extended finite element and meshfree methods

Extended Finite Element And Meshfree Methods
Author: Timon Rabczuk
Publisher: Academic Press
Release Date: 2019-11-13
Pages: 638
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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
Author: G R Liu
Publisher: World Scientific
Release Date: 2002-12-16
Pages: 272
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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

Advances In Meshfree And X Fem Methods
Author: Gui-Rong Liu
Publisher: World Scientific
Release Date: 2003
Pages: 258
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Finite Element Method  Concepts And Applications
Author: Connie Mcguire
Publisher:
Release Date: 2019-06-06
Pages: 237
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

The Finite Element Method In Engineering
Author: Singiresu S. Rao
Publisher: Butterworth-Heinemann
Release Date: 2017-10-31
Pages: 782
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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

Extended Finite Element Method For Crack Propagation
Author: Sylvie Pommier
Publisher: John Wiley & Sons
Release Date: 2013-03-04
Pages: 254
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Extended Finite Element Method
Author: Amir R. Khoei
Publisher: John Wiley & Sons
Release Date: 2015-02-23
Pages: 584
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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

Advances In Meshfree And X Fem Methods
Author: Gui-Rong Liu
Publisher: World Scientific
Release Date: 2003
Pages: 258
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Error Estimates For Advanced Galerkin Methods
Author: Marcus Olavi Rüter
Publisher: Springer Nature
Release Date: 2019-11-07
Pages: 496
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Progress On Meshless Methods
Author: A. J. M. Ferreira
Publisher: Springer Science & Business Media
Release Date: 2008-11-23
Pages: 308
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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
Author: Michael Griebel
Publisher: Springer Science & Business Media
Release Date: 2004-12-02
Pages: 311
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Advances In Meshfree Techniques
Author: V.M.A. Leitao
Publisher: Springer Science & Business Media
Release Date: 2007-05-26
Pages: 315
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Meshfree Methods For Partial Differential Equations V
Author: Michael Griebel
Publisher: Springer Science & Business Media
Release Date: 2010-11-04
Pages: 270
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. 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 Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.

Meshfree Methods For Partial Differential Equations IV
Author: Michael Griebel
Publisher: Springer Science & Business Media
Release Date: 2008-10-10
Pages: 412
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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 proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 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 very active and exciting area of interdisciplinary research and to present recent advances and results in this field.

An Extended Finite Element Method With Discontinuous Enrichment For Applied Mechanics
Author: John Everett Dolbow
Publisher:
Release Date: 1999
Pages: 396
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Extended Finite Element Method
Author: Soheil Mohammadi
Publisher: John Wiley & Sons
Release Date: 2008-04-30
Pages: 280
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Numerical Differential Equations
Author: Source Wikipedia
Publisher: University-Press.org
Release Date: 2013-09
Pages: 116
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 114. Chapters: Discrete element method, Finite difference, Shooting method, Finite-difference time-domain method, Finite element method, MUSCL scheme, Constraint algorithm, Verlet integration, Runge-Kutta methods, Linear multistep method, Stiff equation, Particle-in-cell, Crank-Nicolson method, Finite element method in structural mechanics, Numerical ordinary differential equations, Direct stiffness method, Flux limiter, Smoothed-particle hydrodynamics, Cea's lemma, Finite difference method, Spectral method, Euler method, Transmission line matrix method, List of Runge-Kutta methods, Discrete Laplace operator, Finite pointset method, Eigenvalues and eigenvectors of the second derivative, Finite volume method, Moving particle semi-implicit method, Discrete Poisson equation, Modal analysis using FEM, Boundary element method, Shock capturing methods, Parallel mesh generation, Galerkin method, Cell lists, Godunov's theorem, Five-point stencil, Vorticity confinement, Symplectic integrator, Split-step method, Perfectly matched layer, Weak formulation, Finite difference coefficient, Finite difference methods for option pricing, Energy drift, Meshfree methods, Geometric integrator, Direct multiple shooting method, Kronecker sum of discrete Laplacians, Image-based meshing, Adaptive stepsize, Numerov's method, Method of lines, Semi-implicit Euler method, Upwind scheme, Trefftz method, Interval boundary element method, Beeman's algorithm, AUSM, Rayleigh-Ritz method, Adaptive mesh refinement, Compact stencil, Godunov's scheme, Partial element equivalent circuit, Alternating direction implicit method, History of numerical solution of differential equations using computers, Variational integrator, Dormand-Prince method, Extended finite element method, Fast multipole method, Midpoint method, Explicit and implicit methods, Immersed...

Computational Methods
Author: G.R. Liu
Publisher: Springer Science & Business Media
Release Date: 2007-05-26
Pages: 925
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Computer Methods In Mechanics
Author: Mieczyslaw Kuczma
Publisher: Springer Science & Business Media
Release Date: 2010-03-10
Pages: 528
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Prominent scientists present the latest achievements in computational methods and mechanics in this book. These lectures were held at the CMM 2009 conference.

Geometrically Unfitted Finite Element Methods And Applications
Author: Stéphane P. A. Bordas
Publisher: Springer
Release Date: 2018-03-13
Pages: 361
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.