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Nonlinear Solid Mechanics Theoretical Formulations And Finite Element Solution Methods(2009th Edition)
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Adnan Ibrahimbegovic
Cover Type:Hardcover
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ISBN: 9048123305, 978-9048123308
Book publisher: Springer
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Book Summary: 1 Introduction; 1.1 Motivation And Objectives; 1.2 Outline Of The Main Topics; 1.3 Further Studies Recommendations; 1.4 Summary Of Main Notations; 2 Boundary Value Problem In Linear And Nonlinear Elasticity; 2.1 Boundary Value Problem In Elasticity With Small Displacement Gradients; 2.1.1 Domain And Boundary Conditions; 2.1.2 Strong Form Of Boundary Value Problem In 1D Elasticity; 2.1.3 Weak Form Of Boundary Value Problem In 1D Elasticity And The Principle Of Virtual Work; 2.1.4 Variational Formulation Of Boundary Value Problem In 1D Elasticity And Principle Of Minimum Potential Energy; 2.2 Finite Element Solution Of Boundary Value Problems In 1D Linear And Nonlinear Elasticity; 2.2.1 Qualitative Methods Of Functional Analysis For Solution Existence And Uniqueness; 2.2.2 Approximate Solution Construction By Galerkin, Ritz And Finite Element Methods; 2.2.3 Approximation Error And Convergence Of Finite Element Method; 2.2.4 Solving A System Of Linear Algebraic Equations By Gauss Elimination Method; 2.2.5 Solving A System Of Nonlinear Algebraic Equations By Incremental Analysis; 2.2.6 Solving A System Of Nonlinear Algebraic Equations By Newton's Iterative Method; 2.3 Implementation Of Finite Element Method In ID Boundary Value Problems; 2.3.1 Local Or Elementary Description; 2.3.2 Consistence Of Finite Element Approximation; 2.3.3 Equivalent Nodal External Load Vector; 2.3.4 Higher Order Finite Elements; 2.3.5 Role Of Numerical Integration; 2.3.6 Finite Element Assembly Procedure; 2.4 Boundary Value Problems In 2D And 3D Elasticity; 2.4.1 Tensor, Index And Matrix Notations; 2.4.2 Strong Form Of A Boundary Value Problem In 2D And 3D Elasticity; 2.4.3 Weak Form Of Boundary Value Problem In 2D And 3D Elasticity; 2.5 Detailed Aspects Of The Finite Element Method; 2.5.1 Isoparametric Finite Elements; 2.5.2 Order Of Numerical Integration; 2.5.3 The Patch Test; 2.5.4 Hu-Washizu (mixed) Variational Principle And Method Of Incompatible Modes; 2.5.5 Hu-Washizu (mixed)variational Principle And Assumed Strain Method For Quasi-incompressible Behavior; 3 Inelastic Behavior At Small Strains; 3.1 Boundary Value Problem In Thermomechanics; 3.1.1 Rigid Conductor And Heat Equation; 3.1.2 Numerical Solution By Time-integration Scheme For Heat Transfer Problem; 3.1.3 Thermo-mechanical Coupling In Elasticity; 3.1.4 Thermodynamics Potentials In Elasticity; 3.1.5 Thermodynamics Of Inelastic Behavior: Constitutive Models With Internal Variables; 3.1.6 Internal Variables In Viscoelasticity; 3.1.7 Internal Variables In Viscoplasticity; 3.2 1D Models Of Perfect Plasticity And Plasticity With Hardening; 3.2.1 1D Perfect Plasticity; 3.2.2 1D Plasticity With Isotropic Hardening; 3.2.3 Boundary Value Problem For 1D Plasticity; 3.3 3D Plasticity; 3.3.1 Standard Format Of 3D Plasticity Model: Prandtl-Reuss Equations; 3.3.2 J2 Plasticity Model With Von Mises Plasticity Criterion; 3.3.3 Implicit Backward Euler Scheme And Operator Split For Von Mises Plasticity; 3.3.4 Finite Element Numerical Implementation In 3D Plasticity; 3.4 Refined Models Of 3D Plasticity; 3.4.1 Nonlinear Isotropic Hardening; 3.4.2 Kinematic Hardening; 3.4.3 Plasticity Model Dependent On Rate Of Deformation Or Viscoplasticity; 3.4.4 Multi-surface Plasticity Criterion; 3.4.5 Plasticity Model With Nonlinear Elastic Response; 3.5 Damage Models; 3.5.1 1D Damage Model; 3.5.2 3D Damage Model; 3.5.3 Refinements Of 3D Damage Model; 3.5.4 Isotropic Damage Model Of Kachanov; 3.5.5 Numerical Examples: Damage Model Combining Isotropic And Multisurface Criteria; 3.6 Coupled Plasticity-damage Model; 3.6.1 Theoretical Formulation Of 3D Coupled Model; 3.6.2 Time Integration Of Stress For Coupled Plasticitydamagemodel; 3.6.3 Direct Stress Interpolation For Coupled Plasticitydamagemodel; 4 Large Displacements And Deformations; 4.1 Kinematics Of Large Displacements; 4.1.1 Motion In Large Displacements; 4.1.2 Deformation Gradient; 4.1.3 Large Deformation Measures; 4.2 Equilibrium Equations
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