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 $aWhen using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential 410 0$aWiley series in computational mechanics. 606 $aFinite element method 606 $aNumerical analysis 615 0$aFinite element method. 615 0$aNumerical analysis. 676 $a620.001/51825 676 $a620.00151825 686 $aTEC006000$2bisacsh 700 $aSzabo$b B. A$g(Barna Aladar),$f1935-$031768 701 $aBabus?ka$b Ivo$031769 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910130879203321 996 $aIntroduction to finite element analysis$91960215 997 $aUNINA