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A Matlab program which solves a static nonlinear FEM problem with linear shape functions, for an ideal elastic-plastic material

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hariprasadr1hp/FEM_Matlab

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FEM (Matlab/Octave)

A Matlab/Octave program which solves a static nonlinear FEM problem with linear shape functions, for an ideal elastic-plastic material. Stress-Distribution, elastic and plastic regimes, convergence crteria are generated

How to run?

make

Files:

  • input.m :: The file to start with
  • ElastoPlastic.m :: The file to calculate elastic + plastic strains
  • Elastic.m :: The file to calculate elastic convergence
  • ElementRoutine.m :: to determine J, B, N matrix values
  • MaterialRoutine.m :: Material routine for elastic ideal-plastic material
  • exact.m :: to calculate the analytical solution

Procedure

Change the value in of 'mode' to either '1' or '2' in Input.m file to switch between:

  • mode = 1 -> for calculating elastic convergence,
  • mode = 2 -> for calculating elastic + plastic strains

Can also modify the other parameters based on the needs:

  • elements
  • yield stress, E, Nu
  • inner/outer radius
  • Gauss points
  • time-step

Plots

  • Convergence Study in Elastic Regime
  • widening of outer radius b over time
  • $\sigma_{rr}$ Distribution
  • $\sigma_{\phi \phi}$ Distribution
  • Displacement Distribution $u$ at $t=1$

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A Matlab program which solves a static nonlinear FEM problem with linear shape functions, for an ideal elastic-plastic material

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