A Generalized Finite Element Method For Three Dimensional Branched Cracks
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A Generalized Finite Element Method For Three Dimensional Branched Cracks
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Author : Luziana Grillo Reno
language : en
Publisher:
Release Date : 2006
A Generalized Finite Element Method For Three Dimensional Branched Cracks written by Luziana Grillo Reno and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Stress Intensity Factor Equations For Cracks In Three Dimensional Finite Bodies Subjected To Tension And Bending Loads
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Author : J. C. Newman
language : en
Publisher:
Release Date : 1984
Stress Intensity Factor Equations For Cracks In Three Dimensional Finite Bodies Subjected To Tension And Bending Loads written by J. C. Newman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
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.
Extended Finite Element And Meshfree Methods
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Author : Timon Rabczuk
language : en
Publisher: Academic Press
Release Date : 2019-11-13
Extended Finite Element And Meshfree Methods written by Timon Rabczuk and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-13 with Technology & Engineering categories.
Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work
Extended Finite Element Method
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Author : Zhuo Zhuang
language : en
Publisher: Academic Press
Release Date : 2014-03-24
Extended Finite Element Method written by Zhuo Zhuang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-24 with Technology & Engineering categories.
Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems. The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials. Authored by an expert team from one of China's leading academic and research institutions Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems
A Special Crack Tip Element For Three Dimensional Crack Problems
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Author : R. Jones
language : en
Publisher:
Release Date : 1978
A Special Crack Tip Element For Three Dimensional Crack Problems written by R. Jones and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Airplanes categories.
This paper develops a finite element method for determining the stress intensity factors along the edge of a crack in an arbitrary three-dimensional body. A special element is placed around the crack front and in each special element the stresses and displacements are derived using the asymptotic nature of the stress and displacement fields near a crack tip. The method is based on the authors' previous technique for evaluating the stress intensity factors in cracked sheets, and coincides with this method in the case of a through crack in a thin sheet. As illustrative examples the problems of a semicircular surface flaw and an internal penny shaped crack are considered. In each case the computed values of the stress intensity factors are in excellent agreement with known analytical results.
Meshfree Methods For Partial Differential Equations
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Meshfree Methods For Partial Differential Equations written by Michael Griebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.
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
Singular Phenomena And Scaling In Mathematical Models
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-18
Singular Phenomena And Scaling In Mathematical Models written by Michael Griebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Computers categories.
The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.
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.