Introduction to nonlinear finite element analysis / Nam-Ho Kim.

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

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

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

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

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