1. Error calculations and error convergence Winter Semester 2009-2010

2. 2 Goals  In this workshop, an underground pipe shield will be analyzed under singularity conditions.  You will try to reduced the error value by enlarging the number of elements.  You will use the convergence tool in order to explore the solution accuracy.  The convergence tool controls the relative accuracy of a solution by refining solution results on a particular area of a model.  We will run this analysis 4 times, each time we will change the analysis parameters.

3. 3 Assumptions  We will assume that a system of pipes, leading sewage water, is protected by a concrete shielding.  The pipe shielding in this workshop, is only a part of the entire system.  A force with magnitude of 200N in acting on the shield ’ s edge.  The pipe shielding is mounted with fixed support to the ground.

4. 4 Pipe Shielding Description

5. 5 Model number 1

6. 6 Start Page  From the launcher start Simulation.  Choose “ Geometry > From File... “ and browse to the file “ pipe_shielding.x_t ”.

7. 7 Preprocessing  Set the working units to Metric (mm). “ Units > Metric (mm, kg, N, C, s) ”.  Change the material of the pipe to “ concrete ” Highlight the part in the tree. In the detail window click in the material field and “ Import  Concrete ”.

8. 8 Preprocessing  Start new structural analysis, under the “ New analysis ” menu.  Highlight the “ Static structural ” branch and insert loads and supports.  Load – under the loads menu, add force of 200N along the pipe ’ s edge.

9. 9 Preprocessing  Supports – from the supports menu, add fixed support to the pipe ’ s bottom surfaces

10. 10 Solution  Highlight the solution branch, RMB, add: Equivalent stress, Error.  Solve the model

11. 11 Results  Examine the max error values:  Examine the stress result at specific location:

12. 12 Model number 2

13. 13 Preprocessing  Highlight the model branch and duplicate it by clicking RMB  “ Duplicate ”

14. 14 Refining the mesh  Highlight the “ Mesh ” branch  Under the “ Mesh control ” menu add “ sizing ”  Change the element size to 4mm.  RMB on the “ Mesh ” branch  ” Generate mesh ”  Camper the element ’ s number between the models.

15. 15 Mesh comparison

16. 16 Solution  Solve model 2.  Compare the error results.  Examine the differences in the stress results.  Error results:

17. 17 Model number 3

18. 18 Preprocessing  Duplicate model number 1 (the first model).  A new model, name ‘ model 3 ’, will appear.  Highlight the equivalent stress branch and add a convergence tool.  RMB  Insert  Convergence.  Note that the default convergence criteria is 20%

19. 19 Convergence  Set the convergence max refinement loop number to 1 and the refinement depth to 2.  Highlight the solution branch and set these values under the Details window. Notes: Note number 1: The first calculation loop is default. We can add refinement loops by setting the max allowed loops. It will add loops until the accuracy required will be archived. Note number 2: In case that the required accuracy has been achieved using less loops than defined, the solution will be stopped.

20. 20 Solution  Highlight the model 3 branch and solve the model.  Examine the convergence result.  Note the red exclamation mark near the “ convergence ” ; It means that the solution was not converted.

21. 21 Model number 4

22. 22 Preprocessing  Duplicate model number 3.  A new model, name ‘ model 4 ’, will appear.  Add another equivalent stress for the interior face only.

23. 23 Preprocessing  Solve model number 4.  Add a convergence tool to the equivalent stress calculated for the interior face.  The solution will be stopped only after solution convergence for this specific face has been achieved, regardless the singularity ’ s condition.  Re-solve the model

24. 24 Solution  Examine the convergence results.  Note the green check mark near the convergence branch