Download or read book Convergence Analysis of the Generalized Finite Element Method with Global local Enrichments written by Varun Gupta and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The global-local analysis procedure in the Finite Element Method is broadly used in industry for the analysis of cracks or localized stress concentrations in large, complex, three-dimensional domains. However, the limitations of this technique are well-known. The global-local FEM (GL-FEM) involves two steps: First, the solution of the given problem is computed on a coarse, global, quasi-uniform mesh, in which the cracks or other local features need not be discretized. The solution of this problem is then used as boundary conditions to solve another Finite Element problem, which is basically a local sub-domain, comprised of localized features (like cracks), extracted from the global domain.The efficacy of the so-called Generalized Finite Element Method (GFEM) in solving such multi-scale problems has been quite well proven in past few years. Therefore, combining the two approaches, going one step further from Global-Local Finite Element Analysis, and using the local solution as an enrichment function for the global problem through the Partition of Unity framework of the Generalized Finite Element Method, gives rise to the Generalized Finite Element Method with global-local enrichments (or GFEMg-l). As these classes of methods are relatively new, there are many issues which need to be addressed to make these methods robust enough for their industrial applicability in a comprehensive manner. One of the issues surrounding this GFEMg-l approach concerns the domain size of the local problem containing the complex localized features of a structural problem, and the focus of this study is to provide guidance to address this issue. This study focuses on coming up with guidelines for selecting the size of the enrichment zone for three-dimensional fracture mechanics problems. A theoretical proof and rigorous convergence studies are presented here to provide the guidelines for selecting the size of enrichment zone for practical problems. The effect of inexact boundary conditions, applied to the local problem, on the solution is also investigated.
Download or read book The Generalized Finite Element Method With Global Local Enrichment Functions written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global local Stress Analysis of Composite Panels written by and published by . This book was released on 1989 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Discretization Methods written by Giulio Ventura and published by Springer. This book was released on 2016-08-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.
Download or read book Non Intrusive Extension of a Generalized Finite Element Method for Multiscale Problems to the Abaqus Analysis Platform written by Julia A. Plews and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Several classes of important engineering problems 0́3 in this case, problems exhibiting sharp thermal gradients 0́3 have solution features spanning multiple spatial scales of interest and, therefore, necessitate advanced hp finite element discretizations. Although hp-FEM is unavailable off-the-shelf in many predominant commercial analysis software packages, a novel method is proposed herein which is used to introduce these capabilities via the generalized FEM with global-local enrichments (GFEMgl) non-intrusively in Abaqus, a popular, general-purpose FEA platform. Numerical results show that the techniques utilized allow for accurate resolution of localized thermal features on structural-scale meshes without hp-adaptivity or the ability to account for very localized loads in the FEM framework itself. This methodology enables the user to take advantage of all the benefits of both hp-FEM discretizations and the appealing features of many available CAE/FEA software packages in order to obtain optimal convergence for challenging multiscale problems.
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 Smoothed Finite Element Methods written by G.R. Liu and published by CRC Press. This book was released on 2016-04-19 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve mo
Download or read book Extended Finite Element Method written by Amir R. Khoei and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples
Download or read book Finite Element Methods written by Michel Krizek and published by CRC Press. This book was released on 1998-01-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs."
Download or read book On the Application of Stable Generalized Finite Element Method for One Dimensional Subsurface Flow and Transport Problems written by Tilsa Aryeni and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation concentrates on the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of the Richards equation in unsaturated zone in one-dimensional heterogeneous soil layers. The problem is characterized by spatial discontinuity of the elliptic coefficient that depends on the unknown solution. It is known that unless the partition of the domain matches the discontinuity configuration, the accuracy of standard finite element techniques significantly deteriorates and standard refinement of the partition may not suffice. The GFEM is a viable alternative to overcome this predicament. It is based on the construction of certain enrichment functions supplied to the standard finite element space that capture the effects of the discontinuity. This approach is called stable (SGFEM) if it maintains an optimal rate of convergence and the conditioning of GFEM is not worse than that of the standard FEM. The implementation of the method to the quasilinear elliptic equation with multiple interfaces is carried out to investigate the performance of the method when applied to the purely elliptic portion of Richards equation. A convergence analysis is derived and the performance of the method is illustrated by several numerical examples. Furthermore, it is known that typical global formulations such as FEMs do not enjoy the numerical local conservation property that is crucial in many conservation law- based applications. To remedy this issue, a Lagrange multiplier technique is adopted to enforce local conservation. Numerical examples are given to demonstrate the performance of the proposed technique. In addition, a semi-analytical solution of the Richards Equation posed on a two-layered one-dimensional soil supplied with various boundary conditions is derived under a constraint that the constitutive relations are exponentially dependent on the pressure head. It allows for a transformation of the Richards Equation into a linear parabolic partial differential equation that governs a spatial-temporal function that represents the hydraulic conductivity. This analytical solution is imperative to examine the performance of SGFEM approximation to Richards equation. Several numerical examples are presented and tested with the analytical solution provided.
Download or read book Issues in Computation 2012 Edition written by and published by ScholarlyEditions. This book was released on 2013-01-10 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Computation / 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computational Chemistry. The editors have built Issues in Computation: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computational Chemistry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Meshfree Methods for Partial Differential Equations VII written by Michael Griebel and published by Springer. This book was released on 2014-12-02 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.
Download or read book Multiscale Finite Element Methods written by Yalchin Efendiev and published by Springer Science & Business Media. This book was released on 2009-01-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction and description of the proposed methods and motivating examples. Some new techniques are introduced using formal arguments that are justi?ed later in the last chapter. Numerical examples demonstrating the signi?cance of the proposed methods are presented in each chapter following the description of the methods. In the last chapter, we analyze a few representative cases with the objective of demonstrating the main error sources and the convergence of the proposed methods. A brief outline of the book is as follows. The ?rst chapter gives a general introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond chapter discusses the main idea of the multiscale ?nite element method and its extensions. This chapter also gives an overview of multiscale ?nite element methods and other related methods. The third chapter discusses the ext- sion of multiscale ?nite element methods to nonlinear problems. The fourth chapter focuses on multiscale methods that use limited global information.
Download or read book Computational Methods for Fracture in Porous Media written by René de Borst and published by Elsevier. This book was released on 2017-10-18 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods for Fracture in Porous Media: Isogeometric and Extended Finite Element Methods provides a self-contained presentation of new modeling techniques for simulating crack propagation in fluid-saturated porous materials. This book reviews the basic equations that govern fluid-saturated porous media. A multi-scale approach to modeling fluid transport in joins, cracks, and faults is described in such a way that the resulting formulation allows for a sub-grid representation of the crack and fluid flow in the crack. Interface elements are also analyzed with their extension to the hydromechanical case. The flexibility of Extended Finite Element Method for non-stationary cracks is also explored and their formulation for fracture in porous media described. This book introduces Isogeometric finite element methods and its basic features and properties. The rapidly evolving phase-field approach to fracture is also discussed. The applications of this book's content cover various fields of engineering, making it a valuable resource for researchers in soil, rock and biomechanics. - Teaches both new and upcoming computational techniques for simulating fracture in (partially) fluid-saturated porous media - Helps readers learn how to couple modern computational methods with non-linear fracture mechanics and flow in porous media - Presents tactics on how to simulate fracture propagation in hydraulic fracturing
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 Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis of the convergence of mixed finite element methods written by Rolf Stenberg and published by . This book was released on 1984 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
