Convergence Analysis Of The Generalized Finite Element Method With Global Local Enrichments
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Convergence Analysis Of The Generalized Finite Element Method With Global Local Enrichments
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Author : Varun Gupta
language : en
Publisher:
Release Date : 2010
Convergence Analysis Of The Generalized Finite Element Method With Global Local Enrichments written by Varun Gupta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
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.
The Generalized Finite Element Method With Global Local Enrichment Functions
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Author :
language : en
Publisher:
Release Date : 2009
The Generalized Finite Element Method With Global Local Enrichment Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Fundamentals Of Enriched Finite Element Methods
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Author : Alejandro M. Aragón
language : en
Publisher: Elsevier
Release Date : 2023-11-09
Fundamentals Of Enriched Finite Element Methods written by Alejandro M. Aragón and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-09 with Technology & Engineering categories.
Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and also looks at their real-world applications, recommending in what situations they’re best implemented. It starts with a concise background on the theory required to understand the underlying functioning principles behind enriched finite element methods before outlining detailed instruction on implementation of the techniques in standard displacement-based finite element codes. The strengths and weaknesses of each are discussed, as are computer implementation details, including a standalone generalized finite element package, written in Python. The applications of the methods to a range of scenarios, including multi-phase, fracture, multiscale, and immersed boundary (fictitious domain) problems are covered, and readers can find ready-to-use code, simulation videos, and other useful resources on the companion website to the book. Reviews various enriched finite element methods, providing pros, cons, and scenarios forbest use Provides step-by-step instruction on implementing these methods Covers the theory of general and enriched finite element methods
Non Intrusive Extension Of A Generalized Finite Element Method For Multiscale Problems To The Abaqus Analysis Platform
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Author : Julia A. Plews
language : en
Publisher:
Release Date : 2011
Non Intrusive Extension Of A Generalized Finite Element Method For Multiscale Problems To The Abaqus Analysis Platform written by Julia A. Plews and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
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.
Global Local Stress Analysis Of Composite Panels
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Author :
language : en
Publisher:
Release Date : 1989
Global Local Stress Analysis Of Composite Panels written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Advances In Discretization Methods
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Author : Giulio Ventura
language : en
Publisher: Springer
Release Date : 2016-08-24
Advances In Discretization Methods written by Giulio Ventura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-24 with Technology & Engineering categories.
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.
The Scaled Boundary Finite Element Method
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Author : Chongmin Song
language : en
Publisher: John Wiley & Sons
Release Date : 2018-06-19
The Scaled Boundary Finite Element Method written by Chongmin Song 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 2018-06-19 with Science categories.
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.
Analysis Of Three Dimensional Fracture Mechanics Problems A Non Intrusive Approach Using Abaqus And A Generalized Finite Element Method
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Author : Piyush Gupta
language : en
Publisher:
Release Date : 2011
Analysis Of Three Dimensional Fracture Mechanics Problems A Non Intrusive Approach Using Abaqus And A Generalized Finite Element Method written by Piyush Gupta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
This report shows that the so-called generalized finite element method with global-local enrichment functions (GFEM g-l ) can be implemented non-intrusively in existing closed-source FEM software as an add-on module. The GFEM g-l is based on the solution of interdependent global (structural) and local (crack) scale problems. In the approach presented here, an initial global scale problem is solved by a commercial finite element analysis software like Abaqus, local problems containing 3-D fractures are solved by an hp-adaptive GFEM software and an enriched global scale problem is solved by a combination of the FEM and GFEM solvers. The interactions between the solvers are limited to the exchange of load and solution vectors and does not require the introduction of user subroutines to existing FEM software. As a results, the user can benefit from built-in features of available commercial grade FEM software while adding the benefits of the GFEM for this class of problems. Several three-dimensional fracture mechanics problems aimed at investigating the applicability and accuracy of the proposed two-solver methodology are presented.
Extended Finite Element Method
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Author : Amir R. Khoei
language : en
Publisher: John Wiley & Sons
Release Date : 2015-02-23
Extended Finite Element Method written by Amir R. Khoei 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 2015-02-23 with Science categories.
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
Finite Element Methods
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Author : Michel Krizek
language : en
Publisher: Routledge
Release Date : 2017-11-22
Finite Element Methods written by Michel Krizek and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
""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.