Exercise 2

Non-linear analysis of a cantilever beam with MSC Marc finite element code Problem: Using Marc, Find the vertical displacement imposed by the load P for the non-linear load case. The load P is 6000 lb. The length L of the beam is 100 in. The dimensions of the beam Section A-A (a x b) are 1.0 in x 2.0 in. The Young's Modulus is 30 x 106 and the Poisson's Ratio is 0.3.

Step 1 – Open Model 1) Click on File and then Open.

2) Browse and Select tip_load.mud in working directory. and click Open.

Step 2 – Create Loadcases 1) Click on the Loadcases tab and click on New - Static.

2) Enter the Name as my_nonlinear, and click on Properties. 3) Click on Loads and make sure that both fixed and tip_load loads are selected. Click OK. 4) Select Multi Criteria and click OK.

Step 3 – Create a Job 1) Click on the Jobs tab and then click on New - Structural.

2) Then, enter Name: as nonlinear_job1 and then click on Properties. 3) Under Available, select my_nonlinear. 4) Then, click on Initial Loads.

5) Deselect the Initial Loads in Boundary Conditions and click OK. 6) Under Analysis Dimension, click on Plane Stress, make sure Linear Elastic Analysis is unchecked and then click on Analysis Options.

7) Select Large Strain and then click OK and OK.

Step 4 – Run Analysis Job 1) Under the Jobs tab click Run.

2) Then click Save Model, then click Submit(1). 3) Click Status File after Complete appears in the Status Box. Then click Open Post Results.

Step 5 – Plot Results – Y Displacement 1) Click on the Results tab and click on Model Plot. 2) Under Deformed Shape set style to Deformed & Original. 3) Under Scalar Plot set the style to Contour Bands. 4) Click Scalar and select Displacement Y. Click OK. 5) Click Play. 6) Click FILL.

Step 6 – (Optional) Improving the Results 1) Close the existing results. 2) Delete the existing mesh. 3) Create a new mesh that has the same number of elements lengthwise but has two elements over the height of the beam. 4) Run both linear and nonlinear jobs again.

5) Open the results file and make Results plots as before and compare the Y-displacements with the ones obtained with the coarser (8 x 1) mesh, and the theoretical values. Analytical solution – Verify the results by calculating the analytical solution As shown in the results obtained, inclusion of large deformation effects are very important in realistically modeling the physical behavior of the cantilever model. MARC Results at Various Mesh Densities:

Notice the amount of error as a result of using the Standard formulation Plane-Stress Element, without tuning on the Assumed Strain Parameter. This inaccuracy is due to the shear-locking of the element. The Assumed Strain and Reduced Integration options correct for this inaccuracy. By Default, the Assumed Strain Parameter is turned OFF. Turn this option on when using Standard Integration Plane Strain, Plane Stress, or Hex Elements. (Element Types 3, 7, and 11)