Assignment = 6 Last date for submission 10-05-2016

Note: Assume following for all problems of this assignment (a) Take w = 1.0 (b) Use eight noded isoparametric element (Plane183) for FEA Q1. For the double edge cracked plate as shown in figure determine the normalized SIF (i.e.,

/IK aσ π ) for plane stress conditions and conduct a convergence study as follows. Take three meshes of increasing number of elements. Generate first mesh having around 100 numbers of elements. Create second mesh having around 500 numbers of elements and finally create the third mesh having 2000 elements (approximately). Compute normalized SIF using each of the above meshes (with conventional elements and with quarter point elements at the crack tip) and compare the computed normalized values with that of exact value given in Tada, Paris and Irwin’s Handbook available in the library. Make a table for this purpose as shown in below. Draw a graph of normalized SIF versus number of elements and also included exact solution from the handbook in the graph. Write down your observations from the table and graph.

Sample table Table: Convergence of normalized SIF

/IK aσ π Computed

Mesh No. of Elements No. of Nodes

Conventional Elements

QPEs Handbook

Mesh 1 Mesh 2 Mesh 3

Q2. Compute the normalized SIF of the above configuration using Mesh 3 but now with plane strain conditions instead of plane stress conditions. All other parameters are same as in Q1. Compare plane stress and plane strain normalized SIF and comment on the results. Use conventional elements and QPEs for this purpose.