Introduction to Nonlinear Finite Element Analysis

by N. H. Kim

The objective of this textbook is to simply introduce the nonlinear finite element analysis procedure and to clearly explain the solution procedure to the reader. In contrast to the traditional textbooks which treat a vast amount of nonlinear theories comprehensively; this textbook only addresses the representative problems, detailed theories, solution procedures, and the computer implementation of the nonlinear FEM. Especially by using the MATLAB programming language to introduce the nonlinear solution procedure; those readers who are not familiar with FORTRAN or C++ programming languages can easily understand and add his/her own modules to the nonlinear analysis program. Book in amazon.com or Barns and Noble

Contents:   Preface v 1. Preliminary Concepts 1 2. Nonlinear Finite Element Analysis Procedure 81 3. Finite Element Analysis for Nonlinear Elastic Systems 141 4. Finite Element Analysis for Elastoplastic Problems 241 5. Finite Element Analysis for Contact Problems 367 Index 427

Lectures

• Chapter 1: Preliminary Concepts and Linear Finite Elements
• Chapter 2: Nonlinear Finite Element Analysis Procedures
• Chapter 3: Finite Element Analysis for Nonlinear Elastic Problems
• Chapter 4: Finite Element Analysis for Elastoplastic Problems
• Chapter 5: Finite Element Analysis of Contact Problems

MATLAB Code (NLFEA)

1. Matlab Programs. Need to change the extension ".txt" to ".m" after download.
   
   NLFEA.txt Main program
   ELAST3D.txt Linear elastic material model
   SHAPEL.txt Shape functions and derivatives
   One_tension.txt One-element example
   
   Two_element_example.txt Two_element_example
   
   Mooney.txt Mooney-Rivline material model
   HYPER3D.txt Hyperelastic material model assembly
   
   PLAST3D.txt Plasticity material model assembly
   combHard.txt Linear combined hardening plasticity material
   combHardTan.txt Algorithmic tangent stiffness for linear combined hardening plasticity material
   rotatedStress.txt Objective integration for finite rotation
   mulPlast.txt Multiplicative plasticity material model
   mulPlastTan.txt Algorithmic tangent stiffness for multiplicative plasticity material model
   
   
2. Other Matlab Programs that are not used in NLFEA but used in examples in the textbook.
   
   combHard1D.txt 1D Linear combined hardening plasticity material
   cntelm2d.txt 2D contact formulation between two flexible bodies
   cntelm3d.txt 3D contact formulation between one flexible body and one rigid wall

MATLAB Codes in Examples

1. Matlab Programs. Need to change the extension ".txt" to ".m" after download.
   
   E1_16.txt Example 1.16
   
   E2_3.txt Example 2.3 Newton-Raphson method
   E2_4.txt Example 2.4 Divergence of the Newton-Raphson method
   E2_5.txt Example 2.5 Two nonlinear springs (modified Newton-Raphson method)
   E2_6.txt Example 2.6 Nonlinear algebraic equation (secant method)
   E2_7.txt Example 2.7 Two nonlinear springs (Secant method)
   E2_8.txt Example 2.8 Displacement controlled procedure
   
   E3_8.txt Example 3.8 Uniaxial bar--total Lagrangian formulation
   E3_9.txt Example 3.9 Uniaxial bar--updated Lagrangian formulation
   E3_16.txt Example 3.16 Hyperelastic tension example
   
   E4_5.txt Example 4.5 Two bars in parallel: updating iteration
   E4_15.txt Example 4.15 - Shear deformation of elastoplastic square
   E4_19.txt Example 4.19 - Shear deformation of a square (finite rotation)
   E4_22.txt Example 4.22 - Shear deformation of a square
   
   Bending_5Elem_Linear.txt Bending of cantilevered beam (five elements, linear elastic)