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Full Description
Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and their real-world applications, recommending in what situations they are best implemented. It starts with a concise background on the theory required to understand the underlying principles behind the 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 multiphase, 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 of the book.
Contents
1. Introduction
2. The Finite Element Method.
3. The p-version of the Finite Element Method
4. The Generalized Finite Element Method
5. Discontinuity-enriched Finite Element Formulations
6. GFEM approximations for fractures
7. Approximations for Weak Discontinuities
8. Immerse boundary (fictitious domain) problems
9. Nonconforming mesh coupling and contact
10. Interface-enriched topology optimization
11. Stability of approximations
12. Computational aspects
13. Approximation theory for partition of unity methods
Appendix. Recollections of the origins of the GFEM
