Treatment Of Uncertainties In Finite Element Analysis
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Uncertainty Assessment Of Large Finite Element Systems
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Author : Christian A. Schenk
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-08
Uncertainty Assessment Of Large Finite Element Systems written by Christian A. Schenk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-08 with Technology & Engineering categories.
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.
Treatment Of Uncertainties In Finite Element Analysis
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Author : Masayuki Moriyama
language : en
Publisher:
Release Date : 1990
Treatment Of Uncertainties In Finite Element Analysis written by Masayuki Moriyama and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Nondeterministic Linear Static Finite Element Analysis
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Author : Hao Zhang
language : en
Publisher:
Release Date : 2005
Nondeterministic Linear Static Finite Element Analysis written by Hao Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Finite element method categories.
This thesis presents a nontraditional treatment for uncertainties in the material, geometry, and load parameters in linear static finite element analysis (FEA) for mechanics problems. Uncertainties are introduced as bounded possible values (intervals). FEA with interval parameters (interval FEA, IFEA) calculates the bounds on the system response based on the ranges of the system parameters. The obtained results should be accurate and efficiently computed. Toward this end, a rigorous interval FEA is developed and implemented. In this study, interval arithmetic is used in the formulation to guarantee an enclosure for the response range. The main difficulty associated with interval computation is the dependence problem, which results in severe overestimation of the system response ranges. Particular attention in the development of the present method is given to control the dependence problem for sharp results. The developed method is based on an Element-By-Element (EBE) technique. By using the EBE technique, the interval parameters can be handled more efficiently to control the dependence problem. The penalty method and Lagrange multiplier method are used to impose the necessary constraints for compatibility and equilibrium. The resulting structure equations are a system of parametric linear interval equations. The standard fixed point iteration is modified, enhanced, and used to solve the interval equations accurately and efficiently. The newly developed dependence control algorithm ensures the convergence of the fixed point iteration even for problems with relatively large uncertainties. Further, special algorithms have been developed to calculate sharp results for stress and element nodal force. The present method is generally applicable to linear static interval FEA, regardless of element type. Numerical examples are presented to demonstrate the capabilities of the developed method. It is illustrated that the present method yields rigorous and accurate results which are guaranteed to enclose the true response ranges in all the problems considered, including those with a large number of interval variables (e.g., more than 250). The scalability of the present method is also illustrated. In addition to its accuracy, rigorousness and scalability, the efficiency of the present method is also significantly superior to conventional methods such as the combinatorial, the sensitivity analysis, and the Monte Carlo sampling method.
Uncertain Analysis In Finite Elements Models
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Author : Wenhui Mo
language : en
Publisher: Bentham Science Publishers
Release Date : 2022-08-31
Uncertain Analysis In Finite Elements Models written by Wenhui Mo and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Science categories.
This book explains uncertainty analysis for finite elements and general nonlinear problems. It starts with the fundamentals of the topic and progresses to complex methods through 9 chapters. Each chapter focuses on a specific, relevant topic and provides information in a structured reading format for advanced learners. The author explains different models relevant to the topic where applicable, in an effort to cover the diverse aspects of mathematical analysis. Topics covered in the book include: - Nonlinear stochastic finite element methods - Reliability calculations - Static analysis of interval finite element - Linear and nonlinear vibration analysis - Stochastic, random, fuzzy and mixed fields - Mixed finite element analysis Uncertainty Analysis in Finite Elements Models is an ideal reference for advanced courses in mathematical analysis and engineering that require students to understand the basics of uncertainty analysis and basic reliability calculations.
Uncertainty Modeling In Finite Element Fatigue And Stability Of Systems
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Author : Achintya Haldar
language : en
Publisher: World Scientific
Release Date : 1997
Uncertainty Modeling In Finite Element Fatigue And Stability Of Systems written by Achintya Haldar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Technology & Engineering categories.
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.
Uncertain Input Data Problems And The Worst Scenario Method
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Author : Ivan Hlavacek
language : en
Publisher: Elsevier
Release Date : 2004-12-09
Uncertain Input Data Problems And The Worst Scenario Method written by Ivan Hlavacek and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-09 with Science categories.
This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience. · Rigorous theory is established for the treatment of uncertainty in modeling· Uncertainty is considered in complex models based on partial differential equations or variational inequalities · Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more · Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present· Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form· Fairly self-contained book
Non Intrusive Finite Element Reliability Analysis
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Author : Iason Papaioannou
language : en
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2013-01
Non Intrusive Finite Element Reliability Analysis written by Iason Papaioannou and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01 with categories.
In order to motivate the incorporation of reliability concepts in the structural design and analysis procedures, the engineering community is in need of finite element (FE) software with capabilities of including the stochastic nature of input parameters. This book focuses on the modeling of uncertainties in structural systems and on strategies for the reliability assessment of structures analyzed by FE programs. Concepts are introduced for the numerical treatment of spatially varied uncertain quantities through the discretization of the relevant random fields as well as for robust and efficient finite element reliability analysis and updating of the reliability in light of new information. The presented reliability methods are termed non-intrusive, since they can be programmed in a stand alone fashion without requiring access to the core routines of the FE software.
Characterizing Uncertainty To Manage Risk In Spacecraft Development With Application To Structures And Mass
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Author : Emily Baker Clements
language : en
Publisher:
Release Date : 2013
Characterizing Uncertainty To Manage Risk In Spacecraft Development With Application To Structures And Mass written by Emily Baker Clements and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Most space programs experience significant cost and schedule growth over the course of program development. Poor uncertainty management has been identified as one of the leading causes of program cost and schedule overruns. Traditional methods of uncertainty management are deterministic, using industry standards to predict worst-case inputs and designing systems accordingly. However, this method can lead to inefficient use of resources due to excessive need for redesign of subsystems when other subsystems evolve. Improvements in computational power now allow more sophisticated uncertainty analysis methods using probabilistic techniques. We propose a spacecraft design methodology that uses Monte Carlo and Gradient-based Sensitivity Analysis of system models to reduce program cost and schedule overruns by identifying design issues early when redesign is less expensive. We cover applications to mass budgets and finite element analysis to illustrate this methodology. The META complexity metric is a measure of uncertainty of a quantity of interest based on exponential entropy from information theory. The Trapped Energetic Radiation Satellite (TERSat) structural design process is used as a test case to evaluate the methodology, with a focus on the mass budget and finite element analysis. While traditionally mass budget uncertainty is treated with margins and contingencies, we present a way to model the mass of a system and its components as probability distributions using studies of historical data to model the means and standard deviations. We propagate the uncertainties in the mass budget analysis through the TERSat finite element model to determine the effects of the uncertainty on structural analysis outputs. We show that uncertainty analysis and sensitivity analysis can help to identify design issues early and guide the redesign and refine processes for spacecraft development.
The Scaled Boundary Finite Element Method
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Author : John P. Wolf
language : en
Publisher: John Wiley & Sons
Release Date : 2003-03-14
The Scaled Boundary Finite Element Method written by John P. Wolf and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-14 with Technology & Engineering categories.
A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
A Unified Approach To The Finite Element Method And Error Analysis Procedures
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Author : Julian A. T. Dow
language : en
Publisher: Elsevier
Release Date : 1998-11-09
A Unified Approach To The Finite Element Method And Error Analysis Procedures written by Julian A. T. Dow and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-09 with Technology & Engineering categories.
A Unified Approach to the Finite Element Method and Error Analysis Procedures provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. New, simpler element formulation techniques, model-independent results, and error measures New polynomial-based methods for identifying critical points New procedures for evaluating sheer/strain accuracy Accessible to undergraduates, insightful to researchers, and useful to practitioners Taylor series (polynomial) based Intuitive elemental and point-wise error measures Essential background information provided in 12 appendices