Use the three-parameter zone finite element method or the boundary collocation method to calculate the stress intensity factor K, at the crack tip for the plate shown in the right figure, for r/W=0.4 and a/(W-r) ={0.01, 0.05, 0.1, 0.3, 0.5, 0.7, 0.9}, where r is the radius of the hole. Compare the numerical results with the lecture discussions on Example 2.4. You can choose whatever value is appropriate for a, W, t, and h, assume the plate is under plane strain condition.

Submissions:

1. The computer program or the finite element model for one value of a and the excel file for finite element results processing;

2. A project report that is less than 6 pages long and describes

[1]   Boundary conditions for the finite element model 

[2]   The description of the collocation computer program or the finite element model 

[3]   Describe and show the results on how to calculating K, from stress and displacement components for a/(W-r)=0.05 

[4]   A convergence curve showing the convergence of K, for a/(W-r)=0.05 with increasing number of boundary collocation points or finite elements. Explain the curve in narrative language. 

[5] A plot that compares the calculated K, for the given a/(W-r) values and the lecture discussion on Example 2.4. Explain the comparison of the two approaches and the limitation of the analytical solution in narrative language ;

[6] Your discussions and conclusions on the effect of boundary on K_i .