The Stochastic Finite Element Method
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| Author | : Vissarion Papadopoulos |
| Publisher | : Springer |
| Total Pages | : 151 |
| Release | : 2017-10-28 |
| Genre | : Science |
| ISBN | : 3319645285 |
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 | : Roger G. Ghanem |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 217 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461230942 |
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 | : Achintya Haldar |
| Publisher | : John Wiley & Sons |
| Total Pages | : 356 |
| Release | : 2000-05-22 |
| Genre | : Technology & Engineering |
| ISBN | : 9780471369615 |
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 |
| Total Pages | : 336 |
| Release | : 1993-02-02 |
| Genre | : Technology & Engineering |
| ISBN | : 9780471936268 |
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 |
| Total Pages | : 282 |
| Release | : 2003 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198526315 |
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 | : Sukanta Nayak |
| Publisher | : Academic Press |
| Total Pages | : 170 |
| Release | : 2018-01-23 |
| Genre | : Technology & Engineering |
| ISBN | : 0128129743 |
Interval Finite Element Method with MATLAB provides a thorough introduction to an effective way of investigating problems involving uncertainty using computational modeling. The well-known and versatile Finite Element Method (FEM) is combined with the concept of interval uncertainties to develop the Interval Finite Element Method (IFEM). An interval or stochastic environment in parameters and variables is used in place of crisp ones to make the governing equations interval, thereby allowing modeling of the problem. The concept of interval uncertainties is systematically explained. Several examples are explored with IFEM using MATLAB on topics like spring mass, bar, truss and frame. - Provides a systematic approach to understanding the interval uncertainties caused by vague or imprecise data - Describes the interval finite element method in detail - Gives step-by-step instructions for how to use MATLAB code for IFEM - Provides a range of examples of IFEM in use, with accompanying MATLAB codes
| Author | : Achintya Haldar |
| Publisher | : World Scientific |
| Total Pages | : 437 |
| Release | : 1997 |
| Genre | : Technology & Engineering |
| ISBN | : 9810231288 |
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 | : Christian A. Schenk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 184 |
| Release | : 2005-06-08 |
| Genre | : Technology & Engineering |
| ISBN | : 9783540253433 |
The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. To foster these developments, novel computational procedures for the uncertainty assessment of large finite element systems are presented in this monograph. The stochastic input is modeled by the so-called Karhunen-Loève expansion, which is formulated in this context both for scalar and vector stochastic processes as well as for random fields. Particularly for strongly non-linear structures and systems the direct Monte Carlo simulation technique has proven to be most advantageous as method of solution. The capabilities of the developed procedures are demonstrated by showing some practical applications.
| Author | : Anders Logg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 723 |
| Release | : 2012-02-24 |
| Genre | : Computers |
| ISBN | : 3642230997 |
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
| Author | : T. Ariaratnam |
| Publisher | : CRC Press |
| Total Pages | : 396 |
| Release | : 2020-12-17 |
| Genre | : Mathematics |
| ISBN | : 1000109933 |
This book contains a series of original contributions in the area of Stochastic Dynamics, which demonstrates the impact of Mike Lin's research and teaching in the area of random vibration and structural dynamics.
