2D Large deformations finite element MATLAB code

This MATLAB code is for two-dimensional elastic solid elements with large deformations (Geometric nonlinearity). Both Updated Lagrangian Method and Total Lagrangian Method are available. I have used Newton-Raphson solver. Green-Lagrange strains are used in these codes. The results can be animated.; arbitrary input geometry, nodal loads, and material properties for each element can be defined by user.

An animated result of this code for updated lagrangian algorithm is shown below:

The problem configuration of the analysis using this code is shown below:


Below are the displacement at midspan versus steps of loading:



Below are the number of iterations versus steps of loading:



Below are the reciprocal condition number of stiffness matrix ,RCOND(k), for both total Lagrangian and Updated Lagrangian Methods:


What is large deformation (geometric nonlinearity)?
Geometric nonlinearities involve nonlinearities in kinematic quantities such as the strain-displacement relations in solids. Such nonlinearities can occur due to large displacements, large strains, large rotations, and so on.

How can I get this code (matlab files or functions)?

You may have these codes for your research purposes. Email me at hosseinali.sut@gmail.com using your official/academic email address.

What other codes are available at matlab-fem.com?

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2D Truss elements finite element MATLAB code
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2D Solid elements finite element MATLAB code
2D Penalty and Lagrange Multiplier Contact finite element MATLAB code
2D Large deformations finite element MATLAB code
2D XFEM for Crack eXtended finite element MATLAB code
3D Truss elements finite element MATLAB code
3D Solid elements finite element MATLAB code
3D Large deformations finite element MATLAB code

What is Finite Element Method?

The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. It is also referred to as finite element analysis (FEA). Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution of these problems generally require the solution to boundary value problems for partial differential equations. Read more about Finite Element Methods

What is MATLAB?

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment. A proprietary programming language developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python.

What reference books did I use for my codes?

Some of the main textbooks I used for codes are:
General concepts and basic codes:
  1. Finite Element Procedures by K.J. Bathe
  2. The Finite Element Method (v.1 & v.2 & v.3) by Zienkiewicz & Taylor
  3. Fundamental finite element analysis and applications by M. Asghar Bhatti
Contact mechanics:
  1. Computational Contact Mechanics by Peter Wriggers
Plasticity:
  1. Finite Elements in Plasticity by D. R. J. Owen, E. Hinton
  2. Non-Linear Finite Element Analysis of Solids and Structures (vol. 1 & 2) by M. A. Crisfield