Error Controlled Adaptive Finite Elements In Solid Mechanics

Author : Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich
Publisher : John Wiley & Sons
Page : 422 pages
File Size : 44,5 Mb
Release : 2003-08-01
Category : Technology & Engineering
ISBN : 9780470857977

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Error-controlled Adaptive Finite Elements in Solid Mechanics by Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich Pdf

Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. * First book to go beyond the Finite Element Method in itself * Covers material from a new research area * Presents benchmarks of 2D- and 3D- applications * Fits with the new trend for genetic strategies in engineering

Author : Erwin Stein
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 53,8 Mb
Release : 2007-04-02
Category : Technology & Engineering
ISBN : 9783211380604

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Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics by Erwin Stein Pdf

This course with 6 lecturers intends to present a systematic survey of recent re search results of well-known scientists on error-controlled adaptive finite element methods in solid and structural mechanics with emphasis to problem-dependent concepts for adaptivity, error analysis as well as h- and p-adaptive refinement techniques including meshing and remeshing. Challenging applications are of equal importance, including elastic and elastoplastic deformations of solids, con tact problems and thin-walled structures. Some major topics should be pointed out, namely: (i) The growing importance of goal-oriented and local error estimates for quan tities of interest—in comparison with global error estimates—based on dual finite element solutions; (a) The importance of the p-version of the finite element method in conjunction with parameter-dependent hierarchical approximations of the mathematical model, for example in boundary layers of elastic plates; (Hi) The choice of problem-oriented error measures in suitable norms, consider ing residual, averaging and hierarchical error estimates in conjunction with the efficiency of the associated adaptive computations; (iv) The importance of implicit local postprocessing with enhanced test spaces in order to get constant-free, i. e. absolute-not only relative-discretizati- error estimates; (v) The coupling of error-controlled adaptive discretizations and the mathemat ical modeling in related subdomains, such as boundary layers. The main goals of adaptivity are reliability and efficiency, combined with in sight and access to controls which are independent of the applied discretization methods. By these efforts, new paradigms in Computational Mechanics should be realized, namely verifications and even validations of engineering models.

Author : Wolfgang Bangerth,Rolf Rannacher
Publisher : Birkhäuser
Page : 216 pages
File Size : 43,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034876056

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Adaptive Finite Element Methods for Differential Equations by Wolfgang Bangerth,Rolf Rannacher Pdf

These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.

Author : John O. Dow
Publisher : Momentum Press
Page : 271 pages
File Size : 52,5 Mb
Release : 2012-07-01
Category : Technology & Engineering
ISBN : 9781606503348

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The Essentials of Finite Element Modeling and Adaptive Refinement by John O. Dow Pdf

Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh. " The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures. These improvements are made possible due to a change in notation that embeds knowledge of solid continuum mechanics into the equations used to formulate the stiffness matrices; this allows the modeling characteristics of individual elements to be identified by visual inspection. The ability to visually relate the equations involved in element formulation to the physical process they represent is like having an x-ray of the inner workings of the finite element method; it is similar is to the effect that Graphical User Interfaces or GUI's had on computing. As a result, students at any level of finite element study are provided with an understanding of the capabilities and limitations of this powerful analytic tool. The book presents * A more simplified approach to finite element analysis based on computational continuum mechanics * Physically interpretable notation that identifies a common basis for the finite element and the finite difference methods. * New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics

Author : Peter Wriggers
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 55,5 Mb
Release : 2008-09-24
Category : Mathematics
ISBN : 9783540710004

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Nonlinear Finite Element Methods by Peter Wriggers Pdf

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.

Author : Zhangxin Chen
Publisher : World Scientific Publishing Company
Page : 348 pages
File Size : 53,8 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9789813100657

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The Finite Element Method by Zhangxin Chen Pdf

This Finite Element Method offers a fundamental and practical introduction to the finite element method, its variants, and their applications in engineering. Every concept is introduced in the simplest possible setting, while maintaining a level of treatment that is as rigorous as possible without being unnecessarily abstract. Various finite elements in one, two, and three space dimensions are introduced, and their applications to elliptic, parabolic, hyperbolic, and nonlinear equations and to solid mechanics, fluid mechanics, and porous media flow problems are addressed. The variants include the control volume, multipoint flux approximation, nonconforming, mixed, discontinuous, characteristic, adaptive, and multiscale finite element methods. Illustrative computer programs in Fortran and C++ are described. An extensive set of exercises are provided in each chapter. This book serves as a text a for one-semester course for upper-level undergraduates and beginning graduate students and as a professional reference for engineers, mathematicians, and scientists.

Author : Marcus Olavi Rüter
Publisher : Springer Nature
Page : 496 pages
File Size : 41,5 Mb
Release : 2019-11-07
Category : Science
ISBN : 9783030061739

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Error Estimates for Advanced Galerkin Methods by Marcus Olavi Rüter Pdf

This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

Author : Timothy J. Barth,Herman Deconinck
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 52,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662051894

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Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics by Timothy J. Barth,Herman Deconinck Pdf

As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.

Author : Franz-Theo Suttmeier
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 51,8 Mb
Release : 2009-03-12
Category : Mathematics
ISBN : 9783834895462

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Numerical solution of Variational Inequalities by Adaptive Finite Elements by Franz-Theo Suttmeier Pdf

The author presents a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. The local weighted residuals, that result from an extension of the so-called Dual-Weighted-Residual method, are used in a feed-back process for generating economical meshes. Based on several model problems, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities.

Author : J. E. Akin
Publisher : Elsevier
Page : 465 pages
File Size : 50,9 Mb
Release : 2005-06-22
Category : Technology & Engineering
ISBN : 9780080472751

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Finite Element Analysis with Error Estimators by J. E. Akin Pdf

This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators

Author : Zhenhan Yao,M. W. Yuan,Wanxie Zhong
Publisher : 清华大学出版社有限公司
Page : 712 pages
File Size : 51,5 Mb
Release : 2004
Category : Engineering design
ISBN : 7302093415

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Computational Mechanics by Zhenhan Yao,M. W. Yuan,Wanxie Zhong Pdf

Author : Gleim, Tobias
Publisher : kassel university press GmbH
Page : 339 pages
File Size : 45,9 Mb
Release : 2017-02-10
Category : Electronic
ISBN : 9783737602501

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Simulation of Manufacturing Sequences of Functionally Graded Structures by Gleim, Tobias Pdf

The current paper establishes an axisymmetric model for an inductive heating process. Therein, the fully coupled MAXWELL equations, assuming a temperature dependent permeability, are combined with the non-linear heat conduction equation to yield a monolithic solution strategy. The latter is based on a consistent linearization together with a higher order finite element discretization using GALERKIN'S method in space. For the temporal discretization, the generalized Newmark-? methods, higher order RUNGE-KUTTA methods, and discontinuous and continuous GALERKIN methods are used. Furthermore, the residual error is introduced to open an alternative way to obtain a numerically efficient estimation of the time integration accuracy. Simulation results of the electric, magnetic and thermal fields are provided, together with parameter studies concerning spatial discretization, frequency dependence and penetration depth of the heating zone. Another topic analyzed is the residual error and its estimation quality regarding polynomial degree and time step size. A further aspect of this work is the investigation of the thermal fluid-structure interaction with respect to functionally graded materials. Different coupling strategies for the acceleration of the fixed-point iteration in each time step is in the foreground. Relaxation methods as well as extrapolation methods make it possible to significantly reduce the number of fixed point iterations. At the same time, an adaptive strategy with higher order RUNGE-KUTTA methods can provide a further advantage in combination with acceleration methods.

Author : Georgy Viktorovich Kostin,Vasily V. Saurin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 305 pages
File Size : 52,9 Mb
Release : 2017-11-20
Category : Science
ISBN : 9783110516258

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Dynamics of Solid Structures by Georgy Viktorovich Kostin,Vasily V. Saurin Pdf

This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes. Contents Generalized formulations of parabolic and hyperbolic problems Variational principles in linear elasticity Variational statements in structural mechanics Ritz method for initial-boundary value problems Variational and projection techniques with semi-discretization Integrodifferential approach to eigenvalue problems Spatial vibrations of elastic beams with convex cross-sections Double minimization in optimal control problems Semi-discrete approximations in inverse dynamic problems Modeling and control in mechatronics

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 570 pages
File Size : 52,6 Mb
Release : 2001-08-23
Category : Mathematics
ISBN : 0521803128

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Acta Numerica 2001: Volume 10 by Arieh Iserles Pdf

An annual volume presenting substantive survey articles in numerical analysis and scientific computing.

Author : Georgy V. Kostin,Vasily V. Saurin
Publisher : Walter de Gruyter
Page : 292 pages
File Size : 47,6 Mb
Release : 2012-10-30
Category : Science
ISBN : 9783110271003

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Integrodifferential Relations in Linear Elasticity by Georgy V. Kostin,Vasily V. Saurin Pdf

Deformations of elastic bodies are encountered in many areas in science, engineering and technology. In the last decades, various numerical approaches using the finite element technique have been developed, but many are not adequate to address the full complexity. This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements. Other than comparable books, this work also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.