| Description |
1 online resource (xiii, 296 pages) : illustrations (some color) |
| Contents |
Front Cover -- Fundamentals of Enriched Finite Element Methods -- Copyright -- Contents -- Preface -- 1 Introduction -- 1.1 Enriched finite element methods -- 1.2 Origins and milestones of e-FEMs -- References -- I Fundamentals -- 2 The finite element method -- 2.1 Linear elastostatics in 1-D -- 2.1.1 The strong form -- 2.1.2 The weak (or variational) form -- 2.1.2.1 Sobolev spaces -- 2.1.2.2 Non-homogeneous Dirichlet boundary conditions -- 2.1.3 The Galerkin formulation -- 2.1.3.1 Orthogonality of Galerkin error -- 2.1.4 The finite element discrete equations |
|
2.1.5 The isoparametric mapping -- 2.1.6 A priori error estimates -- 2.1.7 A posteriori error estimate -- 2.2 The elastostatics problem in higher dimensions -- 2.2.1 Strong form -- 2.2.2 Weak form -- 2.2.3 Principle of virtual work -- 2.2.4 Discrete formulation -- 2.2.5 Voigt notation -- 2.2.6 Isoparametric formulation in higher dimensions -- 2.3 Heat conduction -- 2.4 Problems -- References -- 3 The p-version of the finite element method -- 3.1 p-FEM in 1-D -- 3.1.1 A priori error estimates -- 3.2 p-FEM in 2-D -- 3.2.1 Basis functions for quadrangles -- 3.2.2 Basis functions for triangles |
|
3.3 Non-homogeneous essential boundary conditions -- 3.3.1 Interpolation at Gauss-Lobatto quadrature points -- 3.3.2 Projection on the space of edge functions -- 3.4 Problems -- References -- 4 The Generalized Finite Element Method -- 4.1 Finite element approximations -- 4.2 Generalized FEM approximations in 1-D -- 4.2.1 Selection of enrichment functions -- 4.2.2 What makes the GFEM work -- 4.3 Applications of the GFEM -- 4.4 Shifted and scaled enrichments -- 4.5 The p-version of the GFEM -- 4.5.1 High-order GFEM approximations for a strong discontinuity -- 4.6 GFEM approximation spaces |
|
4.7 Exercises -- References -- 5 Discontinuity-enriched finite element formulations -- 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 -- 5.4.1 Treatment of nonzero essential boundary conditions -- 5.4.2 Hierarchical space -- 5.5 Convergence -- 5.6 Weak and strong discontinuities -- 5.7 Recovery of field gradients -- References -- II Applications -- 6 GFEM approximations for fractures -- 6.1 Governing equations: 3-D elasticity -- 6.1.1 Weak form -- 6.2 GFEM approximation for fractures |
|
6.2.1 Approximation of ̂u -- 6.2.1.1 High-order approximations -- 6.2.2 Approximation of ̃̃u -- 6.2.3 Cohesive fracture problems -- 6.2.3.1 High-order approximations -- 6.2.4 Approximation of ̆u -- 6.2.4.1 Elasticity solution in the neighborhood of a crack front -- 6.2.4.2 Oden and Duarte branch enrichment functions -- 6.2.4.3 Belytschko and Black branch enrichment functions -- 6.2.5 Topological and geometrical singular enrichment -- 6.2.6 Discrete equilibrium equations -- 6.3 Convergence of linear GFEM approximations: 2-D edge crack -- 6.3.1 Topological enrichment |
|
6.3.2 Comparison with best-practice FEM |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from digital title page (viewed on October 23, 2024) |
| Subject |
Finite element method.
|
|
Engineering mathematics.
|
|
Engineering mathematics
|
|
Finite element method
|
| Form |
Electronic book
|
| Author |
Duarte, C. Armando, author.
|
| ISBN |
0323855164 |
|
9780323855167 |
|
