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Author: Roger G. Ghanem
Publisher: Springer Science & Business Media
ISBN: 1461230942
Category : Science
Languages : en
Pages : 217
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Book Description
This monograph considers engineering systems with random parame ters. Its context, format, and timing are correlated with the intention of accelerating the evolution of the challenging field of Stochastic Finite Elements. The random system parameters are modeled as second order stochastic processes defined by their mean and covari ance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used' to represent these processes in terms of a countable set of un correlated random vari ables. Thus, the problem is cast in a finite dimensional setting. Then, various spectral approximations for the stochastic response of the system are obtained based on different criteria. Implementing the concept of Generalized Inverse as defined by the Neumann Ex pansion, leads to an explicit expression for the response process as a multivariate polynomial functional of a set of un correlated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral repre sentation in terms of the Polynomial Chaoses is identified. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.
Author: Roger G. Ghanem
Publisher: Springer Science & Business Media
ISBN: 1461230942
Category : Science
Languages : en
Pages : 217
Get Book
Book Description
This monograph considers engineering systems with random parame ters. Its context, format, and timing are correlated with the intention of accelerating the evolution of the challenging field of Stochastic Finite Elements. The random system parameters are modeled as second order stochastic processes defined by their mean and covari ance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used' to represent these processes in terms of a countable set of un correlated random vari ables. Thus, the problem is cast in a finite dimensional setting. Then, various spectral approximations for the stochastic response of the system are obtained based on different criteria. Implementing the concept of Generalized Inverse as defined by the Neumann Ex pansion, leads to an explicit expression for the response process as a multivariate polynomial functional of a set of un correlated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral repre sentation in terms of the Polynomial Chaoses is identified. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.
Author: Roger Ghanem
Publisher: Springer Verlag
ISBN: 9780387974569
Category : Technology & Engineering
Languages : en
Pages : 214
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Book Description
A comprehensive treatment of the theories and concepts behind analyzing a class of discrete mathematical models of engineering systems whose properties and excitations can be represented as random processes. The spectral approach extends the deterministic finite element method to the space of random functions. Addressed to students and researchers in mechanical and other branches of engineering. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Vissarion Papadopoulos
Publisher: Springer
ISBN: 3319645285
Category : Science
Languages : en
Pages : 138
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Book Description
The book provides a self-contained treatment of stochastic finite element methods. It helps the reader to establish a solid background on stochastic and reliability analysis of structural systems and enables practicing engineers to better manage the concepts of analysis and design in the presence of uncertainty. The book covers the basic topics of computational stochastic mechanics focusing on the stochastic analysis of structural systems in the framework of the finite element method. The target audience primarily comprises students in a postgraduate program specializing in structural engineering but the book may also be beneficial to practicing engineers and research experts alike.
Author: Olivier Le Maitre
Publisher: Springer Science & Business Media
ISBN: 9048135206
Category : Science
Languages : en
Pages : 542
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Book Description
This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Author: Adnan Ibrahimbegović
Publisher: IOS Press
ISBN: 9781586034795
Category : Structural analysis (Engineering)
Languages : en
Pages : 428
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Book Description
Author: Jan S. Hesthaven
Publisher: Springer Science & Business Media
ISBN: 3642153372
Category : Mathematics
Languages : en
Pages : 507
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Book Description
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Author: K.J Bathe
Publisher: Elsevier
ISBN: 9780080529479
Category : Science
Languages : en
Pages : 2524
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Book Description
Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics. Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design. The eight tasks are: The automatic solution of mathematical models Effective numerical schemes for fluid flows The development of an effective mesh-free numerical solution method The development of numerical procedures for multiphysics problems The development of numerical procedures for multiscale problems The modelling of uncertainties The analysis of complete life cycles of systems Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features Bridges the gap between academic researchers and practitioners in industry Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis
Author: Isaac Elishakoff
Publisher: Oxford University Press, USA
ISBN: 9780198526315
Category : Language Arts & Disciplines
Languages : en
Pages : 282
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Book Description
The finite element method (FEM) can be successfully applied to various field problems in solid mechanics, fluid mechanics and electrical engineering. This text discusses finite element methods for structures with large stochastic variations.
Author: Michael Kleiber
Publisher: Wiley
ISBN: 9780471936268
Category : Technology & Engineering
Languages : en
Pages : 336
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Book Description
Combines two crucial techniques created to deal with complex problems of modern engineering--the finite element method and stochastic analysis. By utilizing the computationally effective finite element approach, it offers a means to obtain extremely useful insight into the way in which ever-existing structural uncertainties propagate. Includes the latest research on the topic of stochastic finite elements. Computer programs, available on request, demonstrate the theory.
Author: Michael Breitner
Publisher: Springer Science & Business Media
ISBN: 3540742387
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This book shows how modern Applied Mathematics influences everyday life. It features contributors from universities, research institutions and industry, who combine research and review papers to present a survey of current research. More than 20 contributions are divided into scales: nano, micro, macro, space and real life. In addition, coverage includes engaging and informative case studies as well as complex graphics and illustrations, many of them in color.
