Description
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.- Reviews various enriched finite element methods, providing pros, cons, and scenarios forbest use- Provides step-by-step instruction on implementing these methods- Covers the theory of general and enriched finite element methods
Table of Contents
1. Introduction2. The Finite Element Method.3. The p-version of the Finite Element Method4. The Generalized Finite Element Method5. Discontinuity-enriched Finite Element Formulations6. GFEM approximations for fractures7. Approximations for Weak Discontinuities8. Immerse boundary (fictitious domain) problems9. Nonconforming mesh coupling and contact10. Interface-enriched topology optimization11. Stability of approximations12. Computational aspects13. Approximation theory for partition of unity methodsAppendix. Recollections of the origins of the GFEM
