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Extended Finite Element and Meshfree Methods

  • 1st Edition - November 13, 2019
  • Latest edition
  • Authors: Timon Rabczuk, Jeong-Hoon Song, Xiaoying Zhuang, Cosmin Anitescu
  • Language: English

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… Read more

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Description

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.

Key features

  • 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

Readership

Advanced students, researchers, and engineers interested in learning about and coding using meshfree methods, particularly for applications in solid mechanics

Table of contents

1. Introduction2. Weak forms and governing equations3. Extended Finite Element Method4. Phantom Node Method5. Extended Meshfree Methods6. Extended Isogeometric Analysis7. Fracture in plates and shells8. Fracture criteria and crack tracking procedures 9. Multiscale methods for fracture10. A short overview of alternatives11. Implementation details

Product details

  • Edition: 1
  • Latest edition
  • Published: November 13, 2019
  • Language: English

About the authors

TR

Timon Rabczuk

Timon Rabczuk is Professor of Modeling and Simulation, and Chair of Computational Mechanics at the Bauhaus Universität Weimar, Germany. He has published more than 450 SCI papers, many of them on extended finite element and meshfree methods, multiscale methods and isogeometric analysis. He is editor-in-chief of CMC-Computers, Materials and Continua, associated editor of International Journal of Impact Engineering, assistant editor of Computational Mechanics, and executive editor of FSCE-Frontiers of Structural and Civil Engineering. He was listed as one of ISI Highly Cited Researchers in Computer Science and Engineering from 2014 up to now.
Affiliations and expertise
Professor of Modeling and Simulation and Chair of Computational Mechanics, Bauhaus Universitat Weimar, Germany

JS

Jeong-Hoon Song

Jeong-Hoon Song is Assistant Professor of Civil, Environmental, and Architectural Engineering and faculty member of Materials Science and Engineering Program at the University of Colorado, Boulder, USA. He received a Ph.D. in Theoretical and Applied Mechanics at Northwestern University in 2008 and has worked in the area of computational mechanics and physics of solids to develop new computational methods and algorithms for various multiscale/multiphysics phenomena. He has authored over 45 peer-reviewed journal publications and two book chapters and has presented over 70 research lectures at national and international conferences, seminars, and workshops.
Affiliations and expertise
Assistant Professor of Civil, Environmental, and Architectural Engineering and faculty member of Materials Science and Engineering Program at the University of Colorado, Boulder, USA.

XZ

Xiaoying Zhuang

Xiaoying Zhuang is Associate Professor at the Institute of Continuum Mechanics at Leibniz Universität Hannover, Germany. She has been developing computational methods for two-dimensional and three-dimensional fracture problems using partition-of-unity methods, including meshfree methods, the extended finite element method (XFEM), the phantom node and finite cover method, and multiscale methods. She is on the editorial boards of international journals including Theoretical and Applied Fracture Mechanics, KSCE Journal of Civil Engineering, and Engineering Geology.
Affiliations and expertise
Associate Professor, Institute of Continuum Mechanics, Leibniz Universitat Hannover, Germany

CA

Cosmin Anitescu

Cosmin Anitescu is a researcher at the Institute for Structural Mechanics of the Bauhaus Universität Weimar, Germany. His research focuses on the theory and application of extended finite elements, meshfree methods, and isogeometric analysis to engineering problems. He is currently the main contributor and maintainer of IGAFEM, an educational software package written in Matlab for solving computational mechanics problems.
Affiliations and expertise
Researcher, Institute for Structural Mechanics, Bauhaus Universitat Weimar, Germany

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