Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and also looks at their real-world applications, recommending in what situations they’re best implemented. It starts with a concise background on the theory required to understand the underlying functioning principles behind enriched finite element methods before outlining detailed instruction on implementation of the techniques in standard displacement-based finite element codes. The strengths and weaknesses of each are discussed, as are computer implementation details, including a standalone generalized finite element package, written in Python. The applications of the methods to a range of scenarios, including multi-phase, fracture, multiscale, and immersed boundary (fictitious domain) problems are covered, and readers can find ready-to-use code, simulation videos, and other useful resources on the companion website to the book.
1. 1 : Introduction - p. Page xi 2. 2 : The finite element method - p. Page 6 3. 3 : The p-version of the finite element method - p. Page 55 4. 4 : The Generalized Finite Element Method - p. Page 74 5. 5 : Discontinuity-enriched finite element formulations - p. Page 101 6. 6 : GFEM approximations for fractures - p. Page 127 7. 7 : Generalized enrichment functions for weak discontinuities - p. Page 163 8. 8 : Immerse boundary (fictitious domain) problems - p. Page 178 9. 9 : Non-conforming mesh coupling and contact - p. Page 187 10. 10 : Interface-enriched topology optimization - p. Page 200 11. 11 : Stability of approximations - p. Page 219 12. 12 : Computational aspects - p. Page 248 13. 13 : Approximation theory for partition of unity methods - p. Page 261 14. A : Recollections of the origins of the GFEM - p. Page 273 15. Index - p. Page 287
Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and also looks at their real-world applications, recommending in what situations they’re best implemented. It starts with a concise background on the theory required to understand the underlying functioning principles behind enriched finite element methods before outlining detailed instruction on implementation of the techniques in standard displacement-based finite element codes. The strengths and weaknesses of each are discussed, as are computer implementation details, including a standalone generalized finite element package, written in Python. The applications of the methods to a range of scenarios, including multi-phase, fracture, multiscale, and immersed boundary (fictitious domain) problems are covered, and readers can find ready-to-use code, simulation videos, and other useful resources on the companion website to the book.
1. 1 : Introduction - p. Page xi 2. 2 : The finite element method - p. Page 6 3. 3 : The p-version of the finite element method - p. Page 55 4. 4 : The Generalized Finite Element Method - p. Page 74 5. 5 : Discontinuity-enriched finite element formulations - p. Page 101 6. 6 : GFEM approximations for fractures - p. Page 127 7. 7 : Generalized enrichment functions for weak discontinuities - p. Page 163 8. 8 : Immerse boundary (fictitious domain) problems - p. Page 178 9. 9 : Non-conforming mesh coupling and contact - p. Page 187 10. 10 : Interface-enriched topology optimization - p. Page 200 11. 11 : Stability of approximations - p. Page 219 12. 12 : Computational aspects - p. Page 248 13. 13 : Approximation theory for partition of unity methods - p. Page 261 14. A : Recollections of the origins of the GFEM - p. Page 273 15. Index - p. Page 287
