LEADER 05534nam 2200685Ia 450 001 9910130879203321 005 20170815105708.0 010 $a1-283-40554-7 010 $a9786613405548 010 $a1-119-99348-2 010 $a1-119-99382-2 010 $a1-119-99383-0 035 $a(CKB)3460000000000080 035 $a(EBL)699509 035 $a(OCoLC)781613525 035 $a(SSID)ssj0000477003 035 $a(PQKBManifestationID)11335998 035 $a(PQKBTitleCode)TC0000477003 035 $a(PQKBWorkID)10480360 035 $a(PQKB)10287737 035 $a(MiAaPQ)EBC699509 035 $a(PPN)248871188 035 $a(EXLCZ)993460000000000080 100 $a20101203d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to finite element analysis$b[electronic resource] $eformulation, verification and validation /$fBarna Szabo, Ivo Babuska 210 $aChichester, West Sussex $cWiley$d2011 215 $a1 online resource (384 p.) 225 1 $aWiley series in computational mechanics 300 $aDescription based upon print version of record. 311 $a0-470-97728-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction 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 327 $a2.2 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 327 $a2.5.7 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 327 $a3.2.3 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 327 $a4.3 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 327 $a5.4.2 Mapping by the blending function method 330 $aWhen using numerical simulation to make a decision, how can its reliability be determined? 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