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Finite element analysis : method, verification and validation / / Barna Szabô, Ivo Babuška
| Finite element analysis : method, verification and validation / / Barna Szabô, Ivo Babuška |
| Autore | Szabo B. A (Barna Aladar), <1935-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] |
| Descrizione fisica | 1 online resource (387 pages) |
| Disciplina | 620.00151535 |
| Collana | Wiley Series in Computational Mechanics Ser. |
| Soggetto topico | Finite element method |
| ISBN |
1-119-42646-4
1-119-42638-3 1-119-42647-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 -- 3.12 Nodal forces -- 3.12.1 Nodal forces in the h‐version -- 3.12.2 Nodal forces in the p‐version -- 3.12.3 Nodal forces and stress resultants -- 3.13 Chapter summary -- Chapter 4 Pre‐ and postprocessing procedures and verification -- 4.1 Regularity in two and three dimensions -- 4.2 The Laplace equation in two dimensions -- 4.2.1 2D model problem, uEX∈Hk(Ω),k−1< -- p -- 4.2.2 2D model problem, uEX∈Hk(Ω),k−1≤p -- 4.2.3 Computation of the flux vector in a given point -- 4.2.4 Computation of the flux intensity factors -- 4.2.5 Material interfaces -- 4.3 The Laplace equation in three dimensions -- 4.4 Planar elasticity -- 4.4.1 Problems of elasticity on an L‐shaped domain -- 4.4.2 Crack tip singularities in 2D -- 4.4.3 Forcing functions acting on boundaries -- 4.5 Robustness. 4.6 Solution verification -- Chapter 5 Simulation -- 5.1 Development of a very useful mathematical model -- 5.1.1 The Bernoulli‐Euler beam model -- 5.1.2 Historical notes on the Bernoulli‐Euler beam model -- 5.2 Finite element modeling and numerical simulation -- 5.2.1 Numerical simulation -- 5.2.2 Finite element modeling -- 5.2.3 Calibration versus tuning -- 5.2.4 Simulation governance -- 5.2.5 Milestones in numerical simulation -- 5.2.6 Example: The Girkmann problem -- 5.2.7 Example: Fastened structural connection -- 5.2.8 Finite element model -- 5.2.9 Example: Coil spring with displacement boundary conditions -- 5.2.10 Example: Coil spring segment -- Chapter 6 Calibration, validation and ranking -- 6.1 Fatigue data -- 6.1.1 Equivalent stress -- 6.1.2 Statistical models -- 6.1.3 The effect of notches -- 6.1.4 Formulation of predictors of fatigue life -- 6.2 The predictors of Peterson and Neuber -- 6.2.1 The effect of notches - calibration -- 6.2.2 The effect of notches - validation -- 6.2.3 Updated calibration -- 6.2.4 The fatigue limit -- 6.2.5 Discussion -- 6.3 The predictor Gα -- 6.3.1 Calibration of β(V,α) -- 6.3.2 Ranking -- 6.3.3 Comparison of Gα with Peterson's revised predictor -- 6.4 Biaxial test data -- 6.4.1 Axial, torsional and combined in‐phase loading -- 6.4.2 The domain of calibration -- 6.4.3 Out‐of‐phase biaxial loading -- 6.5 Management of model development -- 6.5.1 Obstacles to progress -- Chapter 7 Beams, plates and shells -- 7.1 Beams -- 7.1.1 The Timoshenko beam -- 7.1.2 The Bernoulli‐Euler beam -- 7.2 Plates -- 7.2.1 The Reissner‐Mindlin plate -- 7.2.2 The Kirchhoff plate -- 7.2.3 The transverse variation of displacements -- 7.3 Shells -- 7.3.1 Hierarchic thin solid models -- 7.4 Chapter summary -- Chapter 8 Aspects of multiscale models -- 8.1 Unidirectional fiber‐reinforced laminae. 8.1.1 Determination of material constants -- 8.1.2 The coefficients of thermal expansion -- 8.1.3 Examples -- 8.1.4 Localization -- 8.1.5 Prediction of failure in composite materials -- 8.1.6 Uncertainties -- 8.2 Discussion -- Chapter 9 Non‐linear models -- 9.1 Heat conduction -- 9.1.1 Radiation -- 9.1.2 Nonlinear material properties -- 9.2 Solid mechanics -- 9.2.1 Large strain and rotation -- 9.2.2 Structural stability and stress stiffening -- 9.2.3 Plasticity -- 9.2.4 Mechanical contact -- 9.3 Chapter summary -- Appendix A Definitions -- A.1 Normed linear spaces, linear functionals and bilinear forms -- A.1.1 Normed linear spaces -- A.1.2 Linear forms -- A.1.3 Bilinear forms -- A.2 Convergence in the space X -- A.2.1 The space of continuous functions -- A.2.2 The space Lp(Ω) -- A.2.3 Sobolev space of order 1 -- A.2.4 Sobolev spaces of fractional index -- A.3 The Schwarz inequality for integrals -- Appendix B Proof of h‐convergence -- Appendix C Convergence in 3D: Empirical results -- Appendix D Legendre polynomials -- D.1 Shape functions based on Legendre polynomials -- Appendix E Numerical quadrature -- E.1 Gaussian quadrature -- E.2 Gauss‐Lobatto quadrature -- Appendix F Polynomial mapping functions -- F.1 Interpolation on surfaces -- F.1.1 Interpolation on the standard quadrilateral element -- F.1.2 Interpolation on the standard triangle -- Appendix G Corner singularities in two‐dimensional elasticity -- G.1 The Airy stress function -- G.2 Stress‐free edges -- G.2.1 Symmetric eigenfunctions -- G.2.2 Antisymmetric eigenfunctions -- G.2.3 The L‐shaped domain -- G.2.4 Corner points -- Appendix H Computation of stress intensity factors -- H.1 Singularities at crack tips -- H.2 The contour integral method -- H.3 The energy release rate -- H.3.1 Symmetric (Mode I) loading -- H.3.2 Antisymmetric (Mode II) loading. H.3.3 Combined (Mode I and Mode II) loading -- H.3.4 Computation by the stiffness derivative method -- Appendix I Fundamentals of data analysis -- I.1 Statistical foundations -- I.2 Test data -- I.3 Statistical models -- I.4 Ranking -- I.5 Confidence intervals -- Appendix J Estimation of fastener forces in structural connections -- Appendix K Useful algorithms in solid mechanics -- K.1 The traction vector -- K.2 Transformation of vectors -- K.3 Transformation of stresses -- K.4 Principal stresses -- K.5 The von Mises stress -- K.6 Statically equivalent forces and moments -- K.6.1 Technical formulas for stress -- Bibliography -- Index -- EULA. |
| Record Nr. | UNINA-9910554857303321 |
Szabo B. A (Barna Aladar), <1935->
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite element analysis : method, verification and validation / / Barna Szabô, Ivo Babuška
| Finite element analysis : method, verification and validation / / Barna Szabô, Ivo Babuška |
| Autore | Szabo B. A (Barna Aladar), <1935-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] |
| Descrizione fisica | 1 online resource (387 pages) |
| Disciplina | 620.00151535 |
| Collana | Wiley Series in Computational Mechanics |
| Soggetto topico | Finite element method |
| ISBN |
1-119-42646-4
1-119-42638-3 1-119-42647-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 -- 3.12 Nodal forces -- 3.12.1 Nodal forces in the h‐version -- 3.12.2 Nodal forces in the p‐version -- 3.12.3 Nodal forces and stress resultants -- 3.13 Chapter summary -- Chapter 4 Pre‐ and postprocessing procedures and verification -- 4.1 Regularity in two and three dimensions -- 4.2 The Laplace equation in two dimensions -- 4.2.1 2D model problem, uEX∈Hk(Ω),k−1< -- p -- 4.2.2 2D model problem, uEX∈Hk(Ω),k−1≤p -- 4.2.3 Computation of the flux vector in a given point -- 4.2.4 Computation of the flux intensity factors -- 4.2.5 Material interfaces -- 4.3 The Laplace equation in three dimensions -- 4.4 Planar elasticity -- 4.4.1 Problems of elasticity on an L‐shaped domain -- 4.4.2 Crack tip singularities in 2D -- 4.4.3 Forcing functions acting on boundaries -- 4.5 Robustness. 4.6 Solution verification -- Chapter 5 Simulation -- 5.1 Development of a very useful mathematical model -- 5.1.1 The Bernoulli‐Euler beam model -- 5.1.2 Historical notes on the Bernoulli‐Euler beam model -- 5.2 Finite element modeling and numerical simulation -- 5.2.1 Numerical simulation -- 5.2.2 Finite element modeling -- 5.2.3 Calibration versus tuning -- 5.2.4 Simulation governance -- 5.2.5 Milestones in numerical simulation -- 5.2.6 Example: The Girkmann problem -- 5.2.7 Example: Fastened structural connection -- 5.2.8 Finite element model -- 5.2.9 Example: Coil spring with displacement boundary conditions -- 5.2.10 Example: Coil spring segment -- Chapter 6 Calibration, validation and ranking -- 6.1 Fatigue data -- 6.1.1 Equivalent stress -- 6.1.2 Statistical models -- 6.1.3 The effect of notches -- 6.1.4 Formulation of predictors of fatigue life -- 6.2 The predictors of Peterson and Neuber -- 6.2.1 The effect of notches - calibration -- 6.2.2 The effect of notches - validation -- 6.2.3 Updated calibration -- 6.2.4 The fatigue limit -- 6.2.5 Discussion -- 6.3 The predictor Gα -- 6.3.1 Calibration of β(V,α) -- 6.3.2 Ranking -- 6.3.3 Comparison of Gα with Peterson's revised predictor -- 6.4 Biaxial test data -- 6.4.1 Axial, torsional and combined in‐phase loading -- 6.4.2 The domain of calibration -- 6.4.3 Out‐of‐phase biaxial loading -- 6.5 Management of model development -- 6.5.1 Obstacles to progress -- Chapter 7 Beams, plates and shells -- 7.1 Beams -- 7.1.1 The Timoshenko beam -- 7.1.2 The Bernoulli‐Euler beam -- 7.2 Plates -- 7.2.1 The Reissner‐Mindlin plate -- 7.2.2 The Kirchhoff plate -- 7.2.3 The transverse variation of displacements -- 7.3 Shells -- 7.3.1 Hierarchic thin solid models -- 7.4 Chapter summary -- Chapter 8 Aspects of multiscale models -- 8.1 Unidirectional fiber‐reinforced laminae. 8.1.1 Determination of material constants -- 8.1.2 The coefficients of thermal expansion -- 8.1.3 Examples -- 8.1.4 Localization -- 8.1.5 Prediction of failure in composite materials -- 8.1.6 Uncertainties -- 8.2 Discussion -- Chapter 9 Non‐linear models -- 9.1 Heat conduction -- 9.1.1 Radiation -- 9.1.2 Nonlinear material properties -- 9.2 Solid mechanics -- 9.2.1 Large strain and rotation -- 9.2.2 Structural stability and stress stiffening -- 9.2.3 Plasticity -- 9.2.4 Mechanical contact -- 9.3 Chapter summary -- Appendix A Definitions -- A.1 Normed linear spaces, linear functionals and bilinear forms -- A.1.1 Normed linear spaces -- A.1.2 Linear forms -- A.1.3 Bilinear forms -- A.2 Convergence in the space X -- A.2.1 The space of continuous functions -- A.2.2 The space Lp(Ω) -- A.2.3 Sobolev space of order 1 -- A.2.4 Sobolev spaces of fractional index -- A.3 The Schwarz inequality for integrals -- Appendix B Proof of h‐convergence -- Appendix C Convergence in 3D: Empirical results -- Appendix D Legendre polynomials -- D.1 Shape functions based on Legendre polynomials -- Appendix E Numerical quadrature -- E.1 Gaussian quadrature -- E.2 Gauss‐Lobatto quadrature -- Appendix F Polynomial mapping functions -- F.1 Interpolation on surfaces -- F.1.1 Interpolation on the standard quadrilateral element -- F.1.2 Interpolation on the standard triangle -- Appendix G Corner singularities in two‐dimensional elasticity -- G.1 The Airy stress function -- G.2 Stress‐free edges -- G.2.1 Symmetric eigenfunctions -- G.2.2 Antisymmetric eigenfunctions -- G.2.3 The L‐shaped domain -- G.2.4 Corner points -- Appendix H Computation of stress intensity factors -- H.1 Singularities at crack tips -- H.2 The contour integral method -- H.3 The energy release rate -- H.3.1 Symmetric (Mode I) loading -- H.3.2 Antisymmetric (Mode II) loading. H.3.3 Combined (Mode I and Mode II) loading -- H.3.4 Computation by the stiffness derivative method -- Appendix I Fundamentals of data analysis -- I.1 Statistical foundations -- I.2 Test data -- I.3 Statistical models -- I.4 Ranking -- I.5 Confidence intervals -- Appendix J Estimation of fastener forces in structural connections -- Appendix K Useful algorithms in solid mechanics -- K.1 The traction vector -- K.2 Transformation of vectors -- K.3 Transformation of stresses -- K.4 Principal stresses -- K.5 The von Mises stress -- K.6 Statically equivalent forces and moments -- K.6.1 Technical formulas for stress -- Bibliography -- Index -- EULA. |
| Record Nr. | UNINA-9910829891503321 |
|
Szabo B. A (Barna Aladar), <1935->
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to finite element analysis [[electronic resource] ] : formulation, verification and validation / / Barna Szabo, Ivo Babuska
| Introduction to finite element analysis [[electronic resource] ] : formulation, verification and validation / / Barna Szabo, Ivo Babuska |
| Autore | Szabo B. A (Barna Aladar), <1935-> |
| Pubbl/distr/stampa | Chichester, West Sussex, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (384 p.) |
| Disciplina |
620.001/51825
620.00151825 |
| Altri autori (Persone) | BabuškaIvo |
| Collana | Wiley series in computational mechanics |
| Soggetto topico |
Finite element method
Numerical analysis |
| ISBN |
1-283-40554-7
9786613405548 1-119-99348-2 1-119-99382-2 1-119-99383-0 |
| Classificazione | TEC006000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to FiniteElement Analysis; Contents; About the Authors; Series Preface; Preface; 1 Introduction; 1.1 Numerical simulation; 1.1.1 Conceptualization; 1.1.2 Validation; 1.1.3 Discretization; 1.1.4 Verification; 1.1.5 Decision-making; 1.2 Why is numerical accuracy important?; 1.2.1 Application of design rules; 1.2.2 Formulation of design rules; 1.3 Chapter summary; 2 An outline of the finite element method; 2.1 Mathematical models in one dimension; 2.1.1 The elastic bar; 2.1.2 Conceptualization; 2.1.3 Validation; 2.1.4 The scalar elliptic boundary value problem in one dimension
2.2 Approximate solution2.2.1 Basis functions; 2.3 Generalized formulation in one dimension; 2.3.1 Essential boundary conditions; 2.3.2 Neumann boundary conditions; 2.3.3 Robin boundary conditions; 2.4 Finite element approximations; 2.4.1 Error measures and norms; 2.4.2 The error of approximation in the energy norm; 2.5 FEM in one dimension; 2.5.1 The standard element2.5.1 The standard element; 2.5.2 The standard polynomial space; 2.5.3 Finite element spaces; 2.5.4 Computation of the coefficient matrices; 2.5.5 Computation of the right hand side vector; 2.5.6 Assembly 2.5.7 Treatment of the essential boundary conditions2.5.8 Solution; 2.5.9 Post-solution operations; 2.6 Properties of the generalized formulation; 2.6.1 Uniqueness; 2.6.2 Potential energy; 2.6.3 Error in the energy norm; 2.6.4 Continuity; 2.6.5 Convergence in the energy norm; 2.7 Error estimation based on extrapolation; 2.7.1 The root-mean-square measure of stress; 2.8 Extraction methods; 2.9 Laboratory exercises; 2.10 Chapter summary; 3 Formulation of mathematical models; 3.1 Notation; 3.2 Heat conduction; 3.2.1 The differential equation; 3.2.2 Boundary and initial conditions 3.2.3 Symmetry, antisymmetry and periodicity3.2.4 Dimensional reduction; 3.3 The scalar elliptic boundary value problem; 3.4 Linear elasticity; 3.4.1 The Navier equations; 3.4.2 Boundary and initial conditions; 3.4.3 Symmetry, antisymmetry and periodicity; 3.4.4 Dimensional reduction; 3.5 Incompressible elastic materials; 3.6 Stokes' flow; 3.7 The hierarchic view of mathematical models; 3.8 Chapter summary; 4 Generalized formulations; 4.1 The scalar elliptic problem; 4.1.1 Continuity; 4.1.2 Existence; 4.1.3 Approximation by the finite element method; 4.2 The principle of virtual work 4.3 Elastostatic problems4.3.1 Uniqueness; 4.3.2 The principle of minimum potential energy; 4.4 Elastodynamic models; 4.4.1 Undamped free vibration; 4.5 Incompressible materials; 4.5.1 The saddle point problem; 4.5.2 Poisson's ratio locking; 4.5.3 Solvability; 4.6 Chapter summary; 5 Finite element spaces; 5.1 Standard elements in two dimensions; 5.2 Standard polynomial spaces; 5.2.1 Trunk spaces; 5.2.2 Product spaces; 5.3 Shape functions; 5.3.1 Lagrange shape functions; 5.3.2 Hierarchic shape functions; 5.4 Mapping functions in two dimensions; 5.4.1 Isoparametric mapping 5.4.2 Mapping by the blending function method |
| Record Nr. | UNINA-9910130879203321 |
|
Szabo B. A (Barna Aladar), <1935->
|
||
| Chichester, West Sussex, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to finite element analysis [[electronic resource] ] : formulation, verification and validation / / Barna Szabo, Ivo Babuska
| Introduction to finite element analysis [[electronic resource] ] : formulation, verification and validation / / Barna Szabo, Ivo Babuska |
| Autore | Szabo B. A (Barna Aladar), <1935-> |
| Pubbl/distr/stampa | Chichester, West Sussex, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (384 p.) |
| Disciplina |
620.001/51825
620.00151825 |
| Altri autori (Persone) | BabuškaIvo |
| Collana | Wiley series in computational mechanics |
| Soggetto topico |
Finite element method
Numerical analysis |
| ISBN |
1-283-40554-7
9786613405548 1-119-99348-2 1-119-99382-2 1-119-99383-0 |
| Classificazione | TEC006000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Introduction to FiniteElement Analysis; Contents; About the Authors; Series Preface; Preface; 1 Introduction; 1.1 Numerical simulation; 1.1.1 Conceptualization; 1.1.2 Validation; 1.1.3 Discretization; 1.1.4 Verification; 1.1.5 Decision-making; 1.2 Why is numerical accuracy important?; 1.2.1 Application of design rules; 1.2.2 Formulation of design rules; 1.3 Chapter summary; 2 An outline of the finite element method; 2.1 Mathematical models in one dimension; 2.1.1 The elastic bar; 2.1.2 Conceptualization; 2.1.3 Validation; 2.1.4 The scalar elliptic boundary value problem in one dimension
2.2 Approximate solution2.2.1 Basis functions; 2.3 Generalized formulation in one dimension; 2.3.1 Essential boundary conditions; 2.3.2 Neumann boundary conditions; 2.3.3 Robin boundary conditions; 2.4 Finite element approximations; 2.4.1 Error measures and norms; 2.4.2 The error of approximation in the energy norm; 2.5 FEM in one dimension; 2.5.1 The standard element2.5.1 The standard element; 2.5.2 The standard polynomial space; 2.5.3 Finite element spaces; 2.5.4 Computation of the coefficient matrices; 2.5.5 Computation of the right hand side vector; 2.5.6 Assembly 2.5.7 Treatment of the essential boundary conditions2.5.8 Solution; 2.5.9 Post-solution operations; 2.6 Properties of the generalized formulation; 2.6.1 Uniqueness; 2.6.2 Potential energy; 2.6.3 Error in the energy norm; 2.6.4 Continuity; 2.6.5 Convergence in the energy norm; 2.7 Error estimation based on extrapolation; 2.7.1 The root-mean-square measure of stress; 2.8 Extraction methods; 2.9 Laboratory exercises; 2.10 Chapter summary; 3 Formulation of mathematical models; 3.1 Notation; 3.2 Heat conduction; 3.2.1 The differential equation; 3.2.2 Boundary and initial conditions 3.2.3 Symmetry, antisymmetry and periodicity3.2.4 Dimensional reduction; 3.3 The scalar elliptic boundary value problem; 3.4 Linear elasticity; 3.4.1 The Navier equations; 3.4.2 Boundary and initial conditions; 3.4.3 Symmetry, antisymmetry and periodicity; 3.4.4 Dimensional reduction; 3.5 Incompressible elastic materials; 3.6 Stokes' flow; 3.7 The hierarchic view of mathematical models; 3.8 Chapter summary; 4 Generalized formulations; 4.1 The scalar elliptic problem; 4.1.1 Continuity; 4.1.2 Existence; 4.1.3 Approximation by the finite element method; 4.2 The principle of virtual work 4.3 Elastostatic problems4.3.1 Uniqueness; 4.3.2 The principle of minimum potential energy; 4.4 Elastodynamic models; 4.4.1 Undamped free vibration; 4.5 Incompressible materials; 4.5.1 The saddle point problem; 4.5.2 Poisson's ratio locking; 4.5.3 Solvability; 4.6 Chapter summary; 5 Finite element spaces; 5.1 Standard elements in two dimensions; 5.2 Standard polynomial spaces; 5.2.1 Trunk spaces; 5.2.2 Product spaces; 5.3 Shape functions; 5.3.1 Lagrange shape functions; 5.3.2 Hierarchic shape functions; 5.4 Mapping functions in two dimensions; 5.4.1 Isoparametric mapping 5.4.2 Mapping by the blending function method |
| Record Nr. | UNINA-9910821005403321 |
|
Szabo B. A (Barna Aladar), <1935->
|
||
| Chichester, West Sussex, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||