Finite element analysis: method, verification and validation
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2021
|
| Edition: | Second edition |
| Series: | Wiley series in computational mechanics
|
| Subjects: | |
| Online Access: | DE-1050 DE-91 DE-706 Volltext |
| Physical Description: | 1 Online-Ressource (xvii, 363 Seiten) |
| ISBN: | 9781119426387 9781119426479 9781119426462 |
| DOI: | 10.1002/9781119426479 |
Staff View
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| 505 | 8 | |a Cover -- Title Page -- Copyright -- Contents -- Preface to the second edition -- Preface to the first edition -- Preface -- About the companion website -- Chapter 1 Introduction to the finite element method -- 1.1 An introductory problem -- 1.2 Generalized formulation -- 1.2.1 The exact solution -- 1.2.2 The principle of minimum potential energy -- 1.3 Approximate solutions -- 1.3.1 The standard polynomial space -- 1.3.2 Finite element spaces in one dimension -- 1.3.3 Computation of the coefficient matrices -- 1.3.4 Computation of the right hand side vector -- 1.3.5 Assembly | |
| 505 | 8 | |a 1.3.6 Condensation -- 1.3.7 Enforcement of Dirichlet boundary conditions -- 1.4 Post-solution operations -- 1.4.1 Computation of the quantities of interest -- 1.5 Estimation of error in energy norm -- 1.5.1 Regularity -- 1.5.2 A priori estimation of the rate of convergence -- 1.5.3 A posteriori estimation of error -- 1.5.4 Error in the extracted QoI -- 1.6 The choice of discretization in 1D -- 1.6.1 The exact solution lies in Hk(I), k−1<p -- 1.6.2 The exact solution lies in Hk(I), k−1≤p -- 1.7 Eigenvalue problems -- 1.8 Other finite element methods -- 1.8.1 The mixed method | |
| 505 | 8 | |a 1.8.2 Nitsche's method -- Chapter 2 Boundary value problems -- 2.1 Notation -- 2.2 The scalar elliptic boundary value problem -- 2.2.1 Generalized formulation -- 2.2.2 Continuity -- 2.3 Heat conduction -- 2.3.1 The differential equation -- 2.3.2 Boundary and initial conditions -- 2.3.3 Boundary conditions of convenience -- 2.3.4 Dimensional reduction -- 2.4 Equations of linear elasticity - strong form -- 2.4.1 The Navier equations -- 2.4.2 Boundary and initial conditions -- 2.4.3 Symmetry, antisymmetry and periodicity -- 2.4.4 Dimensional reduction in linear elasticity | |
| 505 | 8 | |a 2.4.5 Incompressible elastic materials -- 2.5 Stokes flow -- 2.6 Generalized formulation of problems of linear elasticity -- 2.6.1 The principle of minimum potential energy -- 2.6.3 The principle of virtual work -- 2.6.4 Uniqueness -- 2.7 Residual stresses -- 2.8 Chapter summary -- Chapter 3 Implementation -- 3.1 Standard elements in two dimensions -- 3.2 Standard polynomial spaces -- 3.2.1 Trunk spaces -- 3.2.2 Product spaces -- 3.3 Shape functions -- 3.3.1 Lagrange shape functions -- 3.3.2 Hierarchic shape functions -- 3.4 Mapping functions in two dimensions -- 3.4.1 Isoparametric mapping | |
| 505 | 8 | |a 3.4.2 Mapping by the blending function method -- 3.4.3 Mapping algorithms for high order elements -- 3.5 Finite element spaces in two dimensions -- 3.6 Essential boundary conditions -- 3.7 Elements in three dimensions -- 3.7.1 Mapping functions in three dimensions -- 3.8 Integration and differentiation -- 3.8.1 Volume and area integrals -- 3.8.2 Surface and contour integrals -- 3.8.3 Differentiation -- 3.9 Stiffness matrices and load vectors -- 3.9.1 Stiffness matrices -- 3.9.2 Load vectors -- 3.10 Post-solution operations -- 3.11 Computation of the solution and its first derivatives | |
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| author | Szabó, Barna A. 1935- Babuška, Ivo 1926-2023 |
| author_GND | (DE-588)1014087902 (DE-588)104653639 |
| author_facet | Szabó, Barna A. 1935- Babuška, Ivo 1926-2023 |
| author_role | aut aut |
| author_sort | Szabó, Barna A. 1935- |
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| building | Verbundindex |
| bvnumber | BV047625518 |
| classification_rvk | SK 910 |
| classification_tum | BAU 154 MTA 009 |
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| contents | Cover -- Title Page -- Copyright -- Contents -- Preface to the second edition -- Preface to the first edition -- Preface -- About the companion website -- Chapter 1 Introduction to the finite element method -- 1.1 An introductory problem -- 1.2 Generalized formulation -- 1.2.1 The exact solution -- 1.2.2 The principle of minimum potential energy -- 1.3 Approximate solutions -- 1.3.1 The standard polynomial space -- 1.3.2 Finite element spaces in one dimension -- 1.3.3 Computation of the coefficient matrices -- 1.3.4 Computation of the right hand side vector -- 1.3.5 Assembly 1.3.6 Condensation -- 1.3.7 Enforcement of Dirichlet boundary conditions -- 1.4 Post-solution operations -- 1.4.1 Computation of the quantities of interest -- 1.5 Estimation of error in energy norm -- 1.5.1 Regularity -- 1.5.2 A priori estimation of the rate of convergence -- 1.5.3 A posteriori estimation of error -- 1.5.4 Error in the extracted QoI -- 1.6 The choice of discretization in 1D -- 1.6.1 The exact solution lies in Hk(I), k−1<p -- 1.6.2 The exact solution lies in Hk(I), k−1≤p -- 1.7 Eigenvalue problems -- 1.8 Other finite element methods -- 1.8.1 The mixed method 1.8.2 Nitsche's method -- Chapter 2 Boundary value problems -- 2.1 Notation -- 2.2 The scalar elliptic boundary value problem -- 2.2.1 Generalized formulation -- 2.2.2 Continuity -- 2.3 Heat conduction -- 2.3.1 The differential equation -- 2.3.2 Boundary and initial conditions -- 2.3.3 Boundary conditions of convenience -- 2.3.4 Dimensional reduction -- 2.4 Equations of linear elasticity - strong form -- 2.4.1 The Navier equations -- 2.4.2 Boundary and initial conditions -- 2.4.3 Symmetry, antisymmetry and periodicity -- 2.4.4 Dimensional reduction in linear elasticity 2.4.5 Incompressible elastic materials -- 2.5 Stokes flow -- 2.6 Generalized formulation of problems of linear elasticity -- 2.6.1 The principle of minimum potential energy -- 2.6.3 The principle of virtual work -- 2.6.4 Uniqueness -- 2.7 Residual stresses -- 2.8 Chapter summary -- Chapter 3 Implementation -- 3.1 Standard elements in two dimensions -- 3.2 Standard polynomial spaces -- 3.2.1 Trunk spaces -- 3.2.2 Product spaces -- 3.3 Shape functions -- 3.3.1 Lagrange shape functions -- 3.3.2 Hierarchic shape functions -- 3.4 Mapping functions in two dimensions -- 3.4.1 Isoparametric mapping 3.4.2 Mapping by the blending function method -- 3.4.3 Mapping algorithms for high order elements -- 3.5 Finite element spaces in two dimensions -- 3.6 Essential boundary conditions -- 3.7 Elements in three dimensions -- 3.7.1 Mapping functions in three dimensions -- 3.8 Integration and differentiation -- 3.8.1 Volume and area integrals -- 3.8.2 Surface and contour integrals -- 3.8.3 Differentiation -- 3.9 Stiffness matrices and load vectors -- 3.9.1 Stiffness matrices -- 3.9.2 Load vectors -- 3.10 Post-solution operations -- 3.11 Computation of the solution and its first derivatives |
| ctrlnum | (ZDB-35-WIC)9781119426479 (OCoLC)1289764681 (DE-599)BVBBV047625518 |
| discipline | Physik Bauingenieurwesen Mathematik |
| discipline_str_mv | Physik Bauingenieurwesen Mathematik |
| doi_str_mv | 10.1002/9781119426479 |
| edition | Second edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:44:16Z |
| indexdate | 2025-05-07T10:00:38Z |
| institution | BVB |
| isbn | 9781119426387 9781119426479 9781119426462 |
| language | English |
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| series2 | Wiley series in computational mechanics |
| spelling | Szabó, Barna A. 1935- Verfasser (DE-588)1014087902 aut Finite element analysis method, verification and validation Barna Szabó, Washington University in St. Louis, Ivo Babuška, The University of Texas at Austin Second edition Hoboken, NJ Wiley 2021 1 Online-Ressource (xvii, 363 Seiten) txt rdacontent c rdamedia cr rdacarrier Wiley series in computational mechanics Cover -- Title Page -- Copyright -- Contents -- Preface to the second edition -- Preface to the first edition -- Preface -- About the companion website -- Chapter 1 Introduction to the finite element method -- 1.1 An introductory problem -- 1.2 Generalized formulation -- 1.2.1 The exact solution -- 1.2.2 The principle of minimum potential energy -- 1.3 Approximate solutions -- 1.3.1 The standard polynomial space -- 1.3.2 Finite element spaces in one dimension -- 1.3.3 Computation of the coefficient matrices -- 1.3.4 Computation of the right hand side vector -- 1.3.5 Assembly 1.3.6 Condensation -- 1.3.7 Enforcement of Dirichlet boundary conditions -- 1.4 Post-solution operations -- 1.4.1 Computation of the quantities of interest -- 1.5 Estimation of error in energy norm -- 1.5.1 Regularity -- 1.5.2 A priori estimation of the rate of convergence -- 1.5.3 A posteriori estimation of error -- 1.5.4 Error in the extracted QoI -- 1.6 The choice of discretization in 1D -- 1.6.1 The exact solution lies in Hk(I), k−1<p -- 1.6.2 The exact solution lies in Hk(I), k−1≤p -- 1.7 Eigenvalue problems -- 1.8 Other finite element methods -- 1.8.1 The mixed method 1.8.2 Nitsche's method -- Chapter 2 Boundary value problems -- 2.1 Notation -- 2.2 The scalar elliptic boundary value problem -- 2.2.1 Generalized formulation -- 2.2.2 Continuity -- 2.3 Heat conduction -- 2.3.1 The differential equation -- 2.3.2 Boundary and initial conditions -- 2.3.3 Boundary conditions of convenience -- 2.3.4 Dimensional reduction -- 2.4 Equations of linear elasticity - strong form -- 2.4.1 The Navier equations -- 2.4.2 Boundary and initial conditions -- 2.4.3 Symmetry, antisymmetry and periodicity -- 2.4.4 Dimensional reduction in linear elasticity 2.4.5 Incompressible elastic materials -- 2.5 Stokes flow -- 2.6 Generalized formulation of problems of linear elasticity -- 2.6.1 The principle of minimum potential energy -- 2.6.3 The principle of virtual work -- 2.6.4 Uniqueness -- 2.7 Residual stresses -- 2.8 Chapter summary -- Chapter 3 Implementation -- 3.1 Standard elements in two dimensions -- 3.2 Standard polynomial spaces -- 3.2.1 Trunk spaces -- 3.2.2 Product spaces -- 3.3 Shape functions -- 3.3.1 Lagrange shape functions -- 3.3.2 Hierarchic shape functions -- 3.4 Mapping functions in two dimensions -- 3.4.1 Isoparametric mapping 3.4.2 Mapping by the blending function method -- 3.4.3 Mapping algorithms for high order elements -- 3.5 Finite element spaces in two dimensions -- 3.6 Essential boundary conditions -- 3.7 Elements in three dimensions -- 3.7.1 Mapping functions in three dimensions -- 3.8 Integration and differentiation -- 3.8.1 Volume and area integrals -- 3.8.2 Surface and contour integrals -- 3.8.3 Differentiation -- 3.9 Stiffness matrices and load vectors -- 3.9.1 Stiffness matrices -- 3.9.2 Load vectors -- 3.10 Post-solution operations -- 3.11 Computation of the solution and its first derivatives Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Babuška, Ivo 1926-2023 Verfasser (DE-588)104653639 aut Erscheint auch als Druck-Ausgabe, cloth 978-1-119-42642-4 https://doi.org/10.1002/9781119426479 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Szabó, Barna A. 1935- Babuška, Ivo 1926-2023 Finite element analysis method, verification and validation Cover -- Title Page -- Copyright -- Contents -- Preface to the second edition -- Preface to the first edition -- Preface -- About the companion website -- Chapter 1 Introduction to the finite element method -- 1.1 An introductory problem -- 1.2 Generalized formulation -- 1.2.1 The exact solution -- 1.2.2 The principle of minimum potential energy -- 1.3 Approximate solutions -- 1.3.1 The standard polynomial space -- 1.3.2 Finite element spaces in one dimension -- 1.3.3 Computation of the coefficient matrices -- 1.3.4 Computation of the right hand side vector -- 1.3.5 Assembly 1.3.6 Condensation -- 1.3.7 Enforcement of Dirichlet boundary conditions -- 1.4 Post-solution operations -- 1.4.1 Computation of the quantities of interest -- 1.5 Estimation of error in energy norm -- 1.5.1 Regularity -- 1.5.2 A priori estimation of the rate of convergence -- 1.5.3 A posteriori estimation of error -- 1.5.4 Error in the extracted QoI -- 1.6 The choice of discretization in 1D -- 1.6.1 The exact solution lies in Hk(I), k−1<p -- 1.6.2 The exact solution lies in Hk(I), k−1≤p -- 1.7 Eigenvalue problems -- 1.8 Other finite element methods -- 1.8.1 The mixed method 1.8.2 Nitsche's method -- Chapter 2 Boundary value problems -- 2.1 Notation -- 2.2 The scalar elliptic boundary value problem -- 2.2.1 Generalized formulation -- 2.2.2 Continuity -- 2.3 Heat conduction -- 2.3.1 The differential equation -- 2.3.2 Boundary and initial conditions -- 2.3.3 Boundary conditions of convenience -- 2.3.4 Dimensional reduction -- 2.4 Equations of linear elasticity - strong form -- 2.4.1 The Navier equations -- 2.4.2 Boundary and initial conditions -- 2.4.3 Symmetry, antisymmetry and periodicity -- 2.4.4 Dimensional reduction in linear elasticity 2.4.5 Incompressible elastic materials -- 2.5 Stokes flow -- 2.6 Generalized formulation of problems of linear elasticity -- 2.6.1 The principle of minimum potential energy -- 2.6.3 The principle of virtual work -- 2.6.4 Uniqueness -- 2.7 Residual stresses -- 2.8 Chapter summary -- Chapter 3 Implementation -- 3.1 Standard elements in two dimensions -- 3.2 Standard polynomial spaces -- 3.2.1 Trunk spaces -- 3.2.2 Product spaces -- 3.3 Shape functions -- 3.3.1 Lagrange shape functions -- 3.3.2 Hierarchic shape functions -- 3.4 Mapping functions in two dimensions -- 3.4.1 Isoparametric mapping 3.4.2 Mapping by the blending function method -- 3.4.3 Mapping algorithms for high order elements -- 3.5 Finite element spaces in two dimensions -- 3.6 Essential boundary conditions -- 3.7 Elements in three dimensions -- 3.7.1 Mapping functions in three dimensions -- 3.8 Integration and differentiation -- 3.8.1 Volume and area integrals -- 3.8.2 Surface and contour integrals -- 3.8.3 Differentiation -- 3.9 Stiffness matrices and load vectors -- 3.9.1 Stiffness matrices -- 3.9.2 Load vectors -- 3.10 Post-solution operations -- 3.11 Computation of the solution and its first derivatives Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4017233-8 |
| title | Finite element analysis method, verification and validation |
| title_auth | Finite element analysis method, verification and validation |
| title_exact_search | Finite element analysis method, verification and validation |
| title_exact_search_txtP | Finite element analysis method, verification and validation |
| title_full | Finite element analysis method, verification and validation Barna Szabó, Washington University in St. Louis, Ivo Babuška, The University of Texas at Austin |
| title_fullStr | Finite element analysis method, verification and validation Barna Szabó, Washington University in St. Louis, Ivo Babuška, The University of Texas at Austin |
| title_full_unstemmed | Finite element analysis method, verification and validation Barna Szabó, Washington University in St. Louis, Ivo Babuška, The University of Texas at Austin |
| title_short | Finite element analysis |
| title_sort | finite element analysis method verification and validation |
| title_sub | method, verification and validation |
| topic | Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite-Elemente-Methode |
| url | https://doi.org/10.1002/9781119426479 |
| work_keys_str_mv | AT szabobarnaa finiteelementanalysismethodverificationandvalidation AT babuskaivo finiteelementanalysismethodverificationandvalidation |