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Fundamentals of Enriched Finite Element Methods
- 1st Edition - November 9, 2023
- Authors: Alejandro M. Aragón, C. Armando Duarte
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 8 5 5 1 5 - 0
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 8 5 5 1 6 - 7
Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and their real-w… Read more
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Request a sales quoteFundamentals 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.
- 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
Researchers working on numerical procedures in sold mechanics, Graduate students in a broad range of engineering disciplines, Professional engineers looking for new FEM techniques
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- 1: Introduction
- Abstract
- 1.1. Enriched finite element methods
- 1.2. Origins and milestones of e-FEMs
- References
- Part One: Fundamentals
- 2: The finite element method
- Abstract
- 2.1. Linear elastostatics in 1-D
- 2.2. The elastostatics problem in higher dimensions
- 2.3. Heat conduction
- 2.4. Problems
- References
- 3: The p-version of the finite element method
- Abstract
- 3.1. p-FEM in 1-D
- 3.2. p-FEM in 2-D
- 3.3. Non-homogeneous essential boundary conditions
- 3.4. Problems
- References
- 4: The Generalized Finite Element Method
- Abstract
- 4.1. Finite element approximations
- 4.2. Generalized FEM approximations in 1-D
- 4.3. Applications of the GFEM
- 4.4. Shifted and scaled enrichments
- 4.5. The p-version of the GFEM
- 4.6. GFEM approximation spaces
- 4.7. Exercises
- References
- 5: Discontinuity-enriched finite element formulations
- Abstract
- 5.1. A weak discontinuity in 1-D
- 5.2. A strong discontinuity in 1-D
- 5.3. Relationship to GFEM
- 5.4. The discontinuity-enriched FEM in multiple dimensions
- 5.5. Convergence
- 5.6. Weak and strong discontinuities
- 5.7. Recovery of field gradients
- References
- Part Two: Applications
- 6: GFEM approximations for fractures
- Abstract
- 6.1. Governing equations: 3-D elasticity
- 6.2. GFEM approximation for fractures
- 6.3. Convergence of linear GFEM approximations: 2-D edge crack
- 6.4. Convergence of linear GFEM approximations: 3-D edge crack
- References
- 7: Generalized enrichment functions for weak discontinuities
- Abstract
- 7.1. Formulation
- 7.2. Discussion and further reading
- References
- 8: Immerse boundary (fictitious domain) problems
- Abstract
- 8.1. Formulation
- References
- 9: Non-conforming mesh coupling and contact
- Abstract
- 9.1. Formulation
- 9.2. Examples
- 9.3. Further reading
- References
- 10: Interface-enriched topology optimization
- Abstract
- 10.1. Formulation
- 10.2. Compliance minimization
- 10.3. Fracture resistance
- 10.4. Discussion and further reading
- References
- Part Three: Computational aspects
- 11: Stability of approximations
- Abstract
- 11.1. Conditioning control of GFEM matrices
- 11.2. Stability of interface-enriched generalized finite element formulations
- References
- 12: Computational aspects
- Abstract
- 12.1. A basic FEM code structure
- 12.2. e-FEM considerations
- References
- 13: Approximation theory for partition of unity methods
- Abstract
- 13.1. Approximation theory for the GFEM
- 13.2. A priori error estimates for partition of unity approximations
- References
- A: Recollections of the origins of the GFEM
- A.1. The hp-cloud method
- A.2. The name partition of unity method is coined
- A.3. A partition of unity method for problems with singularities
- A.4. Wrapping up my PhD at UT Austin
- A.5. Work on partition of unity methods at COMCO and Altair Engineering
- A.6. Early work on partition of unity methods at Texas A&M University
- A.7. Early work on partition of unity methods at Northwestern University
- References
- Index
- No. of pages: 310
- Language: English
- Edition: 1
- Published: November 9, 2023
- Imprint: Elsevier
- Paperback ISBN: 9780323855150
- eBook ISBN: 9780323855167
AA
Alejandro M. Aragón
Alejandro M. Aragón is an Associate Professor in the Department of Precision and Microsystems Engineering at Delft University of Technology in the Netherlands. His research stands at the intersection of engineering and computer science, with a primary focus on pioneering novel enriched finite element methods. This cutting-edge technology, seamlessly integrated in widely applicable software, is leveraged to address complex engineering challenges. Specifically, Dr. Aragón’s innovations have been employed in the analysis and design of a diverse spectrum of (meta)materials and structures, including biomimetic and composite materials, as well as acoustic/elastic metamaterials, photonic/phononic crystals, and even edible fracture metamaterials. Since 2015 he has also been teaching advanced courses on finite element analysis at TU Delft. Dr. Aragón boasts a strong industrial network and holds two patents for the inventive use of acoustic/elastic metamaterials and phononic crystals for noise attenuation.
Affiliations and expertise
Associate Professor, Precision and Microsystems Engineering, Delft University of Technology, NetherlandsCD
C. Armando Duarte
C. Armando Duarte is a Professor in the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign. Prior to joining the UIUC, he was an assistant professor in the Department of Mechanical Engineering at the University of Alberta, Canada, and a visiting professor in the Department of Structural Engineering at the University of Sao Paulo, Brazil. He has five years of industrial experience and has made fundamental and sustained contributions to the fields of computational mechanics and methods, in particular to development of Meshfree, Partition of Unity, and Generalized/eXtended Finite Element Methods. He proposed the first partition of unity method to solve fracture problems and pioneered the use of asymptotic solutions of elasticity equations of cracks as enrichment functions for this class of methods. His group has developed a 3D GFEM for the simulation of hydraulic fracture propagation, interaction, and coalescence, and he has published more than 95 scientific articles and book chapters, and also coedited 2 books on computational methods. He has papers featured on the ScienceDirect top 25 Hottest Articles of Computer Methods in Applied Mechanics and Engineering and Engineering Fracture Mechanics.
Affiliations and expertise
Professor, Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Urbana, IL, USARead Fundamentals of Enriched Finite Element Methods on ScienceDirect