Variational Methods for Structural Optimization PDF Download
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Author: Andrej Cherkaev
Publisher: Springer Science & Business Media
ISBN: 9780387984629
Category : Science
Languages : en
Pages : 578
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Book Description
This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
Author: Andrej Cherkaev
Publisher: Springer Science & Business Media
ISBN: 9780387984629
Category : Science
Languages : en
Pages : 578
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Book Description
This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
Author: Raphael T. Haftka
Publisher: Springer Science & Business Media
ISBN: 9401578621
Category : Technology & Engineering
Languages : en
Pages : 402
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Book Description
The field of structural optimization is still a relatively new field undergoing rapid changes in methods and focus. Until recently there was a severe imbalance between the enormous amount of literature on the subject, and the paucity of applications to practical design problems. This imbalance is being gradually redressed now. There is still no shortage of new publications, but there are also exciting applications of the methods of structural optimizations in the automotive, aerospace, civil engineering, machine design and other engineering fields. As a result of the growing pace of applications, research into structural optimization methods is increasingly driven by real-life problems. Most engineers who design structures employ complex general-purpose software packages for structural analysis. Often they do not have any access to the source the details of program, and even more frequently they have only scant knowledge of the structural analysis algorithms used in this software packages. Therefore the major challenge faced by researchers in structural optimization is to develop methods that are suitable for use with such software packages. Another major challenge is the high computational cost associated with the analysis of many complex real-life problems. In many cases the engineer who has the task of designing a structure cannot afford to analyze it more than a handful of times.
Author: William R. Spillers
Publisher: Springer Science & Business Media
ISBN: 0387958657
Category : Technology & Engineering
Languages : en
Pages : 304
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Book Description
Structural Optimization is intended to supplement the engineer’s box of analysis and design tools making optimization as commonplace as the finite element method in the engineering workplace. It begins with an introduction to structural optimization and the methods of nonlinear programming such as Lagrange multipliers, Kuhn-Tucker conditions, and calculus of variations. It then discusses solution methods for optimization problems such as the classic method of linear programming which leads to the method of sequential linear programming. It then proposes using sequential linear programming together with the incremental equations of structures as a general method for structural optimization. It is furthermore intended to give the engineer an overview of the field of structural optimization.
Author: Aldo Frediani
Publisher: Springer
ISBN: 3319456806
Category : Mathematics
Languages : en
Pages : 535
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Book Description
This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.
Author: Kyung K. Choi
Publisher: Springer Science & Business Media
ISBN: 0387271694
Category : Science
Languages : en
Pages : 457
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Book Description
Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.
Author: Andrej Cherkaev
Publisher: Springer
ISBN: 9781461211891
Category : Science
Languages : en
Pages : 548
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Book Description
This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
Author: Gregoire Allaire
Publisher: Springer Science & Business Media
ISBN: 1468492861
Category : Technology & Engineering
Languages : en
Pages : 470
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Book Description
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: S. Nemat-Nasser
Publisher: Elsevier
ISBN: 1483145832
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.
Author: Arturo Locatelli
Publisher: Springer Science & Business Media
ISBN: 9783764364083
Category : Education
Languages : en
Pages : 318
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Book Description
From the reviews: "The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. . . .In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-to-read fashion." —Measurement and Control
Author: Pablo Pedregal
Publisher: Springer Science & Business Media
ISBN: 9783764356972
Category : Mathematics
Languages : en
Pages : 238
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Book Description
Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the crucial and most delicate step in the so-called direct method of the calculus of variations. A fairly large amount of work has been devoted to determine under what assumptions we can have this lower semicontinuity with respect to weak topologies for nonlin ear functionals in the form of integrals. The conclusion of all this work is that some type of convexity, understood in a broader sense, is usually involved.
