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Fundamentals of enriched finite element methods /

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 re...

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שמור ב:
מידע ביבליוגרפי
Main Authors: Aragón, Alejandro M. (Author), Duarte, C. Armando (Author)
פורמט: אלקטרוני ספר אלקטרוני
שפה:אנגלית
יצא לאור: Amsterdam, Netherlands ; Cambridge, MA, United States : Elsevier, [2024]
נושאים:
Finite element method.
Engineering mathematics.
Méthode des éléments finis.
Mathématiques de l'ingénieur.
Engineering mathematics
Finite element method
גישה מקוונת:ScienceDirect
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תוכן הענינים:
  • 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

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