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Extended Finite Element and Meshfree Methods

Extended Finite Element and Meshfree Methods
A Book

by Timon Rabczuk,Jeong-Hoon Song,Xiaoying Zhuang,Cosmin Anitescu

  • Publisher : Academic Press
  • Release : 2019-11-13
  • Pages : 638
  • ISBN : 0128141077
  • Language : En, Es, Fr & De
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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

Advances in Meshfree and X-FEM Methods

Advances in Meshfree and X-FEM Methods
With CD-ROM(Volume 2)

by G R Liu

  • Publisher : World Scientific
  • Release : 2002-12-16
  • Pages : 272
  • ISBN : 9814486884
  • Language : En, Es, Fr & De
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This book is a collection of the papers from the proceedings of the 1st Asian Workshop on Meshfree Methods held in conjunction with the 2nd International Conference on Structural Stability & Dynamics (ICSSD02) on 16-18 December 2002 in Singapore. It contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents:Meshfree FormulationsMeshfree Methods for Smart Materials/StructuresMeshfree Methods for Fracture AnalysisMeshfree Methods for Membranes, Plates & ShellsMeshfree Methods for SoilMeshfree Methods for CFDBoundary Meshfree MethodsCoding, Error Estimation, ParallisationMeshfree Particle MethodsX-FEM Readership: Graduate and undergraduate students, researchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering. Keywords:Meshfree Method;Meshless Method;SPH;X-FEM;Computational Mechanics;Computational Science;Fluid Dynamics;Modified Variational Principle;Smart Materials

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.

Advances in Meshfree and X-fem Methods

Advances in Meshfree and X-fem Methods
Proceedings of the 1 St Asian Workshop on Meshfree Methods, Singapore, 16-18 December, 2002

by Gui-Rong Liu

  • Publisher : World Scientific
  • Release : 2003
  • Pages : 258
  • ISBN : 9789812382474
  • Language : En, Es, Fr & De
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This book contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents: Meshfree Shape Functions for Weak Formulation, Strong Formulation; Meshfree Methods for Smart Materials/Structures; Meshfree Methods for Fracture Analysis; Meshfree Methods for Membrances, Plates & Shells; Meshfree Methods for Soil; Meshfree Methods for CFD; Boundary Meshfree Methods; Coding, Error Estimation, Parallisation; Meshfree Particle Methods; X-FEM. Readership: Graduate and undergraduate students, reserchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering.

Advances in Meshfree and X-fem Methods

Advances in Meshfree and X-fem Methods
Proceedings of the 1 St Asian Workshop on Meshfree Methods, Singapore, 16-18 December, 2002

by Gui-Rong Liu

  • Publisher : World Scientific
  • Release : 2003
  • Pages : 258
  • ISBN : 9789812382474
  • Language : En, Es, Fr & De
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This book contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents: Meshfree Shape Functions for Weak Formulation, Strong Formulation; Meshfree Methods for Smart Materials/Structures; Meshfree Methods for Fracture Analysis; Meshfree Methods for Membrances, Plates & Shells; Meshfree Methods for Soil; Meshfree Methods for CFD; Boundary Meshfree Methods; Coding, Error Estimation, Parallisation; Meshfree Particle Methods; X-FEM. Readership: Graduate and undergraduate students, reserchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering.

Meshfree Methods for Partial Differential Equations

Meshfree Methods for Partial Differential Equations
A Book

by Michael Griebel,Marc A. Schweitzer

  • Publisher : Springer Science & Business Media
  • Release : 2002-09-18
  • Pages : 471
  • ISBN : 9783540438915
  • Language : En, Es, Fr & De
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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.

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.

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

The Finite Element Method in Engineering

The Finite Element Method in Engineering
A Book

by Singiresu S. Rao

  • Publisher : Butterworth-Heinemann
  • Release : 2017-10-31
  • Pages : 782
  • ISBN : 0128143649
  • Language : En, Es, Fr & De
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The Finite Element Method in Engineering, Sixth Edition, provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique—an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how to set up finite element solutions in civil, mechanical and aerospace engineering applications. The new edition features updated real-world examples from MATLAB, Ansys and Abaqus, and a new chapter on additional FEM topics including extended FEM (X-FEM). Professional engineers will benefit from the introduction to the many useful applications of finite element analysis. Includes revised and updated chapters on MATLAB, Ansys and Abaqus Offers a new chapter, Additional Topics in Finite Element Method Includes discussion of practical considerations, errors and pitfalls in FEM singularity elements Features a brief presentation of recent developments in FEM including extended FEM (X-FEM), augmented FEM (A-FEM) and partition of unity FEM (POUFEM) Features improved pedagogy, including the addition of more design-oriented and practical examples and problems Covers real-life applications, sample review questions at the end of most chapters, and updated references

An Introduction to Meshfree Methods and Their Programming

An Introduction to Meshfree Methods and Their Programming
A Book

by G.R. Liu,Y.T. Gu

  • Publisher : Springer Science & Business Media
  • Release : 2005-12-05
  • Pages : 480
  • ISBN : 9781402034688
  • Language : En, Es, Fr & De
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The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

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.

Error Estimates for Advanced Galerkin Methods

Error Estimates for Advanced Galerkin Methods
A Book

by Marcus Olavi Rüter

  • Publisher : Springer Nature
  • Release : 2019-11-07
  • Pages : 496
  • ISBN : 3030061736
  • Language : En, Es, Fr & De
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This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

XFEM Fracture Analysis of Composites

XFEM Fracture Analysis of Composites
A Book

by Soheil Mohammadi

  • Publisher : John Wiley & Sons
  • Release : 2012-08-27
  • Pages : 400
  • ISBN : 1118443381
  • Language : En, Es, Fr & De
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This book describes the basics and developments of the new XFEMapproach to fracture analysis of composite structures andmaterials. It provides state of the art techniques and algorithmsfor fracture analysis of structures including numeric examples atthe end of each chapter as well as an accompanying website whichwill include MATLAB resources, executables, data files, andsimulation procedures of XFEM. The first reference text for the extended finite element method(XFEM) for fracture analysis of structures and materials Includes theory and applications, with worked numericalproblems and solutions, and MATLAB examples on an accompanyingwebsite with further XFEM resources Provides a comprehensive overview of this new area of research,including a review of Fracture Mechanics, basic through to advancedXFEM theory, as well as current problems and applications Includes a chapter on the future developments in the field, newresearch areas and possible future applications of the method

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.

Progress on Meshless Methods

Progress on Meshless Methods
A Book

by A. J. M. Ferreira,E. J. Kansa,G. E. Fasshauer,V.M.A. Leitao

  • Publisher : Springer Science & Business Media
  • Release : 2008-11-23
  • Pages : 308
  • ISBN : 1402088213
  • Language : En, Es, Fr & De
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In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues. The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Meshfree Methods for Partial Differential Equations II

Meshfree Methods for Partial Differential Equations II
A Book

by Michael Griebel,Marc Alexander Schweitzer

  • Publisher : Springer Science & Business Media
  • Release : 2004-12-02
  • Pages : 311
  • ISBN : 9783540230267
  • Language : En, Es, Fr & De
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The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Second International Workshop on Meshfree Methods held in September 2003 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this new and exciting area of interdisciplinary research and to present recent advances and results in this field.

Computer Methods in Mechanics

Computer Methods in Mechanics
Lectures of the CMM 2009

by Mieczyslaw Kuczma,Krzysztof Wilmanski

  • Publisher : Springer Science & Business Media
  • Release : 2010-03-10
  • Pages : 528
  • ISBN : 364205241X
  • Language : En, Es, Fr & De
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Prominent scientists present the latest achievements in computational methods and mechanics in this book. These lectures were held at the CMM 2009 conference.

Advances in Meshfree Techniques

Advances in Meshfree Techniques
A Book

by V.M.A. Leitao,C.J.S. Alves,C. Armando Duarte

  • Publisher : Springer Science & Business Media
  • Release : 2007-05-26
  • Pages : 315
  • ISBN : 1402060955
  • Language : En, Es, Fr & De
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The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors is a mix of highly distinguished authors as well as promising young researchers. This means that the reader gets a varied and contemporary view on different mesh reduction methods and its range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Encyclopedia of Applied and Computational Mathematics

Encyclopedia of Applied and Computational Mathematics
A Book

by Björn Engquist

  • Publisher : Springer
  • Release : 2016-12-16
  • Pages : 1564
  • ISBN : 9783662528723
  • Language : En, Es, Fr & De
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EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.

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.