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.
1. Chapter One: Introduction - p. xx 2. Chapter Two: Weak forms and governing equations - p. 18 3. Chapter Three: Extended finite element method - p. 28 4. Chapter Four: Phantom node method - p. 151 5. Chapter Five: Extended meshfree methods - p. 160 6. Chapter Six: Extended isogeometric analysis - p. 313 7. Chapter Seven: Fracture in plates and shells - p. 358 8. Chapter Eight: Fracture criteria and crack tracking procedures - p. 435 9. Chapter Nine: Multiscale methods for fracture - p. 470 10. Chapter Ten: A short overview of alternatives for fracture - p. 519 11. Chapter Eleven: Implementation details - p. 579 12. Part One: Appendices - p. 598 13. Appendix A: Derivation of shape derivative for the nanoelasticity problem - p. 598 14. Appendix B: Derivation of the adjoint problem for the nanopiezoelectricity problem - p. 602 15. Index - p. 607
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.
1. Chapter One: Introduction - p. xx 2. Chapter Two: Weak forms and governing equations - p. 18 3. Chapter Three: Extended finite element method - p. 28 4. Chapter Four: Phantom node method - p. 151 5. Chapter Five: Extended meshfree methods - p. 160 6. Chapter Six: Extended isogeometric analysis - p. 313 7. Chapter Seven: Fracture in plates and shells - p. 358 8. Chapter Eight: Fracture criteria and crack tracking procedures - p. 435 9. Chapter Nine: Multiscale methods for fracture - p. 470 10. Chapter Ten: A short overview of alternatives for fracture - p. 519 11. Chapter Eleven: Implementation details - p. 579 12. Part One: Appendices - p. 598 13. Appendix A: Derivation of shape derivative for the nanoelasticity problem - p. 598 14. Appendix B: Derivation of the adjoint problem for the nanopiezoelectricity problem - p. 602 15. Index - p. 607
