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Extended Finite Element Method

Extended Finite Element Method
Theory and Applications

by Amir R. Khoei

  • Publisher : John Wiley & Sons
  • Release : 2015-02-23
  • Pages : 584
  • ISBN : 1118457684
  • Language : En, Es, Fr & De
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Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Extended Finite Element Method: Theory and Applications introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. The XFEM approach is based on an extension of standard finite element method based on the partition of unity method. Extended Finite Element Method: Theory and Applications begins by introducing the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. It then covers the theory and application of XFEM in large deformations, plasticity and contact problems. The implementation of XFEM in fracture mechanics, including the linear, cohesive, and ductile crack propagation is also covered. The theory and applications of the XFEM in multiphase fluid flow, including the hydraulic fracturing in soil saturated media and crack propagation in thermo-hydro-mechanical porous media, is also discussed in detail. 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

Dynamic Extended Finite Element Method (XFEM) Analysis of Discontinuous Media

Dynamic Extended Finite Element Method (XFEM) Analysis of Discontinuous Media
A Book

by Milad Toolabi

  • Publisher : Unknown Publisher
  • Release : 2015
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Extended Finite Element Predictions for Three Dimensional Modeling of Fatigue Crack Growth in Cold-worked Holes

Extended Finite Element Predictions for Three Dimensional Modeling of Fatigue Crack Growth in Cold-worked Holes
A Book

by Mohammad Salman Yasin

  • Publisher : Unknown Publisher
  • Release : 2020
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Cold working has been widely used for enhancing the fatigue life of open holes. The process imparts compressive residual stresses around the hole which slows down the progression of crack under cyclic loading conditions. In the present study, fatigue crack growth in open holes in R260 grade steel, a typical railroad material, has been analyzed using the Extended Finite Element Method (XFEM). Along with the experimental studies, numerical simulation emerges as a powerful tool to predict the fatigue crack growth in rail steel and may deliver important insights to consider more situations by saving time and cost. XFEM modifies the standard displacement-based approximation by adding enrichment functions in the crack region. The investigation explored the capability of the XFEM, for a plate containing plain hole (baseline), pad coined, or split-sleeve cold-worked hole using the commercial finite element package, Abaqus, as a means of fatigue crack growth under constant amplitude loading. The effect of residual stress redistribution has been added to the numerical model to accurately predict the crack evolution. Stress Intensity Factors (SIF) are obtained from the XFEM calculations and the crack growth is estimated until the SIF reaches the fracture toughness of the modeled coupon material. The obtained simulation results are in good agreement with the fatigue experimental results in terms of the fatigue crack growth rates for plain hole (baseline), pad coined, or split-sleeve cold-worked holes. Results from the performed analysis show that cold working of an open hole increases the fatigue life when compared to the one without residual stresses due to the delay of crack initiation and propagation. The results also indicated fatigue life increase almost by a factor of three during crack propagation due to split-sleeve cold expansion in correlation to the baseline and pad coined sample.

Using the EXtended Finite Element Method for Keyhole-based Welding Processes

Using the EXtended Finite Element Method for Keyhole-based Welding Processes
A Book

by Mischa Jahn,Jonathan Montalvo-Urquizo

  • Publisher : Unknown Publisher
  • Release : 2018
  • Pages : 1350
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Crack Identification Using Dynamic Extended Finite Element Method and Thermal Conductivity Engineering for Nanomaterials

Crack Identification Using Dynamic Extended Finite Element Method and Thermal Conductivity Engineering for Nanomaterials
A Book

by Chao Zhang

  • Publisher : Unknown Publisher
  • Release : 2018
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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3D Fracture Modeling by Extended Finite Element Method and Gradient Enhanced Damage

3D Fracture Modeling by Extended Finite Element Method and Gradient Enhanced Damage
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2018
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Abstract: A combined continuous‐discontinuous approach to fracture is presented to model crack propagation in 3D. The damage evolution governs the discrete crack advancement and the direction of the crack propagation. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim).

An Extended Finite Element Method for Turbulent Premixed Combustion

An Extended Finite Element Method for Turbulent Premixed Combustion
A Book

by Florian Henke

  • Publisher : Unknown Publisher
  • Release : 2013
  • Pages : 184
  • ISBN : 9783843911092
  • Language : En, Es, Fr & De
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The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals
A Book

by Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu

  • Publisher : Elsevier
  • Release : 2005-05-26
  • Pages : 752
  • ISBN : 9780080472775
  • Language : En, Es, Fr & De
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The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text

Modeling of concrete fracture applying the eXtended finite element method

Modeling of concrete fracture applying the eXtended finite element method
Ph.D. thesis

by Jesper L. Asferg,Danmarks Tekniske Universitet. BYG.DTU.

  • Publisher : Unknown Publisher
  • Release : 2007
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Extended Finite Element Method

Extended Finite Element Method
for Fracture Analysis of Structures

by Soheil Mohammadi

  • Publisher : John Wiley & Sons
  • Release : 2008-04-30
  • Pages : 280
  • ISBN : 0470697997
  • Language : En, Es, Fr & De
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This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications. One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been extended to nonlinear materials and other disciplines such as modelling contact and interface, simulation of inclusions and holes, moving and changing phase problems, and even to multiscale analyses. The book is self contained, with summaries of both classical and modern computational techniques. The main chapters include a comprehensive range of numerical examples describing various features of XFEM.

Extended Finite Element Method

Extended Finite Element Method
Tsinghua University Press Computational Mechanics Series

by Zhuo Zhuang,Zhanli Liu,Binbin Cheng,Jianhui Liao

  • Publisher : Academic Press
  • Release : 2014-03-24
  • Pages : 286
  • ISBN : 0124078567
  • Language : En, Es, Fr & De
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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

Extended Finite Element Method for Crack Propagation

Extended Finite Element Method for Crack Propagation
A Book

by Sylvie Pommier,Anthony Gravouil,Nicolas Moes,Alain Combescure

  • Publisher : John Wiley & Sons
  • Release : 2013-03-04
  • Pages : 254
  • ISBN : 1118622693
  • Language : En, Es, Fr & De
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Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.

Finite Element Method: Concepts and Applications

Finite Element Method: Concepts and Applications
A Book

by Connie Mcguire

  • Publisher : Unknown Publisher
  • Release : 2019-06-06
  • Pages : 237
  • ISBN : 9781632408525
  • Language : En, Es, Fr & De
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Finite element method refers to the numerical method, which is used to solve problems in mathematical physics and engineering. The areas where finite element method is mostly applied are fluid flow, structural analysis, mass transport, heat transfer and electromagnetic potential problems. This method divides the problem into simpler and smaller parts called finite elements, in order to solve it. Algebraic equations are formulated for each element, which are then assembled into a larger set of equations that models the whole problem. Variational methods are then applied to find an approximate solution by minimizing the associated error function. The different finite element methods are applied element method (AEM), extended finite element method (XFEM), meshfree methods, Loubignac iteration, finite element limit analysis, spectral element method, etc. This book outlines the concepts and applications of finite element method in detail. It strives to provide a fair idea about this discipline and to help develop a better understanding of the latest advances within this area of mathematics. Those in search of information to further their knowledge will be greatly assisted by this book.

An Extended Finite Element Method with Discontinuous Enrichment for Applied Mechanics

An Extended Finite Element Method with Discontinuous Enrichment for Applied Mechanics
A Book

by John Everett Dolbow

  • Publisher : Unknown Publisher
  • Release : 1999
  • Pages : 396
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The modeling of a discontinuous field with a standard finite element approximation presents unique challenges. The construction of an approximating space which is discontinuous across a given line or surface places strict restrictions on the finite element mesh. The simulation of an evolution of the discontinuity is in turn burdened by the requirement to remesh at each stage of the calculation. This work approaches the problem by locally enriching the standard element-based approximation with discontinuous functions. The enriched basis is formed from a union of the set of nodal shape functions with a set of products of nodal shape functions and enrichment functions. The construction of the approximating space in this fashion places the formulation in the class of partition of unity methods. By aligning the discontinuities in the enrichment functions with a specified geometry, a discontinuous field is represented independently of the finite element mesh. This capability is shown to significantly extend the standard method for a number of applications in applied mechanics.

Nonlinear Finite Elements for Continua and Structures

Nonlinear Finite Elements for Continua and Structures
A Book

by Ted Belytschko,Wing Kam Liu,Brian Moran,Khalil Elkhodary

  • Publisher : John Wiley & Sons
  • Release : 2013-11-25
  • Pages : 832
  • ISBN : 1118700082
  • Language : En, Es, Fr & De
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This updated and expanded edition of the bestselling textbookprovides a comprehensive introduction to the methods and theory ofnonlinear finite element analysis. New material provides a conciseintroduction to some of the cutting-edge methods that have evolvedin recent years in the field of nonlinear finite element modeling,and includes the eXtended finite element method (XFEM),multiresolution continuum theory for multiscale microstructures,and dislocation-density-based crystalline plasticity. Nonlinear Finite Elements for Continua and Structures, SecondEdition focuses on the formulation and solution of discreteequations for various classes of problems that are of principalinterest in applications to solid and structural mechanics. Topicscovered include the discretization by finite elements of continuain one dimension and in multi-dimensions; the formulation ofconstitutive equations for nonlinear materials and largedeformations; procedures for the solution of the discreteequations, including considerations of both numerical andmultiscale physical instabilities; and the treatment of structuraland contact-impact problems. Key features: Presents a detailed and rigorous treatment of nonlinear solidmechanics and how it can be implemented in finite elementanalysis Covers many of the material laws used in today's software andresearch Introduces advanced topics in nonlinear finite elementmodelling of continua Introduction of multiresolution continuum theory and XFEM Accompanied by a website hosting a solution manual andMATLAB® and FORTRAN code Nonlinear Finite Elements for Continua and Structures, SecondEdition is a must have textbook for graduate students inmechanical engineering, civil engineering, applied mathematics,engineering mechanics, and materials science, and is also anexcellent source of information for researchers and practitionersin industry.

Geometrically Unfitted Finite Element Methods and Applications

Geometrically Unfitted Finite Element Methods and Applications
Proceedings of the UCL Workshop 2016

by Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii

  • Publisher : Springer
  • Release : 2018-03-13
  • Pages : 361
  • ISBN : 3319714317
  • Language : En, Es, Fr & De
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This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.

Rock Mechanics in Underground Construction

Rock Mechanics in Underground Construction
ISRM International Symposium 2006 : 4th Asian Rock Mechanics Symposium, 8 - 10 November 2006, Singapore

by C. F. Leung,Yingxin Zhou

  • Publisher : World Scientific
  • Release : 2006
  • Pages : 488
  • ISBN : 9812772413
  • Language : En, Es, Fr & De
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This proceedings volume contains over 300 papers on rock mechanics and engineering with contributors from all over Asia and many other parts of the world. Seven keynote papers summarize the state-of-the-art in rock engineering including topics such as underground rock caverns. The technical papers cover a wide range of rock mechanics and engineering topics: rock tunnels, caverns, mining, rock slopes and dams, rock blasting, rock burst and failure, rock properties, rock mass, rock joints, and block theory. Numerous valuable rock engineering case studies are also reported. This volume should serve as a useful reference for the engineers and researchers in rock mechanics and rock engineering. Sample Chapter(s). Chapter 1: Forensic Engineering for Underground Construction (244 KB). Contents: Tunnelling; Rock Caverns; Mining; Blasting and Dynamics; Support and Reinforcement; Rock Mass; Rock Properties; Discontinuities; Block Theory and DDA; Failure, Fracture and Burst; Dams and Slopes; Other Applications. Readership: Graduate students, academics and researchers in civil engineering and engineering mechanics.

Thermo-mechanical Fatigue Using the Extended Space-time Finite Element Method

Thermo-mechanical Fatigue Using the Extended Space-time Finite Element Method
A Book

by Ryan T. Schlinkman

  • Publisher : Unknown Publisher
  • Release : 2019
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Thermomechanical high-cycle fatigue is a major failure mechanism for many engineering components in a diverse range of industries such as aerospace, automotive, and nuclear among others. Engineers trying to determine the fatigue life of a component typically rely on commercial fatigue analysis software which uses traditional fatigue criteria that are limited in their applicability. For instance, they are poor at handling multiaxial and variable amplitude loading. Furthermore, adding variable amplitude thermal loading into the mix makes using these traditional fatigue criteria even less appealing. In recent years, there have been attempts to establish methods for simulating high cycle fatigue based on finite element calculations rather than using it as a post-processing step. These include cohesive zone and continuum damage mechanics models. However, all of these methods employ cycle jumping strategies to cut down on the enormous computational time required. However, cycle jumping is not applicable for a random loading history or with random or out-of-phase temperature variation. Motivated by these current developments, this thesis proposes the use of the extended space-time finite element method (XTFEM) in combination with a two scale progressive fatigue damage model for the direct numerical simulation of thermomechanical high cycle fatigue. Instead of using the conventional explicit or implicit finite difference time integration methods, temporal approximations are introduced with FEM mesh and enriched based on the extended finite element method. After outlining the basic theory for XTFEM with thermomechanical coupling, the effectiveness of the computational framework is demonstrated in numerical examples including a coupled, thermomechanical fatigue simulation of a plate and hat stiffener model representative of a hypersonic aircraft’s structure.

An Automated Hierarchical EXtended Finite Element Approach for Multiphysics Problems Involving Discontinuities

An Automated Hierarchical EXtended Finite Element Approach for Multiphysics Problems Involving Discontinuities
A Book

by Mischa Jahn

  • Publisher : Unknown Publisher
  • Release : 2018
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Computational Methods

Computational Methods
A Book

by G.R. Liu,V.B.C. Tan,X. Han

  • Publisher : Springer Science & Business Media
  • Release : 2007-05-26
  • Pages : 925
  • ISBN : 1402039530
  • Language : En, Es, Fr & De
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The First International Conference on Computational Methods (ICCM04), organized by the department of Mechanical Engineering, National University of Singapore, was held in Singapore, December 15-17, 2004, with great success. This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.