Download or read book Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics written by Erwin Stein and published by Springer Science & Business Media. This book was released on 2007-04-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Finite Element Method Theory Implementation and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Download or read book Anisotropic Finite Elements Local Estimates and Applications written by Thomas Apel and published by . This book was released on 1999-07 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1994 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Differential Equations written by Kenneth Eriksson and published by Cambridge University Press. This book was released on 1996-09-05 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Download or read book FDTD Modeling of Metamaterials Theory and Applications written by Yang Hao and published by Artech House. This book was released on 2008-10-01 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master powerful new modeling tools that let you quantify and represent metamaterial properties with never-before accuracy. This first-of-its-kind book brings you up to speed on breakthrough finite-difference time-domain techniques for modeling metamaterial characteristics and behaviors in electromagnetic systems. This practical resource comes complete with sample FDTD scripts to help you pave the way to new metamaterial applications and advances in antenna, microwave, and optics engineering. You get in-depth coverage of state-of-the-art FDTD modeling techniques and applications for electromagnetic bandgap (EBG) structures, left-handed metamaterials (LHMs), wire medium, metamaterials for optics, and other practical metamaterials. You find steps for computing dispersion diagrams, dealing with material dispersion properties, and verifying the left-handedness. Moreover, this comprehensive volume offers guidance for handling the unique properties possessed by metamaterials, including how to define material parameters, characterize the interface of metamaterial slabs, and quantify their spatial as well as frequency dispersion characteristics. The book also presents conformal and dispersive FDTD modeling of electromagnetic cloaks, perfect lens, and plasmonic waveguides, as well as other novel antenna, microwave, and optical applications. Over 190 illustrations support key topics throughout the book.
Download or read book The Scaled Boundary Finite Element Method written by Chongmin Song and published by John Wiley & Sons. This book was released on 2018-06-19 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.
Download or read book Hybrid High Order Methods written by Matteo Cicuttin and published by Springer Nature. This book was released on 2021-11-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.
Download or read book Isogeometric Analysis written by J. Austin Cottrell and published by John Wiley & Sons. This book was released on 2009-08-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: “The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It is very original. There is no other book on this topic.” —René de Borst, Eindhoven University of Technology Written by leading experts in the field and featuring fully integrated colour throughout, Isogeometric Analysis provides a groundbreaking solution for the integration of CAD and FEA technologies. Tom Hughes and his researchers, Austin Cottrell and Yuri Bazilevs, present their pioneering isogeometric approach, which aims to integrate the two techniques of CAD and FEA using precise NURBS geometry in the FEA application. This technology offers the potential to revolutionise automobile, ship and airplane design and analysis by allowing models to be designed, tested and adjusted in one integrative stage. Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique. The authors offer a clear explanation as to how to add isogeometric capabilities to existing finite element computer programs, demonstrating how to implement and use the technology. Detailed programming examples and datasets are included to impart a thorough knowledge and understanding of the material. Provides examples of different applications, showing the reader how to implement isogeometric models Addresses readers on both sides of the CAD/FEA divide Describes Non-Uniform Rational B-Splines (NURBS) basis functions
Download or read book Solving PDEs in Python written by Hans Petter Langtangen and published by Springer. This book was released on 2017-03-21 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Download or read book Accuracy Estimates and Adaptive Refinements in Finite Element Computations written by Ivo Babuška and published by John Wiley & Sons. This book was released on 1986 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers discussing the recent developments in adaptive methods and their applications, an area of finite elements methods applicable to the needs of civil engineering. Topics covered range from an exposition of basic theory and techniques to detailed discussions of specific applications. Adaptive approaches, and the computer assessment of the reliability of the results obtained are also examined.
Download or read book Computational Engineering Introduction to Numerical Methods written by Michael Schäfer and published by Springer Nature. This book was released on 2021-07-19 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation methods in all engineering disciplines gains more and more importance. The successful and efficient application of such tools requires certain basic knowledge about the underlying numerical techniques. The text gives a practice-oriented introduction in modern numerical methods as they typically are applied in mechanical, chemical, or civil engineering. Problems from heat transfer, structural mechanics, and fluid mechanics constitute a thematical focus of the text. For the basic understanding of the topic aspects of numerical mathematics, natural sciences, computer science, and the corresponding engineering area are simultaneously important. Usually, the necessary information is distributed in different textbooks from the individual disciplines. In the present text the subject matter is presented in a comprehensive multidisciplinary way, where aspects from the different fields are treated insofar as it is necessary for general understanding. Overarching aspects and important questions related to accuracy, efficiency, and cost effectiveness are discussed. The topics are presented in an introductory manner, such that besides basic mathematical standard knowledge in analysis and linear algebra no further prerequisites are necessary. The book is suitable either for self-study or as an accompanying textbook for corresponding lectures. It can be useful for students of engineering disciplines as well as for computational engineers in industrial practice.
Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Springer Science & Business Media. This book was released on 2003-01-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual 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. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.
Download or read book A Posteriori Error Estimation in Finite Element Analysis written by Mark Ainsworth and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.
Download or read book Heat Transfer in Polymer Composite Materials written by Nicolas Boyard and published by John Wiley & Sons. This book was released on 2016-03-28 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses general information, good practices and examples about thermo-physical properties, thermo-kinetic and thermo-mechanical couplings, instrumentation in thermal science, thermal optimization and infrared radiation.
