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E-book
Author Aragón, Alejandro M., author

Title Fundamentals of Enriched Finite Element Methods Alejandro M. Aragón, Armando Duarte
Published San Diego : Elsevier, 2023

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Description 1 online resource (312 p.)
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
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
Notes Description based upon print version of record
6.3.2 Comparison with best-practice FEM
Subject Finite element method.
Engineering mathematics.
Engineering mathematics
Finite element method
Form Electronic book
Author Duarte, C. Armando, author.
ISBN 0323855164
9780323855167