book Rating : 4.6/5 (425 download)
Download or read book Introduction to Shape Optimization written by Jan Sokolowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Michel C. Delfour
Publisher : Springer Science & Business Media
ISBN 13 : 9401127107
Total Pages : 469 pages
Book Rating : 4.4/5 (11 download)
Download or read book Shape Optimization and Free Boundaries written by Michel C. Delfour and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization deals with problems where the design or control variable is no longer a vector of parameters or functions but the shape of a geometric domain. They include engineering applications to shape and structural optimization, but also original applications to image segmentation, control theory, stabilization of membranes and plates by boundary variations, etc. Free and moving boundary problems arise in an impressingly wide range of new and challenging applications to change of phase. The class of problems which are amenable to this approach can arise from such diverse disciplines as combustion, biological growth, reactive geological flows in porous media, solidification, fluid dynamics, electrochemical machining, etc. The objective and orginality of this NATO-ASI was to bring together theories and examples from shape optimization, free and moving boundary problems, and materials with microstructure which are fundamental to static and dynamic domain and boundary problems.
Author : Timo Tiihonen
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.0/5 ( download)
Download or read book Shape Optimization and Unilateral Boundary Value Problems written by Timo Tiihonen and published by . This book was released on 1987 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Haslinger
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (897 download)
Download or read book Shape Optimization and Fictious Domain Approach for Solving Free-boundary Value Problems of Bernoulli Type written by J. Haslinger and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Roland Glowinski
Publisher : CRC Press
ISBN 13 : 1420011154
Total Pages : 474 pages
Book Rating : 4.4/5 (2 download)
Download or read book Free and Moving Boundaries written by Roland Glowinski and published by CRC Press. This book was released on 2007-06-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of mo
Author : Hideyuki Azegami
Publisher : Springer Nature
ISBN 13 : 9811576181
Total Pages : 646 pages
Book Rating : 4.8/5 (115 download)
Download or read book Shape Optimization Problems written by Hideyuki Azegami and published by Springer Nature. This book was released on 2020-09-30 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.
Author : Timo Tiihonen
Publisher :
ISBN 13 : 9789513407063
Total Pages : 19 pages
Book Rating : 4.4/5 (7 download)
Download or read book Shape Optimization and Trial Methods for Free Boundary Problems written by Timo Tiihonen and published by . This book was released on 1996 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gernot Beer
Publisher : Springer Nature
ISBN 13 : 3030233391
Total Pages : 335 pages
Book Rating : 4.0/5 (32 download)
Download or read book The Isogeometric Boundary Element Method written by Gernot Beer and published by Springer Nature. This book was released on 2019-09-21 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.
Author : Dorin Bucur
Publisher : Springer Science & Business Media
ISBN 13 : 0817644032
Total Pages : 218 pages
Book Rating : 4.8/5 (176 download)
Download or read book Variational Methods in Shape Optimization Problems written by Dorin Bucur and published by Springer Science & Business Media. This book was released on 2006-09-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Author : Helmut Harbrecht
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (981 download)
Download or read book Shape Optimization for Free Boundary Problems written by Helmut Harbrecht and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gunther H. Peichl
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (897 download)
Download or read book Shape optimization for mixed boundary value problems based on an embedding domain method written by Gunther H. Peichl and published by . This book was released on 1995 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kumar Muthuraman
Publisher : Now Publishers Inc
ISBN 13 : 1601981686
Total Pages : 94 pages
Book Rating : 4.6/5 (19 download)
Download or read book Solving Free-boundary Problems with Applications in Finance written by Kumar Muthuraman and published by Now Publishers Inc. This book was released on 2008 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outlines and explains a recent computational method that solves free boundary problems by reducing them into a sequence of fixed boundary problems which are relatively easy to solve numerically.
Author : J. Haslinger
Publisher : SIAM
ISBN 13 : 9780898718690
Total Pages : 291 pages
Book Rating : 4.7/5 (186 download)
Download or read book Introduction to Shape Optimization written by J. Haslinger and published by SIAM. This book was released on 2003-01-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization comprehensively, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Applications include contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics. Audience: the book is written primarily for students of applied mathematics, scientific computing, and mechanics. Most of the material is directed toward graduate students, although a portion of it is suitable for senior undergraduate students. Readers are assumed to have some knowledge of partial differential equations and their numerical solution, as well as modern programming language such as C++ Fortran 90.
Author : Hiromichi Itou
Publisher : Springer
ISBN 13 : 9789811096723
Total Pages : 231 pages
Book Rating : 4.0/5 (967 download)
Download or read book Mathematical Analysis of Continuum Mechanics and Industrial Applications written by Hiromichi Itou and published by Springer. This book was released on 2018-06-29 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.
Author : Gregoire Allaire
Publisher : Springer Science & Business Media
ISBN 13 : 1468492861
Total Pages : 470 pages
Book Rating : 4.4/5 (684 download)
Download or read book Shape Optimization by the Homogenization Method written by Gregoire Allaire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Subrata Mukherjee
Publisher : CRC Press
ISBN 13 : 1420027867
Total Pages : 247 pages
Book Rating : 4.4/5 (2 download)
Download or read book Boundary Methods written by Subrata Mukherjee and published by CRC Press. This book was released on 2005-03-17 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Methods: Elements, Contours, and Nodes presents the results of cutting-edge research in boundary-based mesh-free methods. These methods combine the dimensionality advantage of the boundary element method with the ease of discretization of mesh-free methods, both of which, for some problems, hold distinct advantages over the finite element
