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BL
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665555
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dltt
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| Main Entry
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Kim, Nam-ho
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| Title & Author
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Introduction to nonlinear finite element analysis /\ Nam-Ho Kim
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| Page. NO
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1 online resource
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| ISBN
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9781441917461
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: 1441917462
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9781441917454
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1441917454 (hbk.)
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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Preface; Contents; Chapter 1: Preliminary Concepts; 1.1 Introduction; 1.2 Vector and Tensor Calculus; 1.2.1 Vector and Tensor; 1.2.2 Vector and Tensor Calculus; 1.2.3 Integral Theorems; 1.3 Stress and Strain; 1.3.1 Stress; 1.3.2 Strain; 1.3.3 Stress-Strain Relationship; 1.4 Mechanics of Continuous Bodies; 1.4.1 Boundary-Valued Problem; 1.4.2 Principle of Minimum Potential Energy; 1.4.3 Principle of Virtual Work; 1.5 Finite Element Method; 1.5.1 Finite Element Approximation; 1.5.2 Finite Element Equations for a One-Dimensional Problem; 1.5.3 Finite Element Equations for 3D Solid Element
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1.5.4 A MATLAB Code for Finite Element Analysis1.6 Exercises; References; Chapter 2: Nonlinear Finite Element Analysis Procedure; 2.1 Introduction to Nonlinear Systems in Solid Mechanics; 2.1.1 Geometric Nonlinearity; 2.1.2 Material Nonlinearity; 2.1.3 Kinematic Nonlinearity; 2.1.4 Force Nonlinearity; 2.2 Solution Procedures for Nonlinear Algebraic Equations; 2.2.1 Newton-Raphson Method; 2.2.2 Modified Newton-Raphson Method; 2.2.3 Incremental Secant Method; 2.2.4 Incremental Force Method; 2.2.4.1 Load Increment in Commercial Software; 2.2.4.2 Automatic Time Stepping
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2.2.4.3 Force Control vs. Displacement Control2.3 Steps in the Solution of Nonlinear Finite Element Analysis; 2.3.1 State Determination; 2.3.2 Residual Calculation; 2.3.3 Convergence Check; 2.3.4 Linearization; 2.3.5 Solution; 2.4 MATLAB Code for a Nonlinear Finite Element Analysis Procedure; 2.5 Nonlinear Solution Controls Using Commercial Finite Element Programs; 2.5.1 Abaqus; 2.5.2 ANSYS; 2.5.3 NEiNastran; 2.6 Summary; 2.7 Exercises; References; Chapter 3: Finite Element Analysis for Nonlinear Elastic Systems; 3.1 Introduction; 3.2 Stress and Strain Measures in Large Deformation
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3.2.1 Deformation Gradient3.2.2 Lagrangian and Eulerian Strains; 3.2.2.1 Lagrangian Strain; 3.2.2.2 Eulerian Strain; 3.2.3 Polar Decomposition; 3.2.4 Deformation of Surface and Volume; 3.2.4.1 Volume Changes; 3.2.4.2 Area Changes; 3.2.5 Cauchy and Piola-Kirchhoff Stresses; 3.3 Nonlinear Elastic Analysis; 3.3.1 Nonlinear Static Analysis: Total Lagrangian Formulation; 3.3.1.1 Constitutive Relation; 3.3.1.2 Boundary Conditions; 3.3.1.3 Principle of Minimum Potential Energy; 3.3.1.4 Linearization (Tangent Stiffness); 3.3.2 Nonlinear Static Analysis: Updated Lagrangian Formulation
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3.4 Critical Load Analysis3.4.1 One-Point Approach; 3.4.2 Two-Point Approach; 3.4.3 Stability Equation with Actual Critical Load Factor; 3.5 Hyperelastic Materials; 3.5.1 Strain Energy Density; 3.5.2 Nearly Incompressible Hyperelasticity; 3.5.2.1 Mooney-Rivlin Material Model; 3.5.2.2 Selective Reduced Integration; 3.5.2.3 Mixed Formulation; 3.5.2.4 Perturbed Lagrangian Formulation; 3.5.2.5 Algorithm for Stress Calculation; 3.5.3 Variational Equation and Linearization; 3.6 Finite Element Formulation for Nonlinear Elasticity; 3.7 MATLAB Code for Hyperelastic Material Model
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| Abstract
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Introduction to Nonlinear Finite Element Analysis will introduce the key concepts of nonlinear finite element analysis procedures. The book will explain the fundamental theories of the field, and provide instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, only four representative problems are addressed: nonlinear elasticity, elastoplasticity, contact problem, and dynamic problem. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appen
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Finite element method.
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Nonlinear mechanics.
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Finite element method.
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Mathematical optimization.
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Nonlinear mechanics.
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| Dewey Classification
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620.00151825
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| LC Classification
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TA347.F5
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| Added Entry
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Ohio Library and Information Network.
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