The Generalized Finite Element Method With Global Local Enrichment Functions
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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.
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.
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.
Generalized Finite Element Methods For Three Dimensional Crack Growth Simulations
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Author : Jeronymo P. Pereira
language : en
Publisher:
Release Date : 2010
Generalized Finite Element Methods For Three Dimensional Crack Growth Simulations written by Jeronymo P. Pereira 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.
Three-dimensional (3-D) crack growth analysis is crucial for the assessment of structures such as aircrafts, rockets, engines and pressure vessels, which are subjected to extreme loading conditions. The analysis of 3-D arbitrary crack growth using the standard Finite Element Method (FEM) encounters several difficulties. The singularities at crack fronts require strongly refined finite element meshes that must fit the discontinuity surfaces while keeping the aspect ratio of the elements within acceptable bounds. Fully automatic generation of meshes in complex 3-D geometries satisfying these requirements is a daunting task. Partition-of-unity methods, such as the Generalized FEM (GFEM), are promising candidates to surmount the shortcomings of the standard FEM in crack growth simulations. These methods allow the representation of discontinuities and singularities in the solution via geometrical descriptions of crack surfaces, that are independent of the volume mesh, coupled with suitable enrichment functions. As a result, volume meshes need not fit crack surfaces. This work proposes an hp-version of the GFEM (hp-GFEM) for crack growth simulations. This method provides enough flexibility to build high-order discretizations for crack growth simulations. At each crack growth step, high-order approximations on locally refined meshes are automatically created in complex 3-D domains while preserving the aspect ratio of elements, regardless of crack geometry. The hp-GFEM uses explicit surface meshes composed of triangles to represent non-planar 3-D crack surfaces. By design, the proposed methodology allows the crack surface to be arbitrarily located within the GFEM mesh. To track the crack surface evolution, the proposed methodology considers an extension of the Face Offsetting Method (FOM). Based on the hp-GFEM solution, the FOM provides geometrically feasible crack front descriptions by updating the vertex positions and checking for self-intersections of the edges. The hp-GFEM with FOM allows the simulation of arbitrary crack growth independent of the volume mesh. Numerical simulations using the hp-GFEM coupled with the FOM are corroborated by experimental data and experimental observations. As an alternative to large-scale crack growth simulations, this work combines the proposed hp-GFEM with the generalized finite element method with global-local enrichment functions (GFEMgl). The proposed method allows crack growth simulations with arbitrary path in industrial level complexity problems while keeping the global mesh unchanged. Furthermore, this method allows crack growth simulations without solving the entire problem from scratch at each crack growth step. The GFEMgl for crack growth explores solutions from previous crack growth steps, hierarchical property of the enrichment functions as well as static condensation of the global-local degrees of freedom to expedite the solution process. Numerical examples demonstrate the robustness, efficiency and accuracy of the proposed GFEMgl for crack growth simulations.
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
A Multi Scale Generalized Finite Element Method For Sharp Transient Thermal Gradients
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Author : Patrick J. O'Hara
language : en
Publisher:
Release Date : 2010
A Multi Scale Generalized Finite Element Method For Sharp Transient Thermal Gradients written by Patrick J. O'Hara 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.
In this research, heat transfer problems exhibiting sharp thermal gradients are analyzed using the generalized finite element method. Convergence studies show that low order (linear and quadratic) elements require strongly refined meshes for acceptable accuracy. The high mesh density leads to small allowable time-step sizes, and significant increase in the computational cost. When mesh refinement and unrefinement is required between time-steps the mapping of solution vectors and state-dependent variables becomes difficult. A generalized FEM with global-local enrichments is proposed for the class of problems investigated in this research. In this procedure, a global solution space defined on a coarse mesh is enriched through the partition of unity framework of the generalized FEM with solutions of local boundary value problems. The local problems are defined using the same procedure as in the global-local FEM, where boundary conditions are provided by a coarse-scale global solution. Coarse, uniform, global meshes are acceptable even at regions with thermal spikes that are orders of magnitude smaller than the element size. Convergence on these discretizations is achieved even when no or limited convergence is observed in the local problems. The two-way information transfer provided by the proposed generalized FEM is appealing to several classes of problems, especially those involving multiple spatial scales. The proposed methodology brings the benefits of generalized FEM to problems where limited or no information about the solution is known a-priori. The proposed methodology is formulated for, and applied to transient problems, where local domains at time t^{n+1} obtain their boundary conditions from the global domain at t^{n}. No transient effects need to be considered in the local domain. The method has shown the ability to produce accurate and efficient transient simulations in situations where traditional FEM analyses would lead to difficult re-meshing, and solution mapping issues. With the proposed methodology, the enrichment functions are added hierarchically to the stiffness matrix. As such, large portions of the coarse, global meshes may be assembled and factorized only once. The factorizations can then be re-used for multiple loading scenarios, or multiple time-steps so as to significantly improve the computational efficiency of the simulations. The issue of prohibitively small time-step sizes dictated by high mesh density in traditional FEM analyses is also addressed. With the use of appropriate shape functions, sufficient accuracy is obtained without the requirement of highly refined meshes. The resulting critical time-steps are less restrictive, making transient analyses more computationally feasible.
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.
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.
Meshfree Methods For Partial Differential Equations Vii
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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2014-12-02
Meshfree Methods For Partial Differential Equations Vii written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.
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.
Meshfree Methods For Partial Differential Equations Ix
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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2019-06-19
Meshfree Methods For Partial Differential Equations Ix written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Mathematics categories.
This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain. This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the 2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.