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Introduction to Finite Element Analysis : Formulation, Verification and Validation.

Introduction to Finite Element Analysis : Formulation, Verification and Validation.
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10022814 Access this eBook online Ebook for Engineering   GUtech Library . . Available .  
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ISBN 9781119993827
9780470977286
Author Szabo, Barna
Title Introduction to Finite Element Analysis : : Formulation, Verification and Validation.
1st ed.
Description 1 online resource (384 pages)
Contents Introduction to Finite Element 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 solution -- 2.2.1 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 conditions -- 2.5.8 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 periodicity -- 3.2.4 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 problems -- 4.3.1 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 -- 5.4.3 Mapping of high-order elements -- 5.4.4 Rigid body rotations -- 5.5 Elements in three dimensions -- 5.6 Integration and differentiation -- 5.6.1 Volume and area integrals -- 5.6.2 Surface and contour integrals -- 5.6.3 Differentiation -- 5.7 Stiffness matrices and load vectors -- 5.7.1 Stiffness matrices -- 5.7.2 Load vectors -- 5.8 Chapter summary -- 6 Regularity and rates of convergence -- 6.1 Regularity -- 6.2 Classification -- 6.3 The neighborhood of singular points -- 6.3.1 The Laplace equation -- 6.3.2 The Navier equations -- 6.3.3 Material interfaces.
6.3.4 Forcing functions acting on boundaries -- 6.3.5 Strong and weak singular points -- 6.4 Rates of convergence -- 6.4.1 The choice of finite element spaces -- 6.4.2 Uses of a priori information -- 6.4.3 A posteriori error estimation in the energy norm -- 6.4.4 Adaptive and feedback methods -- 6.5 Chapter summary -- 7 Computation and verification of data -- 7.1 Computation of the solution and its first derivatives -- 7.2 Nodal forces -- 7.2.1 Nodal forces in the h-version -- 7.2.2 Nodal forces in the p-version -- 7.2.3 Nodal forces and stress resultants -- 7.3 Verification of computed data -- 7.4 Flux and stress intensity factors -- 7.4.1 The Laplace equation -- 7.4.2 Planar elasticity -- 7.5 Chapter summary -- 8 What should be computed and why? -- 8.1 Basic assumptions -- 8.2 Conceptualization: drivers of damage accumulation -- 8.3 Classical models of metal fatigue -- 8.3.1 Models of damage accumulation -- 8.3.2 Notch sensitivity -- 8.3.3 The theory of critical distances -- 8.4 Linear elastic fracture mechanics -- 8.5 On the existence of a critical distance -- 8.6 Driving forces for damage accumulation -- 8.7 Cycle counting -- 8.8 Validation -- 8.9 Chapter summary -- 9 Beams, plates and shells -- 9.1 Beams -- 9.1.1 The Timoshenko beam -- 9.1.2 The Bernoulli-Euler beam -- 9.2 Plates -- 9.2.1 The Reissner-Mindlin plate -- 9.2.2 The Kirchhoff plate -- 9.2.3 Enforcement of continuity: the HCT element -- 9.3 Shells -- 9.3.1 Hierarchic "thin-solid" models -- 9.4 The Oak Ridge experiments -- 9.4.1 Description -- 9.4.2 Conceptualization -- 9.4.3 Verification -- 9.4.4 Validation: comparison of predicted and observed data -- 9.4.5 Discussion -- 9.5 Chapter summary -- 10 Nonlinear models -- 10.1 Heat conduction -- 10.1.1 Radiation -- 10.1.2 Nonlinear material properties -- 10.2 Solid mechanics -- 10.2.1 Large strain and rotation.
10.2.2 Structural stability and stress stiffening -- 10.2.3 Plasticity -- 10.2.4 Mechanical contact -- 10.3 Chapter summary -- A Definitions -- A.1 Norms and seminorms -- A.2 Normed linear spaces -- A.3 Linear functionals -- A.4 Bilinear forms -- A.5 Convergence -- A.6 Legendre polynomials -- A.7 Analytic functions -- A.7.1 Analytic functions in R2 -- A.7.2 Analytic curves in R2 -- A.8 The Schwarz inequality for integrals -- B Numerical quadrature -- B.1 Gaussian quadrature -- B.2 Gauss-Lobatto quadrature -- C Properties of the stress tensor -- C.1 The traction vector -- C.2 Principal stresses -- C.3 Transformation of vectors -- C.4 Transformation of stresses -- D Computation of stress intensity factors -- D.1 The contour integral method -- D.2 The energy release rate -- D.2.1 Symmetric (Mode I) loading -- D.2.2 Antisymmetric (Mode II) loading -- D.2.3 Combined (Mode I and Mode II) loading -- D.2.4 Computation by the stiffness derivative method -- E Saint-Venant's principle -- E.1 Green's function for the Laplace equation -- E.2 Model problem -- F Solutions for selected exercises -- Bibliography -- Index.
Subject Finite element method
Numerical analysis
Other Author Electronic books.
Other name(s) Babuška, Ivo
Szabo, Barna
Babuska, Professor of Aerospace Engineering and Engineering Science and Professor of Mathematics Ivo
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