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.

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