Introduction to finite element analysis [[electronic resource] ] : formulation, verification and validation / / Barna Szabo, Ivo Babuska

• Record Nr.: UNINA9910130879203321
• Autore: Szabo B. A (Barna Aladar), <1935->
• Pubbl/distr/stampa: Chichester, West Sussex, : Wiley, 2011
• ISBN: 1-283-40554-7; 9786613405548; 1-119-99348-2; 1-119-99382-2; 1-119-99383-0
• Descrizione fisica: 1 online resource (384 p.)
• Collana: Wiley series in computational mechanics
• Classificazione: TEC006000
• Altri autori (Persone): BabuškaIvo
• Disciplina: 620.001/51825; 620.00151825
• Soggetti: Finite element method; Numerical analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• 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
• Sommario/riassunto: When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential