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Introduction to finite element analysis
Introduction to finite element analysis

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3.1 Exercise: Analysis of a plate with a hole

Problem description

This is a simple problem with a known solution. It consists of a tensile-loaded thin plate with a central hole. Because of symmetry we need only model a quarter of the plate. The full plate is 1.0 m × 0.4 m with a thickness of 0.01 m. The central hole has a diameter of 0.2 m.

The plate is made of steel with a Young’s modulus of 2.07×10 11 N/m 2 and a Poisson’s ratio of 0.29. The horizontal tensile loading is in the form of pressure of 1.0 Pa (N/m 2 ), along the vertical edge of the full plate.

Interactive time required

60 to 70 minutes

Features demonstrated

Solid modelling, including primitives, Boolean operations, meshing and refinement.

Summary of steps

  1. Specify title
  2. Define parameters to be used for geometry input
  3. Set preferences
  4. Define element types
  5. Element options
  6. Define material properties
  7. Create rectangular area
  8. Create circular area
  9. Subtract hole from plate
  10. Mesh the area with a default mesh
  11. Apply displacement constrains
  12. Apply pressure load
  13. Solve
  14. Plot the deformed shape
  15. Plot the element stress in the x-direction
  16. Refine mesh
  17. Refine mesh near hole
  18. Re-introduce the loads
  19. Read in the new data set and plot the element stress in the x-direction
  20. Exit the program.