Stochastic Finite Elements: A Spectral Approach PDF Download
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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 Here
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: Vissarion Papadopoulos
Publisher: Springer
ISBN: 3319645285
Category : Science
Languages : en
Pages : 151
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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: Achintya Haldar
Publisher: John Wiley & Sons
ISBN: 9780471369615
Category : Technology & Engineering
Languages : en
Pages : 356
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Book Description
The first complete guide to using the Stochastic Finite Element Method for reliability assessment Unlike other analytical reliability estimation techniques, the Stochastic Finite Element Method (SFEM) can be used for both implicit and explicit performance functions, making it a particularly powerful and robust tool for today's engineer. This book, written by two pioneers in SFEM-based methodologies, shows how to use SFEM for the reliability analysis of a wide range of structures. It begins by reviewing essential risk concepts, currently available risk evaluation procedures, and the use of analytical and sampling methods in estimating risk. Next, it introduces SFEM evaluation procedures, with detailed coverage of displacement-based and stress-based deterministic finite element approaches. Linear, nonlinear, static, and dynamic problems are considered separately to demonstrate the robustness of the methods. The risk or reliability estimation procedure for each case is presented in different chapters, with theory complemented by a useful series of examples. Integrating advanced concepts in risk-based design, finite elements, and mechanics, Reliability Assessment Using Stochastic Finite Element Analysis is vital reading for engineering professionals and students in all areas of the field.
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: 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: Gautam Dasgupta
Publisher: Springer
ISBN: 1493974238
Category : Technology & Engineering
Languages : en
Pages : 358
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Book Description
This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids. The book is divided into two distinct parts of nine chapters and seven appendices. The first chapter reviews the energy concepts in structural mechanics with bar problems, which is continued in the next chapter for truss analysis using Mathematica programs. The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed by four-node elements. Chapters five and six describe Taig’s isoparametric interpolants and Iron’s patch test. Rayleigh vector modes, which satisfy point-wise equilibrium, are elaborated on in chapter seven along with successful patch tests in the physical (x,y) Cartesian frame. Chapter eight explains point-wise incompressibility and employs (Moore-Penrose) inversion of rectangular matrices. The final chapter analyzes patch-tests in all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed in closed algebraic form. Appendices give a short introduction to Mathematica, followed by truss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. All Mathematica codes for theoretical formulations and graphics are included with extensive numerical examples.
Author: Achintya Haldar
Publisher: World Scientific
ISBN: 9810231288
Category : Technology & Engineering
Languages : en
Pages : 437
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Book Description
The functionality of modern structural, mechanical and electrical or electronic systems depends on their ability to perform under uncertain conditions. Consideration of uncertainties and their effect on system behavior is an essential and integral part of defining systems. In eleven chapters, leading experts present an overview of the current state of uncertainty modeling, analysis and design of large systems in four major areas: finite and boundary element methods (common structural analysis techniques), fatigue, stability analysis, and fault-tolerant systems. The content of this book is unique; it describes exciting research developments and challenges in emerging areas, and provide a sophisticated toolbox for tackling uncertainty modeling in real systems.
Author: Gouri Dhatt
Publisher: John Wiley & Sons
ISBN: 1118569709
Category : Mathematics
Languages : en
Pages : 495
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Book Description
This book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences. The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus. The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.
Author: Peter I. Kattan
Publisher: Springer Science & Business Media
ISBN: 3540706984
Category : Technology & Engineering
Languages : en
Pages : 430
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Book Description
later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me (pkattan@tedata. net. jo and pkattan@lsu. edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.
Author: I. St Doltsinis
Publisher: WIT Press
ISBN: 1845646266
Category : Mathematics
Languages : en
Pages : 379
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Book Description
The increasing industrial demand for reliable quantification and management of uncertainty in product performance forces engineers to employ probabilistic models in analysis and design, a fact that has occasioned considerable research and development activities in the field. Notes on Stochastics eventually address the topic of computational stochastic mechanics. The single volume uniquely presents tutorials on essential probabilistics and statistics, recent finite element methods for stochastic analysis by Taylor series expansion as well as Monte Carlo simulation techniques. Design improvement and robust optimisation represent key issues as does reliability assessment. The subject is developed for solids and structures of elastic and elasto-plastic material, large displacements and material deformation processes; principles are transferable to various disciplines. A chapter is devoted to the statistical comparison of systems exhibiting random scatter. Where appropriate examples illustrate the theory, problems to solve appear instructive; applications are presented with relevance to engineering practice. The book, emanating from a university course, includes research and development in the field of computational stochastic analysis and optimization. It is intended for advanced students in engineering and for professionals who wish to extend their knowledge and skills in computational mechanics to the domain of stochastics. Contents: Introduction, Randomness, Structural analysis by Taylor series expansion, Design optimization, Robustness, Monte Carlo techniques for system response and design improvement, Reliability, Time variant phenomena, Material deformation processes, Analysis and comparison of data sets, Probability distribution of test functions.
