A. Proficiency Problems

1. Calculate the strain distribution for the 1989 OSU benchmark test (Fig. 11.28), plane-strain version at punch heights of 20, 40, and 60 mm. Compare with benchmark results.

2. Assuming a Considere-type localization condition (i.e., necking begins at maximum load), what is the maximum punch height attainable in the plane-strain OSU benchmark test, shown in Fig. 11.28?

3. Imagine a uniform mesh of squares arranged in a rectangular array n m, where m > n. Assume that solver times and storage sizes (implicit, direct solution) can be approximated by

   CPU(s) = K ¹/ ²⁵⁰ db ²(s),

   where d is the degrees of freedom (DOF), and b is the bandwidth (equal to the maximum number of degrees of freedom between adjacent nodes, however numbered); and

   MB = 8/1000db(mb).

   1. For fixed mesh dimensions of n = 50, m = 200, compare the CPU times and storage requirements for the following elements:

      membrane:	3 DOF per node or 4 DOF per node, CFS
      shell:	6 DOF per node or 7 DOF per node, CFS
      solid:	3 DOF per node, 4 DOF for CFS in 1 element through-thickness
      solid:	3 DOF per node, 4 DOF for CFS in 25 elements through-thickness

   2. How would the CPU times and storage requirements change for each case in Part (a) if the nodes were numbered alternately?

   3. Plot the CPU times and storage requirements for Part (a) if mesh refinement is carried out:

      1. Part (a): n = 50, m...